ARJ June 2012 Vol 103 No 2 - Microsofteolstoragewe.blob.core.windows.net/wm-418498-cmsimages/... ·...

Vol.103(2) June 2012 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 65

VOL 103 No 2 June 2012

SAIEE Africa Research Journal

SAIEE AFRICA RESEARCH JOURNAL EDITORIAL STAFF ...................... IFC

Automotive Thermal Comfort Control – A Black-box Approach

by J. Kranz, T.I. van Niekerk, H.F.G. Holdack-Janssen and G. Gruhler ......66

Effect of Distance on the Accuracy of RSS-Based Geometric Positioning Methods

by F.M. Dahunsi, B. Dwolatzky and A. Love ................................................77

Rainfall Drop-Size Estimators for Weibull Probability Distribution Using Method of Moments Technique

by A. Alonge and T. Afullo.............................................................................83

A Multi-Dimensional Code-Division-Multiplexed OFDMA Modem Using Cyclic Rotated Orthogonal Complete Complementary Codes

by A.M. Merensky, J.H. van Wyk and L.P. Linde ...........................................94

Vol.103(2) June 2012SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS66

AUTOMOTIVE THERMAL COMFORT CONTROL – A BLACK-BOX APPROACH

J. Kranz*, T.I. van Niekerk*, H.F.G. Holdack-Janssen**, G. Gruhler*** * VWSA-DAAD Chair in Automotive Engineering, Nelson Mandela Metropolitan University, PO 77000 Port Elizabeth 6031, South Africa, E-mail: [email protected], [email protected] ** Faculty of Automotive Engineering, Ostfalia University, Kleiststrasse 14-16, 38440 Wolfsburg, Germany, E-mail: [email protected] *** Department of Mechatronics, Reutlingen University, Alteburgstrasse 150, 72762 Reutlingen, Germany, E-mail: [email protected] Abstract: Thermal comfort is a very vague and a very individual term, which depends on physiological and psychological variables. Thermal comfort in transient environments, like an automotive cabin, is far from understood and general accepted theories do not yet exist. This paper investigates the concept of using a black-box approach for directly associating thermal comfort to field measurements. Artificial intelligence is used to predict blower level, air blend position and in-cabin temperature for a given environment. The results are promising and it is concluded that methods of artificial intelligence can be used as a powerful tool during the development process of vehicle HVAC control units and have great potential to reduce development time and costs. Keywords: Automotive Thermal Comfort, Artificial Neural Networks

1. INTRODUCTION

Mobility has become a substantial part in our society. Since we spend a lot of our life-time on the road, we expect the automotive environment to provide similar comfort levels than residential buildings. In terms of thermal comfort this means that the automotive Heating Ventilation and Air Conditioning (HVAC) unit has to maintain in-cabin thermal comfort levels, irrespective of the ambient environment and the driving situation. Thermal comfort is however a very individual term since its perception to people has enormous variation. This makes it difficult to describe it in terms of clear defined parameters and variables. In 1970, the American Society of Heating, Refrigeration and Air-Conditioning Engineers (ASHRAE) defined thermal comfort as “That condition of mind which expresses satisfaction with the thermal environment”. This vague definition is still part of current thermal comfort standards. To develop and reliably validate thermal comfort models a comprehensive database is needed which contains information about the thermal environment and its correlation to thermal comfort. Most available thermal comfort models have been developed using data acquired from paper-based questionnaires in climate chambers. Due to the transient and inhomogeneous environment in automotive passenger compartments, climate chamber tests are less expressive and real field testing is required. This study investigates the potential of directly learning a technical system with field data without prior thermal comfort modeling. Data is collected from measurement drives and is combined to a database. Methods of data mining are applied, aiming to discover correlations, to remove inconsistencies and for dimensionality reduction. Elements of artificial intelligence are used to determine

the correlation of environmental information to thermal comfort. The overall structure is shown in Figure 1.

Figure 1: Concept structure

2. THERMAL COMFORT PRINCIPLES In the past decades there has been much effort to model and measure thermal comfort. Research in the 1970s has shown that thermal comfort is a function of several physical and physiological variables. These variables are air temperature, mean radiant temperature, air velocity, humidity, metabolic rate and clothing insulation [1]. Additionally, thermal comfort is an individual state of mind to some extent and cannot solely be explained with physical variables. It has shown to be linked to contextual parameters such as local climate, occupants’ expectations, available control over the environment and the processes by which the indoor environment is controlled, perceived, experienced, and interacted with

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[2]. Thermal comfort theories in uniform and steady state environments are nowadays widely accepted and have been defined in standards like ISO 7730 or ASHRAE Standard 55P. In non-uniform and transient environments, overall body thermal sensation seems to be a complaint-driven process [3]. The strongest local sensations tend to dominate overall thermal sensation and whole body thermal sensation tends to follow the cooler local body sensations [4]. Assessment of thermal non-uniform environments is difficult due to a lack of general knowledge about the superposition and the influence of multiple thermal sources [5]. The automobile cabin can be best classified as such an environment [6] and it is characterized by inhomogeneous temperature and air distribution, highly localized air velocities and many radiation sources. Environmental conditions have a strong influence on the vehicle cabin due to limited insulation material as well as due to a large glazing ratio [7], [8]. Unlike buildings, the position of a vehicle is not fixed in space and parameters suffer from strong temporal and local variability. Some researchers argue that due to the enormous differences to buildings, existent standards and methods can hardly be applied to the automotive environment [9].

3. OBJECTIVE The authors assume that thermal comfort is dependent on physiological and psychological variables and is linked to thermal comfort through an unknown function in some statistical sense. It can therefore be addressed as an approximation problem in a multidimensional feature space. Artificial intelligence is commonly used in such fields of research, where it is difficult to obtain exact mathematical knowledge about a process or when knowledge is even unavailable. Many approaches, using methods of artificial intelligence, have been proposed in literature with respect to thermal comfort. On the one hand this may be justified with the fuzzy definition of thermal comfort and on the other hand it is due to the enormous difficulties in measuring and assessing thermal comfort. A lot of effort has been done in approximating Fanger’s Predicted Mean Vote (PMV) model using fuzzy logic and neural networks, e.g. in [10]-[14]. However, only little research is so far available about teaching an intelligent structure with direct mappings of environmental field data and HVAC parameter outputs.

4. SYSTEM DEVELOPMENT Automotive measurement instrumentation is required to monitor data during extensive field data acquisition trips. The aim is to set up a data base which provides all necessary information for later data processing and finally to train Artificial Neural Networks (ANN). The measurement equipment must operate under a variety of environmental conditions. Additionally, it must be insensitive against shocks, vibrations and it is required to continuously monitor the periphery, in order to prevent corrupt sensor recordings. In terms of thermal comfort

evaluation, literature points out that questionnaires are time consuming and may put stress on the test subjects [15]. It is therefore advantageous to use computers for thermal comfort evaluation. This is especially important for automotive thermal comfort evaluation, where test persons are required to evaluate their comfort levels several times per minute, due to the overall transient conditions in the vehicle cabin. All sensor elements must therefore incorporate small response times. Data sources must be synchronized to each other in order to produce consistent data input-output mappings. The measurement equipment must be capable of communicating with the vehicle’s bus systems in order to gather thermal comfort relevant vehicle parameters. Additionally, it must be capable of modifying the HVAC control algorithms in order to provide a reliable framework for thermal comfort assessment. 4.1 Measurement variables The authors emphasize the importance of being consistent with the environmental information measured at the design process of the HVAC unit and within the final product. To prevent discomfort through measurements, the authors have decided not to attach any sensors directly to the human body, nor to acquire internal body physiological variables. Following variables were identified to be relevant for this study: Air temperature When measuring air temperature, special care must be taken to minimize the influence of radiation from surrounding surfaces. This can be achieved with reducing the emission coefficient of the sensor’s surface, reducing the temperature gradient between air and surrounding surfaces, shielding the sensor element against radiation or using air aspirated sensors in order to increase the heat convection between surrounding air and the sensor element. The authors have decided to use a fan-aspirated sensor element to measure mean in-cabin air temperature. Additionally unshielded temperature sensors have been installed at feet and head level. Mean radiant temperature Mean radiant temperature ϑr can be estimated with measurements of surface temperature. Reference [16] proposes equation (1) for approximation.

(1)

Where:

ϑi: Temperature of surface i, Fp-i: Angle factor between a person p and

surface i, N: Number of surrounding surfaces

The angle factors Fp-i depend on the position and orientation of the person relative to the source of radiation [16]. In practice it is considered to be difficult to


determine them exactly and therefore often only surface temperatures are measured instead. In the automotive cabin, the dashboard is the largest continuous part of plastic. Its position close to the windscreen and its black colour make it especially absorbent to radiation. The authors assume that it is the largest radiation source within the vehicle compartment. It is therefore suggested to approximate mean radiant temperature by measuring only dashboard temperature. Air velocity Due to the enormous non-uniformity of air distribution and the variety of possible air-flow patterns inside the vehicle cabin, the authors consider it impossible to measure air velocity with single discrete sensors, at all positions relevant for thermal comfort. It is assumed that air velocity va and air distribution inside the vehicle cabin are a function of mainly: Vehicle speed vv, Air distribution flap position f, Blower load b.

This dependence can be mathematically expressed as:

(2)

It is further assumed that the unknown function f(·) in equation (2) can be approximated by methods of artificial intelligence. Humidity For human heat exchange with the environment, only absolute humidity is of relevance and vapour pressure can be considered as constant within the vehicle cabin [15]. Humidity h is considered to have only a minor influence on thermal comfort and a 10% increase in humidity is equivalent to only Δϑ=0.3ºC rise in air temperature [17]. At low air temperatures, thermal sensation can be even considered as independent of humidity [18]. However, humidity is a contributing factor towards indirect comfort influences like skin moisture, tactile sensation of fabrics, health and air quality. The authors therefore suggest including measurements of relative humidity for thermal comfort determination. Metabolic rate ISO 8996 provides methodologies to determine human metabolic rate. However, these methods are extensive and are hardly applicable to the automotive environment. In case of vehicular application, it is assumed that human internal activity M is predominantly linked to the driving or traffic situation and can be expressed as:

(3)

Where

Tr: An empirical function quantifying the traffic load v: Vehicle speed σv: Standard deviation of vehicle speed

It is assumed that stop-and-go situations put more stress on the driver than driving on a highway with constant speed. According to the authors’ research, a good indicator for the traffic situation is the number of alternating changes in gas and brake pedal activity for a given observation interval. The empirical function Tr can therefore be expressed as:

(4)

Where:

T[n]: Number of brake-gas pedal changes for period n

N: Total observation interval

Equation (4) determines the number of subsequent alternations of gas and brake pedal and therefore indicates the traffic situation for a given period of time. Clothing insulation Measurement of clothing insulation is extremely difficult and is commonly done with heated manikins [19]. In this research, it is assumed that individuals have consistent clothing habits while driving a car. It is considered to be implausible, that a person chooses different clothing insulations for identical thermal environments. However, it must be considered that basic clothing insulation may vary during the year. Solar load Solar load has significant influence on thermal comfort in a vehicle compartment. It is estimated, that 50% of the HVAC unit’s cooling load in recirculation mode is due to solar heat gain [20]. Sun radiation may project complex patterns on the human body which require local cooling [21]. It is therefore suggested to use a three-dimensional solar sensor which is capable of determining the azimuth angle φ, the elevation angle ψ as well as the solar intensity I.

4.2 Automotive testing procedures Operating conditions for automotive HVAC units can be divided into three categories [6]: Transient conditions, Short-transient conditions, Stationary conditions.

Transient conditions refer to heating up and cooling down of the passenger compartment at extreme environmental conditions. An example may be a cooling down process of a passenger vehicle which has been previously soaking in the sun. Short-transient testing conditions aim to simulate small variations of interior and exterior climate. An example may be a change in cabin set-up temperature, ambient temperature, vehicle speed or sun load. Short-transient conditions consolidate the overwhelming majority of conditions in every-day driving situations. Stationary conditions rarely occur in automobiles. Steady-state conditions may be present in a truck cabin


Figure 2: Sensor locations

during the sleeping period of the driver [6]. The measurement equipment must be capable to clearly distinguish between all three situations. 4.3 Experimental setup Measurement equipment has been installed at characteristic locations within the vehicle cabin. The sensor positions are shown in Figure 2. Temperature measurement locations are indicated by ϑi, humidity by h and the solar properties by I, ψ and φ. Data from test drives have been collected over a distance of 20.000 km in Southern Africa during spring, summer and autumn at moderate to hot environmental conditions. An illustration of the experimental setup is given in Figure 3.

Figure 3: Experimental setup

5. DATA MINING Data mining has emerged during the 1980s and is considered as an ensemble of tools and methods for knowledge extraction from large amounts of data. Data mining is a multidisciplinary field including database technology, artificial intelligence, machine learning, statistics, pattern recognition, knowledge-based systems, knowledge acquisition, information retrieval, high-performance computing and data visualization [22].

5.1 Data pre-processing Real world data tend to be incomplete, noisy and inconsistent. In this paper, data cleaning refers to smoothing out of noise, removal of disturbances and inconsistencies. The authors’ research is limited to steady state and short transient conditions. Transient measurement vectors have been deleted upfront. Human beings are fuzzy in their decision space. When measuring human response for a given thermal environment, inconsistencies may occur. However, from a technical point of view, a unique mapping of input and output vector is essential for a successful learning strategy. Given two sets X and Y, this requirement can be written with equation (5).

. (5)

Determination of solar parameters implies sensor exposure to direct sun light. The authors discovered that in terms of measurement of solar angles, diffuse radiation

Control unit(8 bit ECU)

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TnS H

Comfort acquisition unit(16 bit ECU)

ClimateECU

LCD240x128

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Laptop PC

CANoeCANcard XL

RS232

BDM

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bus

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3 5 15

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5 5

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Tx: Temperature sensor xF1: Fan aspirated temperature sensorS: Solar sensorH: Humidity sensorJx: Joystick x

LCD240x128

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IO

I,ψ,φ

ϑ8

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I,ψ,φ

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cannot be handled by the available solar sensor. Research has however shown that the sun intensity I can be used as a first approximation to distinguish between reliable and erroneous solar angular information. However, this correlation might not be complete, because there may also be diffuse radiation with high radiation levels. According to the authors’ investigations, sun radiation level I < 300 W/m2 seems to be appropriate as lower boundary and has only little influence on human’s thermal comfort sensation. In these cases, knowledge of the exact sun position is not necessary, which however results in missing values for the solar angles. Similar situations might occur when re-transformation from Spherical to Cartesian coordinates is undefined. This is especially true when the sun is in zenith relative to the vehicle. There are various methods available to handle missing data [22]. In terms of this research, it seems to be straightforward to output a constant when solar angles can’t be measured or transformed. Rounding and summarizing equivalent samples can be considered as a technique for data reduction. The variable’s accuracy was intentionally reduced to:

Temperatures: Δϑ = ±0.5°C, Vehicle speed: Δv = ± 10km/h, Sun Intensity: ΔI = ± 100W/m2, Solar Angles: ΔΨ, Δφ = ±10°, Humidity: Δh = ±5% RH, Variances: Δσi = ± 10%.

5.2 Feature selection Pareto’s principles states that only 20% of the data account for 80% of the information. An appropriate method for feature selection and for discovering functional relationships is Correlation Analysis. With large data sets, the number of available data pairs increases dramatically, which makes an overview extremely in-transparent. Especially for large data sets, it is therefore often desirable to have a method that transforms variables into a new feature space, in order to facilitate visualization of their properties. Such a methodology is Principle Component Analysis (PCA). PCA is a statistical technique of multivariate data analysis, which is often used for data visualization and reduction of dimensionality. It is also known as Karhunen-Loève transform or Hotelling transform [23], [24]. PCA is based on the assumption that salient information in a given feature space lies in those features which have the largest variance. PCA aims at linearly transforming the original data matrix X into a new data matrix Y. Given a matrix X with , this rotational operation can be defined as:

, (6)

where P is an orthonormal matrix, which maximizes the variance of Y and minimizes its co-variance. PCA has been applied to the data set using the software packages Mathworks Matlab® and CAMO Unscrambler®. Table 1 shows the explained percentage of variance for each

principle component (PC). It is apparent, that the data set contains high redundancy. The first ten PCs already account for 93.4% of the data set’s total variance.

Table 1: Explained variances

Principle component Explained variance [%] PC1 33.9 PC2 49.9 PC3 59.3 PC4 65.6 PC5 71.4 PC6 77.2 PC7 82.2 PC8 86.7 PC9 90.4 PC10 93.4 PC11 95.5 PC12 97.2 PC13 98.2 PC14 98.9 PC15 99.5 PC16 99.9 PC17 100.0

PC11 to PC17 only explain 6.6% of the remaining variance and can be therefore considered as noise. Figure 4 shows the corresponding Scree plot.

Figure 4: Scree plot

There is one distinctive „elbow‟ between PC3 and PC4. A second „elbow‟, with a less gradient occurs between PC6 and PC7. The Scree criterion would therefore suggest keeping three or four factors [25]. The eigenvalues for PC4 and PC5 are 1.063 and 0.988 respectively. According to the Kaiser-Guttman criterion, only PC1 to PC4 would be relevant. Table 1 shows that the first three components account for about 59.3% of the dataset’s variance. If PC4 is added, 65.6% variance can be explained. Considering the second „elbow‟ in Figure 4, six components should be retained, accounting for a total explained variance of 77.2%. This interpretation is fairly confirmed by Cattel’s straight line approximation. The authors therefore recommend considering six PCs for further processing. Table 2 shows the PCA variable loadings of the first six PCs. The meaning of the variables is given in Table 3. The correlation loadings for ϑF and ϑA on PC1 to PC6 suggest that these variables are very


Table 2: PCA correlation loadings for all variables

Principle component PC1 PC2 PC3 PC4 PC5 PC6

ϑF -0.85 0.26 0.07 0.22 0.03 0.10 v 0.49 -0.16 -0.62 0.13 0.05 0.09 h 0.38 0.12 0.28 0.64 -0.32 0.01 ϑA -0.85 0.27 0.08 0.22 0.02 0.11 ϑ1 0.84 0.20 0.02 0.11 -0.09 0.05 ϑ2 -0.30 0.52 -0.18 0.29 -0.03 0.35 ϑ4 -0.70 0.51 -0.07 0.19 -0.02 -0.12 ϑ5 -0.86 0.38 -0.02 -0.05 0.05 -0.02 ϑ7 -0.39 0.50 -0.46 -0.17 0.03 -0.42 I -0.75 -0.41 -0.20 -0.06 -0.10 -0.09 φ -0.44 -0.74 0.15 0.10 0.03 0.34 ψ -0.12 0.39 0.04 -0.47 0.14 0.62 T -0.22 0.07 0.66 -0.12 -0.11 0.04 σI 0.15 -0.09 0.12 0.31 0.90 -0.06 σE 0.74 0.58 0.07 -0.01 0.04 0.02 σA 0.60 0.60 0.15 -0.09 0.04 0.04 σV -0.14 0.08 0.59 -0.17 0.09 -0.37 similar. The correlation-loadings also suggest that variables σE, and σA are highly negatively correlated to I and ψ. Correlation loadings for variables σE, σA and I are

Table 3: Variable meanings

Symbol Meaning ϑF Filtered ambient temperature v Vehicle speed h Relative humidity ϑA Ambient temperature ϑ1 Air outlet temperature ϑ2 In-cabin air temperature ϑ4 Driver head temperature ϑ5 Cabin roof temperature ϑ7 Dashboard temperature I Sun intensity φ Sun azimuth angle ψ Sun elevation angle T Empirical traffic function σI Standard deviation of sun intensity σE Standard deviation of sun elevation angle σA Standard deviation of sun azimuth angle σV Standard deviation of vehicle speed

in opposite direction with exception of PC4. However, the influence of PC4 is not significant, since it only contributes 0.3% towards I, 0.01% towards σE and 0.77% towards σA. A score plot shows that samples with higher than average values for σE and σA and lower than average values for I are linearly separable from the rest of the data cloud. The researchers assume that these samples contain diffuse solar radiation levels. These variables contain redundant information and variables σA and σE can be removed from the data set. Table 4 shows the correlation loadings for a PCA recalculated without the influence of variables ϑF,, σA and σE. It is apparent that the variables ϑA, ϑ4 and ϑ5 share similar variance with PC1 (72.2%, 62.1%, 86.7%) but only moderately differ on PC2 (0.0%, 14%, 2.6%). It is assumed that they are similar in effect. However, the correlation loadings only indicate some rough similarity but no clear redundancy. In Figure 5, the variables ϑA, ϑ4 and ϑ5 are plotted in dependence of all samples. It is obvious, that ϑ4 and ϑ5 fairly share the same tendency and follow the course of ϑA. ϑ4 and ϑ5 specify

Table 4: PCA correlation loadings without ϑF, σA, σV

Principle component PC1 PC2 PC3 PC4 PC5 PC6

v 0.54 -0.15 -0.58 0.06 0.05 -0.11 h 0.39 -0.20 0.39 0.40 -0.40 -0.31 ϑA -0.85 -0.01 0.05 0.15 -0.04 -0.16 ϑ1 0.78 -0.40 0.18 0.00 -0.04 -0.10 ϑ2 -0.39 -0.52 -0.02 0.13 0.02 -0.52 ϑ4 -0.79 -0.37 0.04 0.23 -0.08 -0.02 ϑ5 -0.93 -0.16 0.01 0.03 0.04 0.01 ϑ7 -0.50 -0.58 -0.28 0.06 0.01 0.39 I -0.66 0.46 -0.33 0.04 -0.13 0.02 φ -0.27 0.80 -0.08 0.03 0.04 -0.39 ψ -0.21 -0.33 0.13 -0.63 0.44 -0.33 T -0.25 0.15 0.65 -0.12 -0.04 -0.05 σI 0.17 0.09 0.10 0.58 0.77 0.00 σv -0.17 0.09 0.61 0.01 0.09 0.39

Figure 5: Influence of ambient temperature

the temperature at head and roof level. The head area is especially sensitive to climatic extremities. The clear influence of ϑA towards ϑ4 and ϑ5 is an amazing insight, which suggests that thermal comfort perception inside the vehicle cabin is considerably influenced by the ambient temperature, even if the cabin interior is air-conditioned and decoupled from the exterior environment. In this context, it shall be mentioned, that temperature sensors ϑ4 and ϑ5 have not been shielded against radiation. The research vehicle’s black colour might have intensified radiation effects. However, it is apparent, that this dependency is not linear. Figure 5 suggests that there seems to be a saturation effect in ϑ4 and ϑ5 towards lower and higher values of ϑA. This is indicated by the dashed lines. These non-linear saturation effects may limit the expressiveness of the bivariate correlation coefficient and the PCA results and might also be the reason why ϑA, ϑ4 and ϑ5 share most of their common variance on PC1, but distinguish on PC2. For this research, linear correlation is not a necessary requirement. Methods of artificial intelligence are capable of theoretically realizing any non-linear mapping. Therefore, ϑ4 and ϑ5 can be considered to be redundant to ϑA and can be removed from the dataset. Most of the data acquisition was done on sunny days with low values for σI. The available database does not contain the necessary number of samples allowing for statistical expressiveness of σI. The variable σI is therefore not covered by the further course of the investigations and further data acquisition, especially on cloudy days, is considered as advantageous. Table 4 reveals that 76.7% of ϑ1’s variance is explained by PC1 and PC2. The authors assume that ϑ1 might be highly negatively correlated to ϑA. However, ϑA is not correlated to PC2, while PC2 adds additional 16%


variance towards ϑ1. Figure 6 shows a scatter plot of ϑA and ϑ1. For ϑA<+36ºC, ϑA and ϑ1 are fairly negatively linearly correlated. This is indicated by the red line on the left-hand side of the plot. For ϑA>+36ºC, ϑ1 seems to be fairly positively linearly correlated to ambient temperatures

Figure 6: Outlet temperature

An explanation of this effect might be that for increasing ambient temperatures the required cooling load must increase, in order to maintain in-cabin comfort levels. This means, that the air outlet temperature must decrease. At a certain point, when the available cooling power is exhausted, or the maximum setup point of the HVAC unit has been reached, a further increase in ambient temperature forces the outlet temperature to rise as well. With a reasonable degree of accuracy, ϑ1 can therefore be removed from the dataset, because its information can be described with variable ϑA. Table 5 shows the correlation loadings of the data set removed by the influence of variables σI, ϑ1, ϑ4 and ϑ5.

Table 5: PCA correlation loadings without σI, ϑ1, ϑ4, ϑ5

Principle components PC1 PC2 PC3 PC4 PC5 PC6

v -0.63 0.16 -0.49 0.10 0.01 -0.13 h -0.40 -0.03 0.45 0.23 0.62 -0.05 ϑA 0.79 0.16 -0.01 0.10 0.24 -0.03 ϑ2 0.35 0.57 0.01 0.42 0.34 -0.22 ϑ7 0.34 0.73 -0.17 -0.43 0.08 0.14 I 0.71 -0.23 -0.49 -0.13 0.13 0.01 ψ 0.43 -0.71 -0.32 0.33 0.02 -0.14 φ 0.23 0.42 0.20 0.50 -0.60 -0.09 T 0.38 -0.20 0.58 0.06 -0.02 0.52 σv 0.28 -0.15 0.56 -0.40 -0.10 -0.60

Vehicle speed is largely explained by PC1 (39.1%) and PC3 (24.4%). The remaining loadings are insignificant. The first three components explain 41.59% of σv’s and 51.9% of T’s total variance. It is apparent, that on the first three factors, v is in opposite direction of σv and T. For a first approximation, the authors therefore suggest to omit the variables T and σv from the dataset, since a large proportion of their common variance is negatively correlated. There is a logical explanation for these findings. When the vehicle speed is high, the vehicle is most probably driving on a highway. Changes in vehicle speed and variations of gas and brake pedal activity probably occur less frequent. At low vehicle speed, the vehicle is most likely driving under urban traffic conditions. Therefore changes in speed, due to acceleration and deceleration, may occur more

frequently. Differences on higher factors can be explained with the memory effect of variable T.

6. MODELLING

The environmental climate inside the vehicle cabin is mainly controlled by the blower level, flap positions and the temperature setup. The available data base for this research has been collected from test drives. Assumptions of linear parametric dependency and any predefined underlying probability distribution, can therefore not be guaranteed. The authors have identified non-linear and non-parametric models as suitable implementation. Due to a lack of knowledge about the process itself, a black-box approach has been chosen and an exemplary implementation using Artificial Neural Networks is shown. 6.1 Artificial Neural Networks Artificial neural networks consist of many single processing units which are typically arranged in layers. These processing units are called neurons. The schematic of a neuron is shown in Figure 7.

Figure 7: Neural processing unit

Each neuron is capable of processing an input vector and outputs a scalar y. The weight vector shall thereby imitate biological synapses in NNs,

which determine the influence of each xi on the neuron’s output y. The weighted summation of the input vector x is called ‘net’ and can be mathematically expressed as:

(7)

The input signal Ɵ is a constant, which is often referred to as bias term. Sometimes it is not mentioned explicitly and is incorporated into the input vector x. The scalar output signal y can then be expressed as:

(8)

The function f(·) is called activation or transfer function. The activation function can theoretically be any linear or non-linear function. However, in practice often non-linear sigmoid or logistic functions are used due to their mathematical properties like monotonicity, continuity and differentiability. Latter property is required for effective


learning algorithms. A sigmoid transfer function, which is also used in this research, is given in equation (9).

(9)

6.2 Network design When designing a neural network, the engineer has to identify a suitable network structure. Today the amount of possible ANNs is enormous, including highly specific network structures. Today, there are about 50 types of networks available [26]. However, modelling will be limited to Feed-forward ANNs, since they are common for pattern analysis problems. The three most important design parameters are sample size, number of hidden layers and number of hidden layer neurons. The generalization capability of a neural network predominantly depends on three properties [27]:

Size of the training set and its expressiveness, the architecture of the neural network, the complexity of the approximation problem.

The last factor is hardly controllable, since when considering an implementation using ANN, the researcher has generally only little knowledge about the process’ underlying complexity. The first and the second factor are dependent of each other. However, assuming that the researcher has chosen a suitable neural network structure and an expressive training data set for the problem at hand, [27] suggests equation (10) for determination of the required number of training samples Ns.

(10)

Where:

Nv: Total number of free parameters within the network

ε: Fraction of classification errors permitted on test data

: Order of quantity enclosed in

The free parameters in a FNN are the number of weights and bias terms. A FNN with an arbitrary large number of non-linear hidden layer neurons can approximate any continuous function [26], [27]. In literature, there is however disagreement if one or two hidden layers should be used in terms of optimal generalization performance. Generalization therefore refers to the network’s performance with respect to previously unseen data. However, there seems to be consensus that more than two hidden layers are not required. There is currently no sound theory on which approach performs better. In terms of this research the authors follow the concept of [26], who first recommends trying a network with one hidden layer, before implementing an ANN with two hidden layers. Blower level prediction can be described as

mapping. The number of input nodes is therefore determined to be eight and the number of output neurons is defined as four. Flap position prediction can be described as mapping, meaning eight input

layer nodes but only three output layer neurons. Since only little a-priori knowledge about blower level and flap position prediction is available, the number of hidden layer neurons must be chosen according to the complexity of the underlying functionality. For training the ANNs, about 3000 consistent data samples have been available. According to equation (10), this allows for training of networks with a total sum of Nv=300 free parameters with an error probability ε=0.1. The recommended upper bound of hidden layer neurons is thereby determined to be 23 for blower level prediction and 25 for flap position prediction. To determine the number of hidden layer neurons for blower level and flap position prediction, networks with different numbers of hidden layer neurons have been trained and their performance has been compared. When training a FNN, the weights within the network are randomly initialized. However, improper initialization of weights may result in infinite training times or stopping at a local minimum of performance.

Figure 8: Blower network performance

Figure 9: Flap network performance

Therefore 200 networks have been trained for each hidden layer configuration. The best 150 results for training and validation performance have been taken into account and have been plotted as average in Figure 8 for blower level prediction and in Figure 9 for flap position


prediction. This procedure prevents that poor weights initialization affect the performance plots and additionally provides statistical confidence concerning the results. It is apparent that the networks’ performances initially increase and level off towards higher numbers of hidden layer neurons. There are no apparent local minima. However, it is also apparent that mean square error only slowly decreases towards high numbers of hidden layer neurons. Literature suggests selecting as few as possible hidden layer neurons, in order to minimize the number of free parameters within the network, meaning a trade-off between precision and cost [28]. In Figure 8 it is apparent that hidden layer neurons 12 to 25 form a more or less straight line, indicating only little further improvements in prediction performance. In Figure 9, this straight line can be found for hidden layer neurons 10 to 25. The researcher therefore suggests implementing 12 hidden layer neurons for blower level prediction and 10 hidden layer neurons for flap position prediction. With these findings, the neural network structures have been determined as shown in Figure 10 and Figure 11.

Figure 10: Blower level network structure

Figure 11: Flap position network structure

The input variables to both networks have been z-core transformed in order to minimize the bias of one feature over another. A max-picker functionality has been implemented for unique classification results. The total number of free parameters can be determined as Nv=169

for the blower level prediction network in (a) and as Nv=128 for the flap position prediction network in (b). According to equation (10), this means that the networks can be efficiently trained with about Ns=1700 for blower level and with about Ns=1300 (good) samples for flap position prediction. 6.3 Training of the networks The neural networks have been trained using the Conjugate gradient descent algorithm for training. The data set has been divided into 65% training data, 15% validation data and 20% testing data. Training data was used for system learning and validation data was used as cross validation for preventing the network from over-fitting. The networks have been finally tested with the randomized and previously unseen test data. The testing results for blower level prediction are shown in Table 6.

Table 6: Confusion matrix for blower level prediction Test data Blower level Identified

[%] L1 L2 L3 L4 L1 139 9 11 0 87.4 L2 14 119 15 0 80.4 L3 2 15 101 4 82.8 L4 7 1 2 139 93.3

Correctly classified [%]

85.5 82.6 78.3 97.2 86.2

It is apparent that a total of 86.2% of the test cases were correctly classified. The results for validation and training data are given in [21] and show similar performance. It is apparent that blower level „1‟ and blower level „4‟ have been best classified, suggesting that extreme conditions are well separable. Blower level „1‟ could be correctly predicted in 85.5%, blower level „2‟ in 82.6%, blower level „3‟ in 78.3% and blower level „4‟ in 97.2% of all cases. The classification performance between blower level „2‟ and blower level „3‟ seems not to be that clear. It is apparent that most cases of misclassification occur in neighboring classes. Table 6 therefore suggests that the operator had more difficulties to uniquely distinguish between blower level „2‟ and blower level „3‟ than between extreme situations. There seems to be an estimated 20% overlap between blower level „2‟ and blower level „3‟. This tendency is present in the training, validation and testing plots. There are various possible explanations for these phenomena. One could conclude that humans are fuzzy in evaluation of their thermal environment. This evaluation might also be time and location-variant to some extent. Another possible explanation might be the use of a manual HVAC system, which only allows for setting up a discrete output space. Problems may especially occur when the environmental situations demand an output value in between two discrete output classes. This could result in an increased range of decision fuzziness. The verification results with previously unseen data for flap position prediction are shown in Table 7. It is apparent that in 87% the network is able to produce the correct output. Similar to blower level prediction, the extreme values „breast‟ (P1) and „head‟ (P3) have been predicted best with 86 % and


92.2% correct classifications. Flap position „breast-head‟ (P2) has been correctly classified for 82.8% of all cases. This suggests an overlap between flap positions „breast‟ and „breast head‟ as well as for flap positions „breast-head‟ and head.

Table 7: Confusion matrix for flap position prediction Test data Flap position Identified

[%] P1 P2 P3 P1 172 20 1 89.1

P2 25 154 14 79.8

P3 3 12 177 92.2

Correctly classified [%] 86.0 82.8 92.2 87.0

Possible explanations for these phenomena follow exactly the argumentation of blower prediction network. 6.4 Temperature reference modelling The data mining process revealed that temperature knob setting is fairly segmental linear dependent on ambient temperature ϑA. This is shown in Figure 12. The authors suggest to model temperature reference value Tk with two straight lines, which have been added in Figure 12. A best fit straight line was therefore determined, so that for each (xi,yi)

(11)

is fulfilled. The coefficients have been calculated as

a=-1.061, b=113.

The result is summarized in equation (12).

(12)

Figure 12: Temperature set-up

7. CONCLUSIONS

Thermal comfort in transient environments, like an automotive cabin, is still far from being understood completely and generally accepted theories do not exist. This paper introduces a novel methodology to directly correlate environmental information to HVAC output control parameters. Data acquisition has been conducted in moderate to hot environments during spring, autumn and summer conditions in Southern Africa. Methods of data mining have been used for data integration, data cleaning, reduction of data dimensions, data transformation and have been implemented in Mathworks Matlab®. Principles of multivariate statistics have been applied to reveal variable interrelationships and correlations, in order to reduce the dimensionality of the feature space. Special importance has been attached to PCA, a dimensionality reduction and visualization technique, which successively explains maximal variance. The dimension of the input space was reduced from to . The necessary variables have been identified as vehicle speed, relative humidity, ambient temperature, in-cabin temperature, dashboard temperature, sun intensity, sun elevation angle and sun azimuth angle. ANNs have been applied to thermal comfort research in order to predict blower level as well as the heater box’s air distribution flap position. Research has been conducted to determine the optimal structure of the ANNs. An 8-12-4 FNN was found for blower level prediction and an 8-10-3 FNN for flap position prediction. The networks have both been trained with about 3000 samples, however it was shown that 1700 and 1300 expressive samples should be sufficient to train the blower and the flap network respectively. The term expressive cannot be specified with formal means. In practice, this means that samples have to be collected which include representative information about the environment. In terms of thermal comfort this means that samples must cover a representative variety of environmental conditions, including moderate as well as extreme conditions. The resulting overall testing classification performance is about 87% for blower and flap prediction. Extreme values for blower level and flap position were predicted best. It was shown that data classes overlap to some extent which might be a result of human fuzziness in thermal comfort evaluation. However it might be also a consequence of the manual HVAC unit, which has been used for this research project. The ANNs performance has been verified against independent data, which have been randomly chosen from the data set and which have not been used for system training. It has been shown that it is possible to extract thermal comfort knowledge directly from measurement data. Prior modeling of human’s thermo-regularity system and human’s response is not necessary. It has therefore also been shown that it is possible to adapt a technical system to the thermal comfort preferences of an individual. Temperature knob prediction was found to be primarily dependent on ambient temperature and can be fairly approximated by a stepwise linear function.


8. REFERENCES

[1] Fanger, P. O.: Thermal comfort analysis and applications in environmental engineering. New York: McGraw-Hill, 1972, 1970.

[2] R. Becker and M. Paciuk: “Thermal comfort in residential buildings - Failure to predict by Standard model,” Building and Environment, vol. 44, no. 5, pp. 948–960.

[3] Zhang, H., Arens, E., Huizenga, C., and Han, T.: “Thermal sensation and comfort models for non-uniform and transient environments, part III: Whole-body sensation and comfort,” Building and Environment, Vol. 45, No. 2, pp. 399–410, 2010.

[4] Gielda TP, Hosni MH: Transient Thermal Comfort Predictions for Automotive Environments. http://www.grrt.fr/html/travaux/download.php?filename=00gieldahosni.pdf

[5] Dear, R. de: “Thermal comfort in practice,” Indoor Air, Vol. 14, No. s7, pp. 32–39, 2004.

[6] Cisternino M: Thermal climate in cabs and measurement problems, Paper for the CABCLI seminar - EC Cost Contract No SMT4-CT98-6537 (DG12 BRPR), 1999, Dissemination of results from EQUIV - EC Cost Contract No SMT4-CT95-2017.

[7] Silva, M. C. G. d.: “Measurements of comfort in vehicles,” Meas. Sci. Technol, Vol. 13, No. 6, pp. R41, 2002.

[8] Ormuz K, Muftic O: “Main Ambient Factors Influencing Passenger Vehicle Comfort”. In: Proceedings of the 2nd International Ergonomics Conference, Zagreb Croatia, pp. 77-82, Oct 2004

[9] Devonshire and M, J.: The effects of infrared-reflective and antireflective glazing on thermal comfort and visual performance: a literature review: Deep Blue at the University of Michigan: University of Michigan, Ann Arbor, Transportation Research Institute, 2007. http://deepblue.lib.umich.edu/handle/2027.42/49457).

[10] Farzaneh, Y. and Tootoonchi, A.: “Controlling automobile thermal comfort using optimized fuzzy controller,” Applied Thermal Engineering, vol. 28, no. 14-15, pp. 1906–1917, 2008.

[11] Calvino, F.: “The control of indoor thermal comfort conditions: introducing a fuzzy adaptive controller,” Energy and Buildings, vol. 36, no. 2, pp. 97–102, 2004.

[12] Hamdi, M.: “A new predictive thermal sensation index of human response,” Energy and Buildings, vol. 29, no. 2, pp. 167–178, 1999.

[13] Zhi-Hua Zhou and Ying Xia: The application of artificial neural network in HVAC system: Proceedings of 2005 International Conference on Machine Learning and Cybernetics, Guangzhou, pp. 4800-4804, 2005.

[14] Liang J, Du R.: “Design of intelligent comfort control system with human learning and minimum power control strategies,” Energy Conversion and

Management, Vol. 49, No. 4, pp. 517–528, 2008. [15] Deutsches Institut fuer Normung e.V.: DIN14505,

Ergonmomie der thermischen Umgebung – Beurteilung der thermischen Umgebung in Fahrzeugen. Berlin, Beuth Verlag GmbH, 2007.

[16] Deutsches Insitut für Normung e.V.: DIN EN ISO 7730:2005. Ergonomie der thermischen Umgebung-Analytische Bestimmung und Interpretation der thermischen Behaglichkeit durch Berechnung des PMV- und des PPD-Indexes und Kriterien der lokalen thermischen Behaglichkeit. Berlin, Beuth Verlag GmbH, 2006.

[17] Olesen BW.: Evaluation of the thermal environment in vehicles. Application note, Bruel & Kjaer, Denmark, 1988.

[18] Sedlbauer, K.: “Raumklima und Innovation. Eine Aufgabe der Bauphysik,” Wksb. Zeitschrift für Wärmeschutz, Kälteschutz, Schallschutz, Brandschutz, Vol. 51, No. Nr.57, pp. 9–16, 2006.

[19] Deutsches Insitut für Normung e.V.: DIN EN ISO 9920:2009. Abschätzung der Wärmeisolation und des Verdunstungswiderstandes einer Bekleidungskombination. Berlin, Beuth Verlag GmbH, 2009.

[20] Walgama, C., Fackrell, S., Karimi, M., Fartaj, A., and Rankin, G. W.: “Passenger Thermal Comfort in Vehicles - A Review,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 220, No. 5, pp. 543–562, 2006.

[21] J Kranz: Intelligent thermal comfort control, PhD thesis, Nelson Mandela Metropolitan University, 2011.

[22] Kamber, M. and Pei, J.: Data Mining: Concepts and Techniques, Second Edition (The Morgan Kaufmann Series in Data Management Systems), 2nd ed. Morgan Kaufmann, 2006.

[23] Bortz, J.: Statistik: für Human- und Sozialwissenschaftler (Springer-Lehrbuch) (German Edition), 6th ed. Springer, 2005.

[24] Izenman, A. J.: Modern multivariate statistical techniques: Regression, classification, and manifold learning. Springer texts in statistics. New York, London: Springer, 2008.

[25] Jolliffe, I. T.: Principal component analysis,. Springer series in statistics, New York: Springer, 2002.

[26] Kecman, V.: Learning and soft computing: Support vector machines, neural networks, and fuzzy logic models. Complex adaptive systems. Cambridge Mass: MIT Press, 2001.

[27] Haykin, S. S.: Neural networks and learning machines, 3rd. New York: Prentice Hall, 2009.

[28] Priddy, K. L. and Keller, P. E.: Artificial neural networks: An introduction. Tutorial texts in optical engineering TT 68. Bellingham Wash: SPIE Press, 2005.


EFFECT OF DISTANCE ON THE ACCURACY OF RSS-BASED GEOMETRIC POSITIONING METHODS

F.M. Dahunsi*1, B. Dwolatzky*, A. Love**

*School of Electrical and Information Engineering, **School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa. E-mail: [email protected]*, [email protected]*, [email protected]**

Abstract: The accuracy of Received Signal Strength (RSS)-based positioning methods is highly variable due to its dependence on various varying parameters such as the wireless environment, topology of the network, propagation model utilized etc. In this paper, drive test data were analyzed to examine the effect of distances from the Mobile Station to the serving and neighbouring base stations (BSs) on the accuracy of four RSS-based geometric positioning methods. The relationship between the accuracy of these positioning methods and distances between the BSs were also considered. There is relatively varying differences that the topologies of the network have on the accuracy of the positioning algorithms. The RSS-based geometric algorithms considered include the Centre of Gravity, the Circular Trilateration, Circular Trilateration and the Least Square algorithms. Keywords: Received Signal Strength, location accuracy, topology, distance, geometric methods

1. INTRODUCTION

The Federal Communications Commission (FCC) of the United State (US) in 1996 adopted a report that enforced mobile operators in the US to provide and deliver wireless emergency service (E911) [1,2]. The E911 became a major driver of location-based services (LBS) to enhance effective location based emergency service delivery [2]. Furthermore, the European Emergency forum in 2003 enforced location enhanced 112 (E-112) a variant of the US E911. This lead to a wide range of research to provide accurate positioning of a mobile station (MS) for the provision of a good quality LBS to mobile users. This research focused mainly on the needs of developed countries where smart phones are more affordable and network infrastructure better established. The mobile operators in a bid to obey the FCC rules also invested considerable resources in their networks thereby paving the way for commercial LBS as well [3].

In developing countries, most of the network infrastructures are GSM networks. Smart phones are not affordable and only a few urban business areas have 3G coverage. This has lead mobile operators to depend largely on network-based positioning methods for the provision of LBS to users. Currently most research carried out on positioning technologies are geared towards developed countries, little research is carried out on further improving network-based positioning methods which might be more applicable in developing countries. This paper investigates distance related geometric challenges posed by Received Signal Strength (RSS)-based geometric positioning methods.

RSS measurements are readily available to all MSs (part of the handoff algorithm) with no extra cost to the users

and little modification on the mobile operator’s network [4]. If the propagation model is known, the RSS measurements can be mapped to distance measurements which can be used for positioning and consequently provision of LBS. The major challenge with RSS-based positioning algorithms is the estimation error which is relatively higher than obtainable in other localization methods which utilizes smart phones and/or satellite positioning. The movement of the MS also introduces fast fading error to the measurements which hampers correctly mapping RSS measurements to distance measurements.

2. RSS-BASED POSITIONING ALGORITHM

2.1 RSS measurement model

Path loss prediction models provide mathematical relationship between RSS received and distance between the MS and BS [5,6]. Such model includes the Hata model, Lee model, Cost 231 models etc.

Considering two dimensional positioning; the mathematical relationship between distance, di (distance between the MS and ith BS), the true location of the MS denoted by [xm ,ym ] T and the coordinates of the ith BS, [xi ,yi] T is given by:

(

where i = 1, 2, …, n and n is the total number of BSs with adequate received signal strength level which is typically between 29dBm and -114dBm according to GSM specifications [6].

Assuming a noise-free received power, RSS at the ith BS is expressed in [5,7] as:


, i = 1, 2, …, n (

The powers transmitted and received are denoted as and respectively, where is the propagation constant and is other factors that might affect the received power which might include antenna height, antenna gain and multipath propagation. It should however be noted that the effect of multipath propagation cannot be totally mitigated. can be estimated through measurements by finding the path loss slope, ideally, is equal to 2 in free space i.e. rural areas and could range from 3 - 6 for urban or suburban [5,7].

The distance related measurement can then be modelled, as expressed in [5]:

(3)

where is the estimated distance between the MS and ith BS and ni denotes measurement noise introduced to the estimated distance. From equations 2 and 3, can then be expressed as:

(4)

, i =1, 2, …, n (5)

2.2 Geometric RSS-based methods The geometric approach uses deterministic information derived from RSS measurements which are interpreted geometrically and then used to estimate the MS position. The geometric techniques can be classified into two; the empirical approach and propagation model based approach. The former approach is based on the use of digital maps of a specific area which requires a lot of manpower hours and is computationally intensive. The geometric approach utilizes the relationship between RSS and distance for MS position estimation. It is also considered in this paper because it is relatively easier to implement and deemed best to fit the need of developing countries that are often posed with computational power challenges and lack of adequate professional expertise. The geometric algorithms considered in this paper were explicitly explained in [8].

Centre of Gravity algorithm proposed by Zhou et al (2003) assumes that the relationship between RSS and distance between the MS and a given BS is based on an inverse square law . where is the propagation constant which takes into account error introduced by the environment, R is the RSS and d is the distance between the MS and a given BS [9,10].

Circular Trilateration (CT) algorithm is also based on the construction of three (3) circles using RSS from three BSs and known coordinates of the BSs to estimate the position of the MS. The intersection of the circles gives an estimate of the location of the MS.

The algorithm also assumes that an inverse square law given by d (N + R)- can be used to describe the relationship between distance from the MS to a given BS and the RSS, where is the propagation constant as previously explained, N is the normalization constant and R is the RSS [10]. The Trilateration (TRI) algorithm is one of the most common algorithms used for RSS based MS location estimation. It assumes that three acceptable RSS level can be obtained for MS location estimation. Using a path loss prediction model, the distance between the MS and BSs with acceptable RSS level can be estimated and a circle with estimated distance as its radius can be constructed. The BSs are located at the centre of the radius and the MS located somewhere on the circle. In most cases to eliminate ambiguity, three circles are required [11].

When more than three acceptable RSS levels can be received, the number of independent equations becomes greater than the number of unknown parameters. This grants the opportunity for the Least Square (LS) algorithm to be applied in order to optimize the redundant measurements and obtain improved location estimates [11].

The four afore-mentioned RSS-based algorithms were investigated in this paper to analyze the effect the geometry of the network has on the accuracy of positioning algorithms. Two major parameters which determine the geometry of a network will be considered: firstly, the distance of the BSs relative to the MS and secondly, the distance of the BSs relative to each other.

3. MEASUREMENTS

Drive test measurements were collected in the Gauteng province of South Africa. The measurements were taken from two different environments; built-up urban areas and a rural area with flat fields and some hilly terrain. The frequency of the measurements was 900MHz. The RSS measurements were collected at a mobile station receiving signals from fixed BSs with known location coordinates. Some of the data collected which is of importance to this paper includes; position of the MS as estimated by the Global Positioning System (GPS) which was used as the benchmark for accuracy. RSS measurement of the serving BS and 6 neighbouring BSs as received by the MS; and the coordinates of the BSs. Measurements were collected from 65 BSs and analyzed for the purpose of this paper.

3.1 Correlation Analysis

The afore-mentioned RSS-based geometric positioning algorithms were used to estimate the location of the MS based on the RSS measurements and coordinates of the serving BSs and neighbour BSs. The estimated locations derived from these methods are then subtracted from the true position of the MS as derived by the GPS; this we call the “Location Error” for the positioning algorithms. In this paper we considered two dimensional estimation


but this method can easily be applied to a three dimensional system.

A cellular network as shown in Figures 1 and 2 with two types of distance measurements considered which will be called Case One and Case Two as shown in the Figures. Let us follow the dashed lines in Figures 1 and 2 and assume that at the star symbol, MS is connected to BS1, BS2, BS3, BS7, BSa, BSb and BSc. BS1 is the serving BS. Where the MS is presently, it can receive signals from BS1, BS2, BS3, BS4, BS5, BS6 and BS7. Moving further down the path to the triangular symbol, it can receive signals from BS1, BS2, BS3, BS4, BS5, BS6 and BSd. In this paper MS positions algorithms are analyzed in relation to its communication with a particular serving BS as it moves along the path. The Serving BS remains constant and the neighbour BS changes as the MS moves along.

Figure1: Case One

BS1 represents the serving BS and BS2, BS3, BS4, BS5, BS6 and BS7 are the neighbour BSs the MS is currently connected to. Distances from the MS to BS1, BS2, BS3, BS4, BS5, BS6 and BS7 are denoted as d1, d2, d3, d4, d5, d6 and d7 respectively. D1, D2, D3, D4, D5, D6 and D7 denote distances from BS1 to BS2, BS2 to BS3, BS3 to BS4, BS4 to BS5, BS5 to BS6 and BS7 to BS1 respectively.

A standard Pearson product-moment correlation coefficient analysis [12] was carried out on the location errors from the aforementioned algorithms and distances to determine the effect distance has on location error which is directly related to the location accuracy. The analysis carried out is explained in the steps below;

Step1: Positioning methods aforementioned were used to estimate the location of MS. Step 2: Location error was calculated by subtracting estimated location of the MS from their actual location.

Step 3: Actual distance of BSs to MS and BSs from each other as shown in Figures 1 and 2 was calculated using known coordinates of BSs and GPS coordinates of MS Step 4: A Pearson Correlation analysis was carried out to analyse how well related location errors obtained are to distances as described in Case One and Case Two. Step 5: Analysis was carried out on rural and urban environments.

Figure 2: Case Two

4. RESULT AND DISCUSSION “Pearson correlation coefficient analysis is used to describe the strength and direction of the linear relationship between two variables” [12]. Preliminary analysis was performed to ensure no violation of the assumption of normality and linearity.

RSS measurements are highly affected by interference in the wireless environment. Data used in calculation of MS location using the positioning algorithms are collected from the cellular network, therefore it is expected that there will be other variables interfering with the output such as multipath, shadowing, diffraction etc. This might be why the curves on the graphs shown in Figures 3-6 are not smooth but they are good enough to explain the relationships analyzed in this paper.

It should be noted that some of the correlation relationships as shown in Tables 1 - 4 are negative correlation. The sign in front of the correlation coefficient indicates positive or negative correlation between variables and absolute value of correlation coefficient indicates the strength of the correlation [12]. The negative values in the tables below have been normalized to show only the strength of the correlation for the purpose of Figures 3 - 6. Error (Actual location - Estimated location) estimated from the positioning algorithms is directly proportional to accuracy obtained from the algorithms. Error was estimated using the Root Mean Square Error (RMSE) which is a widely used error variable to estimate the error

MS

BS1

BS2

BS3

BS4

BS5

d1

BS7

BS6

d2 d3

d4

d5 d6

d7

BSa

BSb BSc

BSd

D5

BS4 BS7 MS

BS1

BS2

BS3

BS5

D1

BS6

D2

D3

D4 D6

D7

BSa

BSb BSc

BSd


introduced during estimation and hence evaluate the accuracy of the location algorithms [9]. Let the actual location be given as and the estimated location as , the RMSE is given as:

(6)

where N is the total number of MS locations estimated and .

A strong correlation between location errors and distances shows a high dependency of the positioning algorithm to distances under consideration. This in turn explains the dependence of accuracy obtained from the algorithm to topology/geometry of the BSs to the MS and relative to each other. A weak correlation shows a weak relationship between the topology/geometry and accuracy of the positioning algorithm indicating a lower dependence.

4.1 Rural analysis: Case One

The relationship between Case One and location errors is summarized in Table 1 and Figure 3.

There is a strong correlation between variable d4 and COG location errors, medium correlation between d1, d2 and COG location errors and small correlation between d3, d5, d6 and d7 and COG location errors. There is a small relationship between CT location errors with d1 and d2, medium correlation with d4 and a strong correlation with d5. CT location errors correlation with d3, d6 and d7 are very small.

Table 1: Rural analysis: Case One Distance COG CT LS TRI

d1 0.46 -0.15 0.02 0.54 d2 0.41 -0.14 0.01 0.52 d3 -0.17 0.02 0.04 0.29 d4 0.98 -0.34 0.12 0.15 d5 -0.13 0.54 0.11 0.11 d6 0.13 0.03 0.12 0.12 d7 -0.13 -0.06 -0.06 0.22

For example, consider the COG distance relationship shown in Figure 3. COG’s accuracy is more dependent on distance between the MS and the third BS than distances between the MS and the first two BSs. It is least affected by distances between the MS and BSs 5, 6 and 7.

There is a small correlation between variable d4, d5 and d6 with LS location errors, while the other distances have relatively very small correlation with LS location errors. A strong relationship exists between TRI location errors with d1 and d2, medium correlation with small correlation with other distances.

Figure 3: Correlation analysis of location errors with

distances between the MS and BSs in rural environment

4.2 Rural analysis: Case Two

Table 2 and Figure 3 summarize the correlation between distances in Case Two and location errors.

There is a strong correlation between variable D3 and COG location errors, medium correlation between D2 and COG location errors and small correlation between D4, D5, D6 and D7 and COG location errors. It should be noted that some of the relationships are negative correlation. There is relatively a small relationship between D1 and COG location errors. There is a small relationship between CT location errors with D1 and D2, medium correlation with D4 and a strong correlation with D5. CT location errors correlation with D3, D6 and D7 are very small.

Table 2: Rural analysis: Case Two Distance COG CT LS TRI

D1 -0.03 0.04 -0.18 0.59 D2 0.34 0.11 0.00 0.06 D3 0.81 -0.28 0.17 0.23 D4 0.14 0.56 0.10 0.16 D5 0.13 0.33 0.15 0.14 D6 0.29 -0.18 0.10 0.11 D7 -0.12 -0.11 -0.05 0.18

There is a small correlation between variable D4, D5 and D6 with LS location errors, while the other distances have relatively very small correlation with LS location errors. There is a strong relationship between TRI location errors with D1 and D2, medium correlation with small correlation with other distances.

The two cases studied in the rural environment shows that COG location errors has the strongest relationship with distances which points to a higher dependence on geometry of BSs and MS for its accuracy than CT and LS location errors. The two cases also show similarities in correlation with the distances especially d3 and d4 in Case One and D3, D4 and D5 in Case Two.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

d1 d2 d3 d4 d5 d6 d7

Pear

son

Cor

rela

tion

Num

ber

Base stations (Rural)

COGCTLSTRI



distances between BSs in rural environment

4.3 Urban analysis: Case One

The relationship between Case One and location errors is summarized in Table 3 and Figure 5.

Table 3: Urban analysis: Case One Distance COG CT LS TRI

d1 0.92 -0.50 0.22 0.76 d2 0.93 -0.43 0.20 0.80 d3 0.58 -0.06 -0.13 0.84 d4 1.00 -0.36 0.22 0.68 d5 0.55 -0.12 0.28 0.45 d6 0.56 -0.03 0.01 0.67 d7 0.53 -0.18 0.11 0.43


distances between the MS and BSs in urban environment

There is a strong correlation between all the distances and COG location errors. There is a small relationship between CT location errors with d5 and d7, medium correlation with d4 and a strong correlation with d1 and d2. CT location errors correlations with d3, d6 are very small.

There is a small correlation between all distances with LS location errors except d6 with a relatively low correlation coefficient. There is a strong relationship between TRI

location errors with all the distances investigated in Case One. 4.4 Urban analysis: Case Two Table 4 summarizes the correlation between distances in Case Two and location errors which are represented in Figure 6.

Table 4: Urban analysis: Case Two Distance COG CT LS TRI

D1 -0.20 0.58 -0.28 0.06 D2 0.77 -0.28 0.03 0.79 D3 0.69 -0.42 -0.02 0.68 D4 0.53 -0.37 0.47 0.01 D5 0.66 -0.27 0.23 0.59 D6 -0.14 0.45 -0.29 -0.03 D7 -0.27 0.53 -0.35 -0.06


distances between the BSs in urban environment

There is a strong correlation between the variable D2, D3, D4 and D5 with COG location errors and small correlation between D1, D7. There is a small relationship between CT location errors with D2 and D5, and a strong relationship with other distances. There is very small correlation between LS location errors with D2 and D3, a small correlation with D1, D5 and D6 and a strong correlation with D4 and D7. There is a strong relationship between TRI location errors with D2, D3 and D5, and small relationships with D1, D4, D6 and D7.

COG location errors also have the strongest relationship with distances in urban environment followed by CT with LS location errors being least affected. Figures 5 and 6 show a correlation with distances especially d3 and d4 in Case One and D2, D3, D4 and D5 in Case Two. In Figure 5, location errors is more correlated with the distances from the MS to the BSs than in figure 6 which are the BSs to each other. The distance of the MS to the BSs affects location errors more than distances of BSs to each other.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

D1 D2 D3 D4 D5 D6 D7

Pear

son

Cor

rela

tion

Num

ber

Base stations (Rural)

COGCTLSTRI

0.00

0.20

0.40

0.60

0.80

1.00

1.20

d1 d2 d3 d4 d5 d6 d7

Pear

son

Cor

rela

tion

Num

ber

Base stations (Urban)

COGCTLSTRI

0.00

0.20

0.40

0.60

0.80

1.00

1.20

D1 D2 D3 D4 D5 D6 D7

Pear

son

Cor

rela

tion

Num

ber

Base stations (Urban)

COGCTLSTRI


5. CONCLUSION AND FURTHER WORK Geometric positioning algorithms applied to urban environments shows more dependence on the topology/geometry of the network than in rural environments. This may be because the BSs in urban environment are more closely spaced than those obtained in rural environments. In general, comparing the two cases in both rural and urban environments, the distances in Case One have more correlation with location errors than the distances in Case Two. LS positioning algorithm is least affected by topology/geometry in all cases and environments considered but it also gave the worst estimate of MS location from previous works [8]. Even though it was least affected by the correlation coefficients obtained in Tables 1 - 4, it is large enough to be considered. For example in Table 4, looking at correlation between LS location errors and D7; the correlation coefficient is 0.35, which when squared indicates a 12.25% shared variance. Distance between the BS 1 and BS 7 helps to explain about 12% of the variance in the effect of distance on LS location errors [8]. The COG positioning algorithm has the strongest correlation at distance d3 and D3 in all cases studied except Urban Case Two where it was the second strongest. This show that distance between BS3 and MS and BS2 to BS3 is an important variable in the accuracy obtained in COG positioning algorithm. Varying correlation performance of all variables considered in rural and urban environments shows that geometry affects the position error which is directly proportional to accuracy provided by the positioning algorithm. Analyzing the geometry of the BSs and introducing this into MS location calculations might improve the accuracy of positioning algorithms. Further work needs to be carried out in developing a model that better fits the relationship between location errors and topology of the cellular network. Although, there are additional factors to be considered in addition to the geometry/topology such as the wireless environment, the network density, propagation model etc, the geometry/topology of the network is a very important variable and should not be neglected. This is of importance in developing countries where smart phones are a luxury and geometric techniques are used.

6. REFERENCES

[1] Y. Zhao, "Standardization of mobile phone positioning for 3G systems," IEEE Communications Magazine, pp. 108-116, July 2002.

[2] Federal Communication Commission, "Guidelines for Testing and Verifying the Accuracy of Wireless E911 Location Systems," USA, OET Bulletin No 71, 2000.

[3] E Beinat and E. S. Dias. (2003) Workpaper GIPSY project, (Inst. for Env. Studies (IVM)) Amsterdam, the Netherlands. [Online]. http://www.feweb.vu.nl/gis/research/LUCAS/Publications/docs/gipsy_2004_7.pdf

[4] J. Weiss, "On the Accuracy of a Cellular Location System Based on RSS Measurements," IEEE Transactions on Vehicular Technology, vol. 52, no. 6, pp. 1508 - 1518, 2003.

[5] K. W. Cheung, H. C. So, W. K. Ma, and Y. T. Chan, "Received signal strength based mobile positioning via constrained weighted least squares," in International Conference on Acoustics, Speech, and Signal Processing, 2003, pp. 137 - 140, April.

[6] S. Gezici, "A Survey on Wireless Position Estimation," Wireless Personal Communication, vol. 44, pp. 263 - 282, 2008.

[7] H. L. Song, "Automatic Vehicle Location in Cellular Communication Systems," IEEE Transaction on Vehicular Technology, vol. 43, no. 4, pp. 902 - 908, 1994.

[8] F.M. Dahunsi and B. Dwolatzky, "Performance Analysis of RSS-Based Geometric Positioning Methods in GSM Networks," in Southern Africa Telecommunication Networks and Applications Conference, 2010.

[9] J. K. Ng, S. K. Chun Chan, and S. Song, "A Study on the Sensitivity of the Center of Gravity Algorithm for Location Estimation," Hong Kong Baptist University, Kowloon Tong, Hong Kong, Technical report COMP-03-014, 2003.

[10] J. Zhou and J.K. Ng, "A Data Fusion Approach to Mobile Location Estimation based on Ellipse Propagation Model within a Cellular Radio Network," in 21st International Conference on Advanced Networking and Applications (AINA'07), Niagara Falls, Canada, 2007, pp. 458 - 466.

[11] K. Yu, I. Sharp, and Y. J. Guo, Ground Based Wireless Positioning, 1st ed.: John Wiley and Sons Ltd, IEEE Press Series on Digital and Mobile Communication.

[12] J. Pallant, SPSS Survival Manual: A step by step guide to data analysis using SPSS for Windows (version 12), 2nd ed. Australia: Allen and Unwin,Chapters 10 and 11, 2005.


RAINFALL DROP-SIZE ESTIMATORS FOR WEIBULL PROBABILITY DISTRIBUTION USING METHOD OF MOMENTS TECHNIQUE

A. Alonge* and T. Afullo**

* School of Electrical, Electronic & Computer Engineering, University of KwaZulu-Natal, Private Bag X54001, Durban 4041, South Africa E-mail: [email protected] ** School of Electrical, Electronic & Computer Engineering, University of KwaZulu-Natal, Private Bag X54001, Durban 4041, South Africa E-mail: [email protected]

Abstract: This paper proposes a new approach for deriving the input estimators for the Weibull probability rain drop-size distribution (DSD) using the Method of Moments (MM). The Stirling’s approximation is used to estimate the gamma function which is part of the raw moment function of the Weibull probability distribution. The parameters No, and are estimated using a comparative analysis with the likely measured moments of a statistical data. The new parameters are then tested with collected data at Durban, South Africa by using least squares regression fitting technique to derive their power-law relationships with rainfall rate. The results show that the proposed Weibull distribution fits well with the measured data at tested rainfall rates. In comparison with the ITU-R P. 838-3, the average RMSE of its specific attenuation is 0.99 for horizontal polarization and 1.40 for vertical polarization at selected rainfall rates for a frequency range of 0 to 100 GHz. Keywords: Method of moments, raindrop-size distribution, rainfall attenuation, Weibull probability distribution.

1. INTRODUCTION

The effects of rainfall attenuation in microwave and satellite communication becomes increasingly disturbing at frequencies above 10 GHz [1, 2]. At these higher frequencies (smaller wavelengths), the perturbations from the rain droplets in rainy medium often lead to signal absorption and scattering, and therefore, signal outage and deterioration [3]. Signal outages reduce bandwidth efficiency and spectrum utilization, which comes at great cost to providers of network services [3–5]. Usually, the aim of service providers is to ensure availability of services by compensating for this inadequacies through several corrective schemes such as complex base station power control algorithm. This process can be made possible by short term (or preferably long term) studies of rainfall, which of course, depend on the availability of rainfall data.

Rainfall is a complex phenomena, which is very random in nature, especially when considering the active natural variables that induce it. A method of studying its characteristics is by predicting empirically (apriori), from measurements, the behaviour of rainfall for a locality; other methods involve analytical formulations [6]. These methods allow for the identification of microstructural parameters, especially rainfall rate and rainfall drop-size distribution (DSD), which directly contribute to the determination of rainfall attenuation. Rainfall rate has been exhaustively used to predict attenuation in different parts of the world [1–2, 6–8]. However, the availability of rainfall DSD measurements provide a much more qualitative insight for radio engineers since it takes into reckoning the mechanics of rainfall microstructure [2, 6].

Efforts have been made in the past to identify appropriate statistical models to represent rainfall DSD [9–14], this is noticeable in the array and robustness of such models currently in use. Popular among these statistical models include Marshall-Palmer negative exponential model [11], modified gamma model [14] and lognormal model [9–10]. In this paper, we employ the Weibull probability DSD model to examine its suitability in modeling rainfall DSD. Sekine et al. [12–13, 15] in their contribution identified the Weibull DSD model as an appropriate model and proposed a graphical method for deriving the DSD input parameters from measurement. Their empirical estimation involved direct fitting procedure for which the scale and shape parameters of the Weibull distribution model were obtained.

In this paper, we present a new method of estimating the input parameters of the Weibull probability model using the Method of Moments technique. The third, fourth and sixth moments of the RD-80 disdrometer measurements is used to derive our parameters for Durban, South Africa. Our model for Durban is tested at rainfall rates of 0.91 mm/h, 5.51 mm/h, 43.90 mm/h, 62.30 mm/h and 117.15 mm/h. We applied the derived model to estimate specific rainfall attenuation with frequency ranging from 0 to 100 GHz at four rainfall rates – 5 mm/h, 10 mm/h, 50 m/h and 100 mm/h.

2. MATHEMATICAL DERIVATION OF PARAMETERS FOR WEIBULL RAINFALL DSD

The two-parameter Weibull probability density function in [16] is given by:

[email protected]


In (1) above, the data series xi is the input variable of a known process either random or deterministic. is the shape parameter, while is the scale parameter. Statistically, (1) increases monotically when 1 and becomes unimodal when > 1; therefore, is largely the determinant of the shape of the Weibull function [16]. Weibull is a type III minimum–value asymptotic distribution which has been extensively used for analysis of strength of materials and reliability studies [16, 17].

In related rainfall DSD research [9–15], several authors have acknowledged a minimum of two input parameters as sufficient for rainfall DSD models – they are, diameter of the drop size and the number of drops per unit volume. By virtue of this, it follows that the Weibull rainfall drop-size distribution should be represented with these parameters as:

and thus, our Weibull expression becomes:

where No is the number of rain drops per volumetric sweep of the point cell and Di is the diameter of the rain drops present in the same point cell.

In order to estimate the parameters No, and in (3), different estimation techniques can be utilized; among them include the method of maximum likelihood (MML), method of moments (MM), Kernel estimation and Bayesian estimation [16]. In this study, we employ the Method of Moments (MM) technique because of its exhaustive use in rainfall-related research and its unique relationship to measurable rainfall quantities [9, 18–20]. In this technique, we assume that our corresponding data sample Di exists such that its moment, mi at its point of origin is given by:

Then, the equivalent Weibull probability distribution raw moments Mn of the data sample at its point of origin is given in [16] as:

This can be reduced to:

By modifying (6) to suit our new parameter No, our nthraw moment becomes:

It follows from the findings of Kozu et al. [18] (see also Timothy et al. [19] and Das et al. [20]), that the typical values of n useful for radio and microwave engineering studies are the values of 3, 4 and 6. This is because they correspond to the liquid water content (LWC), specific attenuation and radar reflectivity of the measured data. By adopting these values, we have three sets of equation representing the third, fourth and sixth moment of the Weibull distribution as below:

By basic definition of gamma functions, it follows that and thus, . In this

definition, x is assumed as a positive integer. By making a further assumption that , we find a suitable expression for our gamma functions in (11) – (13) so that:

By restricting the results of to an integer, it follows that our representation might be difficult to express as a recurrent factorial order. Thus, in order to find an adequate representation for this problem, we employ the Stirling’s asymptotic approximation [21, 22]. This is defined as:

where the constant, e = 2.718281828, is the Napierian index. By simplification, the gamma function in (11) – (13) can be represented as below:

where k in this case corresponds to 3, 4 and 6. In this paper, the maximum error bound, , attributed to Stirling’s approximation is 8 % for the range 1 10


Fig 9: Performance of Weibull rainfall DSD model at 117.15 mm/h.

4. RAIN ATTENUATION PREDICTION FROM WEIBULL DSD PROBABILITY MODEL

4.1 Estimation of scattering parameters and specific attenuation

Rain attenuation prediction from rainfall for signal transmision along a terrestrial path can be estimated from the expression in ITU-R P.530-13[25] as:

where As is given as the specific attenuation and deff is the effective transmission distance which is a product of the actual link distance and the path reduction factor (please see ITU-R P.530–13 for more information on procedures for this).

By extension, the specific attenuation is given by:

where the extinction cross section (ECS) is Qext(D) in mm2 and dD is the change in diameter (or diameter interval) in mm. The drop size distribution is represented by N(D) and in this case will be replaced with our alternative Weibull DSD model.

The ECS is computed by employing the procedure of Odedina et al. [26–27] and Mulangu et al. [28] for spherical rainfall droplets. Their work estimated the scattering parameters by using a combination of Liebe’s complex refractive index for water [29], Mie scattering theory [30] and Mätzler equations [31–32]. In the Mie scattering theory, the real part of the forward scattering amplitude is used to determine the scattering parameters. By definition, the forward scattering amplitude is given as:

where an and bn correspond to the Mie scattering coefficients which are dependent on the ambient temperature during rainfall, complex refractive index of water and frequency of transmitted signals. The nth truncation of the infinite series can be determined from [33], where:

for

where k = 2 / for all wavelengths and is the radius for a spherical drop assumption.

The ECS of a transmitted signal can thus be estimated by multiplying the real part of s(o) by a factor as given below:

Odedina et al. [26–27] concluded that the terms of Qextfor Durban at an average temperature of 20oC can be reduced to a frequency-specific power law function in the form of :

Thus, (28) can be reduced to an expression for specified 20 diametric sizes based on our disdrometer channels given by:

4.2 Attenuation relationships based on rainfall rate and frequencies

The specific attenuation estimated from our Weibull DSD model for Durban is based on two schemes: variation of frequency, while keeping rainfall rate constant and variation of rainfall rate, while keeping frequency constant.

In the case of varying the rainfall rates while keeping the assumed transmission frequency constant. This is shown in Fig. 10 for six different frequencies: 2 GHz, 10 GHz, 25 GHz, 40 GHz, 70 GHz and 100 GHz. The graphical results indicate a progressive increase in the specific attenuation as the rainfall rate increases at all frequencies. Table 1 shows the specific attenuations from our proposed Weibull distribution at R0.01 = 60 mm/h for Durban and at the maximum rainfall rate (120 mm/h) for Durban. It is observed that the specific attenuation at R0.01 approximately twice when R = 120 mm/h most especially at high frequencies. Also, it is also noted that the increments in specific attenuation at frequencies above 70 GHz are quite small, this may be due to saturation in the


Fig. 10: Specific attenuation due to Weibull probability DSD model for rainfall rates up to 120 mm/h at different

frequencies at 20oC.

Fig. 11: Specific attenuation due to Weibull probability DSD model for frequencies from 0 to 100 GHz at

different rainfall rates at 20oC.

scattering coefficients.

In order to obtain a specific attenuation law for our Weibull distribution, we follow the ITU-R P.838-3 [8] report which represents specific attenuation as a power-law function of rainfall rate in which the power law coefficients k and are given at different frequencies. By using this approach, we can also find the power-law equivalent of our Weibull Rainfall DSD model which is given as:

where kweibull and weibull are the power-law coefficients for our Weibull probability distribution.

Table 2 gives values of kweibull and weibull for 10 different frequencies of our Weibull rainfall DSD and their respective coefficient of determination (R2). The specific attenuation coefficients in the Table 2 show a progressive increase in the value of kweibull at all frequencies, while there is increase in value of weibull until a decline starts between 40 GHz and 60 GHz. From our observation, it appears that the contribution of the scale parameter,

Table 1: Specific attenuation due to Weibull probability model at R0.01 and maximum rainfall rate in Durban

Frequency (GHz)

SPECIFIC ATTENUATION (dB/km)

R0.01 = 60 mm/h R=120 mm/h 2 6

10 15

19.5 25 40 60 70 100

0.009005 0.360939 1.699086 3.989358 6.510417 9.425099 14.89449 19.58553 21.14816 24.31733

0.018811 0.91887 4.42393 10.06107 16.03424 22.44157 32.414

39.0795 40.85433 43.88076

Table 2: Power-law coefficients for specific attenuation due to Weibull probability model in Durban for 0 mm/h >

R > 120 mm/h

Frequency (GHz) kweibull weibull R2

2 4 6

10 12 15

19.5 25 40 60 70

100

0.0001 0.0007 0.0019 0.008 0.0129 0.0226 0.0423 0.0744 0.1949 0.412 0.5296 0.8758

1.0055 1.1276 1.2781 1.3103 1.2895 1.2647 1.2312 1.1839 1.0606 0.9445 0.9018 0.8129

0.9993 0.9992 0.999 0.999 0.999 0.9991 0.9991 0.9991 0.9992 0.9994 0.9995 0.9996

kweibull, to the As is much more prominent at frequencies above 40 GHz. The shape parameter, weibull, however appears to contribute less to As above 40 GHz. Thus, there is a likelihood that the shapes of the specific attenuation function for our Weibull distribution are similar above this frequency.

Fig. 11 also shows the variation in the frequency while the rainfall rate is kept constant. The graph confirms the increment in specific attenuation with an increase in rainfall rate.

4.3 Comparison of proposed Weibull model with existing models

By considering the various different rain drop-size distribution models used globally for rainfall attenuation estimation, we compared them with results from the proposed Weibull model. The four rainfall DSD models used are: lognormal model by Ajayi and Olsen [9], negative exponential model by Marshall and Palmer [11], modified gamma models by Atlas and Ulbrich [14] and Weibull model by Sekine and Lind [12]. The ITU-R P.838-3 model for horizontal polarization and vertical polarization are used to compare the various specific attenuations at different frequencies. The comparison is done at four rainfall rates: 5 mm/h, 10 mm/h, 50 mm/h and 100 m/h, while the maximum frequency is 100 GHz.


The input parameters for the other models are summarized in Table 3.

In Fig. 12, it was noticed that at lower extreme boundary of rainfall rate (1 mm/h), the modified gamma model (AU) least fitted both the proposed Weibull model and ITU-R estimation; Table 4 gives an indication of the compared models at 5 mm/h to verify this. However, compared models in Fig. 13 show that at an upper extreme boundary of rain rate (100 mm/h), the negative exponential model least fitted our proposed model and ITU-R estimation; Table 7 shows the values of all compared models at this rainfall rate. Tables 5 and 6 also shows the performances of our compared models at 10 mm/h and 50 mm/h respectively.

Table 3: Parameters of existing models for model comparison

MODELS INPUT PARAMETERS

Lognormal model

(Ajayi and Olsen)

Negative exponential model by (Marshall

and Palmer) Modified gamma

model (Atlas and Ulbrich)

Weibull model by

(Sekine and Lind)

Fig 12. Comparison of specific attenuation for different models with varying frequencies at 1 mm/h.

Fig 13. Comparison of specific attenuation for different models with varying frequencies at 100 mm/h.

In all the presented results, it is shown that our proposed model performs reasonably well especially when compared with ITU-R specifications for both vertical and horizontal polarization. However, an error test can be used to verify the performance of our model.

Table 4: Comparison of specific attenuation of different models with our proposed model in Durban at 20oC with R = 5 mm/h

Frequency (GHz)


Lognormal (AO)

Negative Exponential

(MP)

Modified gamma (AU)

Proposed Weibull (Durban)

Weibull (SL)

ITU-R P.838-3

(H)

ITU-R P.838-3

(V) 2 4 6 8

10 12 15 20 25 30 40 50 60 70 90 100

0.001098 0.007161 0.030144 0.076208 0.135741 0.207263 0.339378 0.608501 0.896956 1.163388 1.682963 2.165344 2.596112 2.969028 3.580736 3.834718

0.000749 0.004239 0.015571 0.038051 0.068435 0.106128 0.177172 0.327758 0.502271 0.68103 1.072805 1.494551 1.925183 2.347415 3.151671 3.527069

0.000473 0.0027

0.009834 0.023871 0.043026 0.066928 0.112077 0.208081 0.319667 0.433755 0.68105 0.942109 1.202955 1.453168 1.916171 2.127111

0.000723 0.004087 0.014418 0.034521 0.062484 0.097804 0.164921 0.309115 0.479335 0.655576 1.038428 1.439938 1.8359

2.209675 2.884675 3.185427

0.00066 0.004043 0.016173 0.04043 0.072239 0.110871 0.182742 0.331295 0.495442 0.653898 0.98072 1.308999 1.626003 1.922627 2.460065 2.702283

0.000471 0.001408 0.009116 0.038565 0.092019

0.16 0.273181 0.501976 0.784238 1.10576 1.789197 2.424014 2.950391 3.363657 3.91529 4.093558

0.00046 0.001833 0.00613 0.031775 0.07985 0.149258 0.26873 0.468787 0.706104 0.995523 1.657214 2.296905 2.840414 3.274219 3.869049 4.063425


Table 5: Comparison of specific attenuation of different models with our proposed model in Durban at 20oC with r = 10 mm/h

Frequency (GHz)


Lognormal (AO)


(MP)

Modified gamma (AU)


Weibull (SL)

ITU-R P.838-3

(H)

ITU-R P.838-3

(V) 2 4 6 8

10 12 15 20 25 30 40 50 60 70 90 100

0.002115 0.014565 0.065207 0.167784 0.297325 0.450346 0.730292 1.289907 1.868065 2.377113 3.323523 4.152338 4.855999 5.437398 6.342011 6.703444

0.001336 0.008108 0.032638 0.082113 0.146412 0.224062 0.368256 0.665513 0.993344 1.31087 1.973928 2.653063 3.321617 3.958381 5.136301 5.675507

0.001084 0.00681

0.027806 0.069823 0.124605 0.190848 0.313737 0.566258 0.841901 1.103365 1.630856 2.144842 2.626778 3.065069 3.831517 4.167259

0.001423 0.008726 0.034027 0.083989 0.150667 0.232578 0.385758 0.705141 1.062435 1.409848 2.120745 2.818811 3.472584 4.063798 5.084567 5.525591

0.001344 0.008857 0.038432 0.098309 0.174489 0.265006 0.431293 0.766653 1.120082 1.44131 2.065275 2.649266 3.18118 3.654294 4.465934 4.818076

0.000987 0.004274 0.027463 0.101167 0.220061 0.363341 0.595404 1.044753 1.568186 2.134858 3.265181 4.246609 5.017581 5.598331 6.337702 6.567244

0.000888 0.004354 0.018249 0.082735 0.185542 0.324929 0.554359 0.928086 1.363822 1.87515 2.971919 3.964918 4.773926 5.400559 6.233384 6.496334


Frequency (GHz)


Lognormal (AO)


(MP)

Modified gamma (AU)


Weibull (SL)

ITU-R P.838-3

(H)

ITU-R P.838-3

(V) 2 4 6 8

10 12 15 20 25 30 40 50 60 70 90 100

0.009617 0.075058 0.386883 1.036387 1.81513 2.699248 4.281299 7.307224 10.16365 12.38088 16.01257 18.70515 20.66265 22.04218 23.80938 24.41955

0.005197 0.038005 0.192893 0.520035 0.908665 1.347378 2.13244 3.63766 5.079355 6.248478 8.346515 10.18014 11.79456 13.2056 15.62438 16.68611

0.007299 0.056949 0.300135 0.812475 1.418372 2.099202 3.312123 5.613392 7.756548 9.401918 12.12157 14.20759 15.81137 17.03151 18.80548 19.49836

0.007369 0.055492 0.278949 0.743827 1.304344 1.943754 3.09175 5.303629 7.428888 9.131303 12.04772 14.38029 16.23401 17.68749 19.86195 20.72309

0.008099 0.065822 0.36122 0.988042 1.719751 2.533197 3.973493 6.671287 9.112462 10.90226 13.71346 15.71462 17.14239 18.14438 19.46871 19.95571

0.005456 0.055647 0.351332 0.939966 1.650984 2.418671 3.604613 5.685427 7.779939 9.766065 13.11372 15.51867 17.12021 18.17277 19.29197 19.58154

0.004064 0.03217 0.227104 0.755511 1.302413 1.961785 2.955489 4.499264 6.244905 8.102177 11.46334 14.00288 15.85093 17.16922 18.76871 19.21547


Frequency (GHz)


Lognormal (AO)


(MP)

Modified gamma (AU)


Weibull (SL)

ITU-R P.838-3

(H)

ITU-R P.838-3

(V) 2 4 6 8

10 12 15 20 25 30 40 50 60 70 90

100

0.018579 0.153045 0.838383 2.285266 3.982191 5.875028 9.229695 15.52147 21.21547 25.36087 31.71441 35.98768 38.78782 40.52184 42.34602 42.87131

0.009519 0.075325 0.416944 1.150912 1.997362 2.929958 4.576461 7.646712 10.41504 12.46729 15.85298 18.53363 20.72758 22.53749 25.50391 26.78491

0.016352 0.138763 0.804121 2.236492 3.873687 5.662706 8.802488 14.57814 19.60336 23.07319 28.22808 31.62745 33.88279 35.34088 37.09395 37.70876

0.015526 0.128362 0.722346 1.992146 3.458995 5.076032 7.927191 13.22277 17.93081 21.2968 26.48056 30.09081 32.63012 34.39361 36.72383 37.59249

0.018327 0.16423 1.004544 2.833275 4.887703 7.099534 10.94938 17.90703 23.71126 27.42676 32.46695 35.29013 36.79679 37.47174 37.80108 37.81366

0.0115 0.170447 1.067969 2.485249 3.976405 5.529304 7.90633 11.90379 15.64502 18.95631 24.04926 27.3114 29.24161 30.37171 31.35071 31.53554

0.007891 0.076968 0.68209 1.982527 3.047151 4.297852 6.132878 8.957124 12.12669 15.33999 20.65544 24.27943 26.75375 28.43485 30.3557 30.83799


Table 8: RMS errors of specific attenuation for all frequencies due to existing models at 20oC for horizontal polarization

Rainfall Rate

(mm/h)

ROOT-MEAN-SQUARE ERROR

Lognormal(AO)


(MP)

Modified gamma (AU)


Weibull (SL)

1 5

10 25 50 75 100

0.137159 0.168966 0.165084 0.860155 2.447295 4.359628 6.126207

0.166611 0.508542 0.874962 1.822229 3.122958 4.385922 5.44491

0.391043 0.976994 1.323004 1.496782 0.606261 1.420399 3.421323

0.221448 0.581344 0.811641 0.995715 0.643802 1.157427 2.495932

0.251375 0.713594 0.979639 0.981585 0.667673 3.179908 6.046243

Table 9: RMS errors of specific attenuation for all frequencies due to existing models at 20oC for vertical polarization

Rainfall Rate

(mm/h)

ROOT-MEAN-SQUARE ERROR

Lognormal(AO)


(MP)

Modified gamma (AU)


Weibull (SL)

1 5

10 25 50 75 100

0.133653 0.150134 0.287178 1.327018 3.437566 5.939748 8.23965

0.161729 0.442340 0.717934 1.362846 2.128818 2.774042 3.262600

0.387042 0.917787 1.180699 1.08788

0.750687 3.087541 5.668165

0.216989 0.518107 0.659196

0.5435 0.709052 2.563384 4.563134

0.247363 0.65533 0.8423

0.665583 1.722305 4.95571

8.433228

Error estimates for our proposed model were obtained using RMS error test with the ITU-R estimates considered as the actual model. The RMS error in Timothy et al. [19] is given by:

Where xmodel, i are the samples of our proposed Weibull model, xactual, i are the samples of the ITU-R estimates and N is the total number of samples.

Two RMS tests were undertaken: one for ITU-R horizontal polarization and the other, for ITU-R vertical polarization. This is considered because the spherical assumption for our scattering parameters is almost independent of polarization sequence. Results from the RMS tests are given in Table 8 and 9.

The average RMSE for all the models are arranged in the following order as they appear in the table. For Table 8 (horizontal), we have: 2.04, 2.33, 1.38, 0.99 and 1.83 respectively and for Table 9 (vertical), we have: 2.79, 1.55, 1.87, 1.40 and 2.50 respectively. Our proposed Weibull model has an average RMSE of 0.99 for horizontal polarization and 1.40 for vertical polarization. From all indications, our proposed Weibull model has the lowest RMSE for both horizontal and vertical polarization in Durban and therefore, is clearly the best and closest among other existing models with respect to ITU-R P.838-3 recommendation.

5. CONCLUSION

In this paper, we proposed a method of estimating the parameters for the Weibull rainfall drop-size distribution using the third, fourth and sixth moments of the method of moments. With our new estimators, we fitted the Weibull parametric relationships for our locality –Durban, South Africa. It was also shown that power-law estimates can be obtained for Weibull distribution at different frequencies. Using horizontal polarization and vertical polarization, the specific attenuation due to the proposed model for Durban was compared with existing models. Our proposed Weibull model compares well with the ITU-R estimation for specific attenuation with an average RMS error of 0.99 (horizontal polarization) and 1.40 (vertical polarization) for all selected rainfall rates and frequencies. In general, the results from our modeling have shown that the Weibull probability distribution is an appropriate rainfall distribution for Durban.

6. FUTURE WORK

The assumption of drop-size sphericity used in this study, usually becomes less accurate as the rainfall drop diameter and frequency increases, with consequent effects on depolarization and asymmetrical drop axial influences [34–35] from rainfall dynamics. The resulting specific attenuation prediction from our Mie scattering will therefore be lower than the ITU-R prediction and will have a multiplier effect on the path attenuation. In order to correct this, the Pruppacher and Pitter drop-size shape model [36] can be applied to cater for polarization effects particularly at frequencies beyond 10 GHz.


7. REFERENCES

[1] G.O. Ajayi, S. Feng, S.M. Radicella, B.M. Reddy:Handbook on Radiopropagation Related to Satellite Communications in Tropical and Subtropical Countries, ICTP, Trieste, pp. 7–14, 1996.

[2] R.K. Crane: Electromagnetic Wave Propagation Through Rain, John Wiley and Sons Inc., New York, pp. 1–40, 1996.

[3] R.K. Crane, “Prediction of attenuation by rain”, IEEE Trans. Antennas, Vol. 28, no. 9, pp. 1717–1733, Sept. 1980.

[3] L. Li, T. Yeo, P. Kooi and M. Leong, “An efficient calcululation approach to evaluation of microwave specific attenuation”, IEEE Trans. Antennas, Vol. 48, No 8, pp. 1220–1229, Aug. 2000.

[4] L. Li, P. Kooi, M. Leong and T. Yeo, “Microwave attenuation by realistically distorted raindrops: part I–theory”, IEEE Trans. Antennas, Vol. 43, no. 8, pp. 811–822, Aug. 1995.

[5] C.T. Mulangu and T.J Afullo, “Variability of the propagation coefficients due to rain for microwave links in Southern Africa”, Radio Science, Vol. 44, RS30006, 2009.

[6] R.K. Crane: Propagation Handbook for Wireless Communication System Design, CRC Press, Florida, pp. 74–76, 2003.

[7] ITU-R Rec. P.837-5, Characteristics of Precipitation for Propagation Modelling, ITU-R, Geneva, 2007.

[8] ITU-R Rec. P.838-3, Specific Attenuation Model for Rain for use in Prediction Methods, ITU-R, Geneva, 2005.

[9] G.O. Ajayi and R.L. Olsen, “Modeling of a tropical raindrop size distribution for microwave and millimeter wave applications”, Radio Science, Vol. 20, number 2, pp. 193–202, Apr. 1985.

[10] I.A Adimula and G.O. Ajayi, “Variation in raindrop size distribution and specific attenuation due to rain in Nigeria”, Ann. Telecom, Vol. 51, No. 1-2, pp. 87–93, 1996.

[11] J. S. Marshall and W. Palmer, “The distributions of raindrop with size”, Journal of Meteorology, 5, pp.165–166, 1948.

[12] M. Sekine and G. Lind, “Rain attenuation of centimeter, millimeter and submillimeter radio waves”, Proc. of 12th European Microwave Conference, pp. 584–589, 1982.

[13] H. Jiang, M. Sano and M. Sekine, “Weibull raindrop-size distribution and its application to rain attenuation”, IEE Proc Microw. Antennas propag., Vol. 144, no. 3, June 1997.

[14] D. Atlas and C.W. Ulbrich, “The physical basis for attenuation-rainfall relationships and the measurement of rainfall parameters by combined attenuation and radar methods”, J. Rech. Atmos., 8, pp. 275–298, 1974.

[15] M. Sekine, C. Chen and T. Musha, “Rain attenuation from log-normal and Weibull raindrop-size distribution”, IEEE Trans. Antennas propagat., Vol. 35, no. 3, Mar. 1985.

[16] D.N. Murthy, M. Xie and R. Jiang: Weibull models, John Wiley and Sons Inc., New York, pp. 50–58, 68–74, 2004,

[17] W. Weibull, “A statistical distribution function of wide applicability”, J. of App. Mechanics, pp. 293–297, Sept. 1951.

[18]T. Kozu and K. Nakamura, “Rainfall parameter estimation from dual-radar measurements combining reflectivity profile and path-integrated attenuation”, J. of Atmos. and Oceanic tech.,” pp. 259–270, 1991.

[19] K.I. Timothy, J.T. Ong and E.B.L. Choo, “ Raindrop size distribution using method of moments for terrestrial and satellite communication applications in Singapore”, IEEE Antennas Propagat., Vol. 50, pp. 1420–1424, October 2002.

[20] S. Das, A. Maitra and A.K. Shukla, “Rain attenuation modeling in the 10-100 GHz frequency using drop size distributions for different climatic zones in tropical India”, Progress in Electromagnetics Research, Vol. 25, pp. 211–224, 2010.

[21] A.E. Taylor and W.R. Mann: Advanced Calculus, John Wiley and Sons Inc., pp. 699–703, 1983.

[22] H.J. Weber and G.B. Arfken: Essential Mathematical Methods for Physicists, Academic Press, San Diego, pp. 523–544, 2003.

[23] M.O. Odedina and T.J. Afullo, “Characteristics of seasonal attenuation and fading for line-of-sight links in South Africa”, Proc. of SATNAC, pp. 203–208, Sept. 2008.

[24] P.A. Owolawi and T.J. Afullo, “Rainfall rate modelling and worst month statistics for millimetric line-of–sight radio links in South Africa”, Radio Sci., vol. 42, 2007.

[25] ITU-R Rec. P.530-13, Propagation data and prediction methods for the design of terrestrial line-of-sight systems, ITU-R, Geneva, 2009.

[26] M.O. Odedina and T.J. Afullo, “Determination of rain attenuation from electromagnetic scattering by spherical raindrops: Theory and experiment”, Radio Sci., Vol. 45, 2010.

[27] M.O. Odedina and T.J. Afullo, “Analytical modeling of rain attenuation and its application to terrestrial LOS links”, Proc. of SATNAC, 2009.

[28] C.T. Mulangu and T.J. Afullo, “Variability of the propagation coefficients for microwave links in Southern Africa”, Radio Sci., vol. 44, 2009.

[29] H.J. Liebe, G.A. Hufford and T. Manabe,“A model for the complex permittivity of water at frequencies below 1 THz”, Inter. J. of Infrared and Millimeter Waves, Vol. 12, no. 7, pp. 659–678, 1991.

[30] G. Mie, “Beiträge zur optik trüber medien, speziell kolldaler metallösungen”, Ann. Phys., 25, pp. 377–445, doi:10np.19083300302.

[31] C. Mätzler, “Drop-size distributions and Mie computation”, IAP Res. Rep. 2002-16, Univ. Of Bern, Bern, Nov. 2002.

[32] C. Mätzler, “MATLAB functions for Mie scattering and absorption”, IAP Res. Rep. 2002-08, Univ. Of Bern, Bern, June 2002.


[33] C.F. Bohren, D.R. Huffman, Absorption and scattering of light particles, Wienheim: John Wiley, 2004.

[34] C. Mätzler, “Advanced model of extinction by rain and measurements at 38 GHz and 94 GHz and in the

visible range”, IAP Res. Rep. 2003-18, Univ. of Bern Bern, February 2003.

,

[35] H.R. Pruppacher and J.D. Klett, Microphysics of clouds and precipitation. Dordrecht:Riedel, 1978.

[36] H.R. Pruppacher and R.L. Pitter, “A semi-empirical determintaion of the shape of cloud and raindrops”,J. Atmos. Sci., 28, pp. 86–94, 1971.


A MULTI-DIMENSIONAL CODE-DIVISION-MULTIPLEXEDOFDMA MODEM USING CYCLIC ROTATED ORTHOGONALCOMPLETE COMPLEMENTARY CODES

A.M. Merensky, J.H. van Wyk and L.P. Linde

Dept. of Electrical, Electronic & Computer Engineering, Corner of University Road and LynnwoodRoad, University of Pretoria, Pretoria 0002, South Africa

Abstract: In this paper we present a novel multiple access scheme based on a combination of

Dept. of Electrical, Electronic & Computer Engineering, Corner of University Road and Lynnwood Road, University of Pretoria, Pretoria 0002, South Africa, E-mail: [email protected],[email protected]

A.M. Merensky, J.H. van Wyk* and L.P. Linde**

Abstract: In this paper we present a novel multiple access scheme based on a combination ofmulti-carrier OFDMA techniques and a multi-dimensional spread spectrum modem that makes useof rotated mutually orthogonal complete complementary codes. A multi-dimensional code-divisionmultiple access (MD-CDMA) modem with recent designs of perfectly orthogonal completecomplementary codes, produces an innovative modulation technique, which is further improved uponby exploiting the rotational properties of the spreading codes to increase the throughput and spectralefficiency. The system is extended by making use of multiple carrier frequencies as in orthogonalfrequency-division multiple access (OFDMA), providing additional benefits such as diversity bybeing able to spread the data in frequency and/or in time. The proposed modem offers multipleaccess interference (MAI)-free operation due to the perfect autocorrelation and zero cross-correlationproperties of the spreading codes. The uniquely proposed modulation technique together with theintegration of rotated complete complementary codes, produces a system with better spectral efficiencycompared to a theoretical non-spread system, with high data throughput rates, better noise tolerancesin harsh channel conditions and an increased user capacity. Various other benefits such as low complexchannel estimation and synchronisation, rate adaption, and resistance to the near-far problem can beattributed to the system.

Key words: Code-division multiple access, cyclic rotated complete complementary codes, multi-carriermodulation, multiple access, multi-dimensional modem, orthogonal frequency-division multiplexing.

1. INTRODUCTION

The need for a modulation technique that can reliablytransmit at high data rates and with high bandwidthefficiency has risen in the last decades, due to the enormousgrowth of wireless services (local-area networks, cellulartelephones, to name but a few). With the growing demandof services such as digital audio/video broadcasting,the availability of spectrum has become a seriousproblem [1]. Orthogonal frequency-division multiplexing(OFDM) has been applied extensively in many high speedwireline and wireless communication standards, suchas in ADSL, VDSL, WiMAX, WLAN radio interfaces(IEEE 802.11a,b,g,n) and in many other mobile broadbandsolutions, due to its efficient usage of the availablefrequency bandwidth and robustness to frequency selectivefading environments. Meanwhile, WCDMA has provenits spectral efficiency through flexible frequency reuse andmultiple access techniques [1, 2].

The combination of multiple access techniques likeCDMA and OFDM, demonstrated increased spectralefficiency, flexibility in radio resource allocation andimproved anti-multipath and anti-interference features [2].Thus, these combined systems have received significantattention as they capitalise on the benefits of both schemesand combine high bandwidth efficiency and high data rateswith robustness against multipath distortion.

An important factor in the overall performance ofa WCDMA multi-carrier type modulation scheme is

the perfect autocorrelation and zero cross-correlationproperties of the spreading codes. Due to non-idealspreading codes used in current standardised CDMAsystems, such as those used in existing 2-3G systems,problems of self-interference are evident [3], [4]. Existingproblems, such as slow transmission rate, low capacity,and complex system implementation in current systemsare caused by the imperfect spreading codes employed [5].For example, according to [6], the Walsh-Hadamardsequences in the IS-95 (cdmaOne) standard and theOVSF codes in WCDMA (UMTS) standards made itimpossible to ensure symmetric data throughput at thevery beginning of the system design because of theirimperfect correlation characteristics in asynchronous andsynchronous transmission modes.

This article presents an innovative modulation techniquethat combines the architecture of a multi-dimensionalspread spectrum modem with recent designs of perfectlyorthogonal complete complementary (CC) codes. Therotational or shift properties of the spreading codes arefurther exploited in a novel way to improve spectralefficiency and spreading code usage. Additionally, alow complexity periodic cross-correlation method at thereceiver has been implemented to optimally despread anddecode these cyclic rotated spreading codes. The entiresystem architecture allows for a high processing gain (PG)for interference suppression without limiting the amountof users. The system is extended by making use ofmultiple carrier frequencies (OFDMA) and can thus spreadthe information in frequency and/or in time, leading to


an overall gain in diversity. Traditional CDMA-basedsystems (i.e. IS-95, cdma2000, and WCDMA), andeven multi-carrier adaptations, have a spreading efficiencyproportional to 1/L information bits per chip per link(where L is the sequence length) [3, 7], whereas the novelmodulation technique proposed here can transmit at doublethe theoretical spectral efficiency (2 bits/s/Hz) of the digitalmodulation method used when implementing unspreadedbinary phase shift keying (BPSK). This eliminates any lossin efficiency caused by spreading, resulting in greater datathroughput.

The rest of the paper is outlined as follows. In the nextsection, we will introduce the basic multi-dimensionalWCDMA modem building block. Section 3 will explainhow the cyclically rotated spreading codes are generatedand can be used in the system. An implementation schemeof the combined system is proposed in Section 4, togetherwith the multi-carrier implementation and receiver design.Several concluding remarks and performance evaluationsare presented in Section 5, followed by the conclusiongiven in Section 6.

2. MULTI-DIMENSIONAL WCDMA MODEMBUILDING BLOCK

The novel multi-layered modulation technique makes useof a MD modem to improve spreading code usage,throughput and overall performance of the system.The term multi-layered modulation specifically refersto the use of practically all available diversity meansto modulate and spread in all possible dimensions,excluding the spatial domain, which is addressed in afuture paper. The modem is implemented with cyclicrotated super-orthogonal complete complementary codes(CRCC) to offer MAI-free operation, only possible dueto the perfect autocorrelation and zero cross-correlationproperties of the codes. Hence, super-orthogonality refersto the perfect periodic and a-periodic even and odd autoand cross-correlation properties of the family of CC codesutilised.

It was shown by [8, 9], that a 4D-WCDMA modembuilding block (without the newly implemented CRCCcodes) has data throughput rates equivalent to that ofa 16-ary quadrature amplitude modulated (16-QAM)WCDMA modulation scheme, but with the bit error rate(BER) performance equivalent to that of BPSK/QPSKin both additive white Gaussian noise (AWGN) andfading multipath channel scenarios, given identicalspreading sequence lengths L and spreading bandwidthsBs, respectively.

2.1 Building Block Description of a 4-DimensionalModem

An example of a 4D-CDMA modem transmitter buildingblock can be seen in Figure 1. The input sequence issplit up into four parallel data streams d1(t) to d4(t). Theupper two streams are spread using orthogonal CC codes(C) to produce the inphase component and likewise, the

2z (t)

2x (t)

4

2y (t)

1y (t)

3

1

1

cos(w t)c

d(t) s(t)

d (t)

3d (t)

4d (t) x (t)

x (t)

x (t)

2

1

z (t)

d (t)

90 o

c (t)r

c (t)i

c (t)i

c (t)r

S/P

Figure 1: A 4D (CDMA) modem transmitter building block [8].

4

^1

h (t)3

h (t)4

h (t)2

h (t)1

1v (t) 1w (t)Ts

⎯1Ts

∫0

dt

Ts

⎯1Ts

∫0

dt

Ts

⎯1Ts

∫0

dt

g (t)1

g (t)3

g (t)4

^

2

Ts

⎯1Ts

∫0

dt

d (t)

r(t)

d (t)3

d (t)

d (t)2

g (t)f (t)2

f (t)1

w (t)2

f (t)4

f (t)3

2v (t)

Sample Clock

90o

c (t)

c (t)

r

i

c (t)i

c (t)r

Figure 2: A 4D (CDMA) modem correlation-type receiver

building block [9].

lower two streams are spread to produce the quadraturecomponent. The inphase and quadrature components arethen modulated onto quadrature carriers and summed toproduce a transmitted signal as given by

s(t) =[d1(t)cr(t)+d2(t)ci(t)]cos(ωct)+ [d3(t)cr(t)+d4(t)ci(t)]sin(ωct), (1)

where cr =C and ci = jC. Due to the orthogonal propertiesof the carrier signals, the quadrature modulated signals canbe independently detected. This allows the quadrature andinphase components to optionally use the same set of codesand thus save code elements of the CRCC code family.

The building block depicted in Figure 1 can be extendedto more dimensions by adding more 4D blocks inparallel, each using additional spreading codes from thefamily of CRCC codes. This can be achieved whilestill maintaining the respective BER performance of oneoriginal building block [8]. Figure 2 shows a typical lowcomplexity matched filter correlation-type receiver for a4D modem. The receiver is depicted without the periodiccross correlation receiver structure needed when using therotated codes (CRCC). In the newly proposed system, themodem is further exploited by cyclic rotated CC codes,which improve the throughput and negates the loss inspectral efficiency resulting from the spreading of the data.


This multi-layered building block forms the foundationof the proposed modulation technique. The signal ofthe novel system is generated using a combination ofCDMA and OFDMA techniques. Multiple transmitterblocks are combined and parallelised by the CRCCcodes to form a high throughput modulation techniquewhich is spectrally efficient and capable of exploiting thediversity in the radio channel to improve performance.The usage of the CRCC codes enables the data frommultiple combined multi-dimensional building blocks tobe transmitted simultaneously with a high throughputover one channel, since the rotated spreading codes allowthe data to be differentiated again at the receiver, asis the case with CDMA techniques. A collection ofthese combined blocks can then be spread onto differentsub-carrier frequencies using OFDMA principles.

3. CYCLIC ROTATED COMPLETECOMPLEMENTARY CODES

An important factor in the performance of any WCDMAtype system is the ideal orthogonality, auto andcross-correlation property of the spreading code used,since this determine the amount of users that can beaccommodated in the system, the robustness in harshchannel conditions, and the division amongst the differentusers. If the correlation functions are not ideal, every useror additional data stream can be viewed as another sourceof noise. Therefore, low cross-correlation values betweenspreading codes allow the receiver to separate user signals,whereas low autocorrelation sidelobe values aid in filteringout multiple received signals which are delayed dueto multipath propagation [10]. If a CDMA system isnot MAI- and multipath interference (MI)-free, due tonon-ideal cross-correlation and autocorrelation propertiesrespectively, then the capacity of the overall system canmerely achieve approximately one-third to a half of itsprocessing gain, which is currently seen in availableWCDMA based 2-3G wireless systems [6,11]. The designor selection of the spreading codes is very important at anearly stage of a CDMA system design. Shortcomings inthe system architecture due to the use of unsuitable codesnecessitates the use of complex and very costly multi-userinterference cancellation techniques. Examples thereofcan be found in numerous 2G to 3G standards, wherenon-optimal code design was carried through to successivestandards [12], [13].

3.1 Orthogonal Complete Complementary Codes

The main difference between traditional CDMA and CCcodes is that the orthogonality of CC codes is based on aset of element codes called a flock, instead of a single code[7]. These codes have a zero autocorrelation for all shiftsexcept the zero shift and zero cross-correlation function forall possible shifts [3].

The family size or number of flocks is equal to the numberof element codes in one flock and can be defined asM =

√L. The processing gain of the codes can then

be defined by L.√

L, where L is the length of every

element code sequence [3, 7]. The autocorrelation andcross-correlation of the code can be expressed as follows[14]:

φxx(k) =

L2−1

∑n=− L

2

√L

∑i=1

a(x)n,i a(x)n+k,i =

{L√

L, k = 00, k �= 0

(2)

φxy(k) =

L2−1

∑n=− L

2

√L

∑i=1

a(x)n,i a(y)n+k,i = 0, ∀k (3)

where φxx is the autocorrelation function (2) of set x, φxy isthe cross-correlation function (3) of sets x, and y, k is thenumber of shifts between the sequences, and n is the nthelement of each code sequence [14].

3.2 Complete Complementary Code Generation

There are various ways to construct CC codes. In[6, 13] an algebraic method is used to generate supercomplementary code sets, called the real environmentadapted linearisation (REAL) approach. The REALapproach generates interference-free CDMA code setswith perfect auto- and cross-correlation properties. Thisapproach however, requires a great computational load [5].Below, a more practical approach to generating the codesis shown according to the algorithm outlined in [4].

A matrix approach is taken in generating the code setsusing a

√L-dimensional orthogonal matrix, where L is the

length of the element code generated [13]. Define an N×Ndimensional orthogonal matrix A,

A =

⎛⎜⎜⎝

A1

A2

...AN

⎞⎟⎟⎠=

⎛⎜⎜⎝

a11 a12 · · · a1Na21 a22 · · · a2N

......

......

aN1 aN2 · · · aNN

⎞⎟⎟⎠ , (4)

consisting of aik for i= 1,2, ...,N and k = 1,2, ...3 complexelements, such that the absolute values are |aik| = 1 andthe inner product of any two different rows in the matrixshould be zero, or

N

∑i=1

aika∗mi = 0, where k �= m. (5)

From this it can be shown that the autocorrelation functionof the sequence or matrix A is zero for all N-multipleshifts, except the zero shift [15]. Then let B be anotherN×N orthogonal matrix as given above for A, from whichN sequences of length N2 can be constructed as follows:

E1 =(b11A1,b12A2, . . . ,b1NAN) = (e11,e12, . . . ,e1N2)

E2 =(b21A1,b22A2, . . . ,b2NAN) = (e21,e22, . . . ,e2N2)

...

EN =(bN1A1,bN2A2, . . . ,bNNAN)

=(eN1,eN2, . . . ,eNN2) , (6)

where Ai is the ith row of the A matrix [5]. Each


Ei (1≤ i≤ N) has an autocorrelation of zero for any shiftexcept the zero shift and the cross-correlation of any twosequences is zero for all shifts.

Again let D be another N-dimensional orthogonal matrixfrom which the final spreading sequences can beconstructed by

Cik =(ei1dk1, . . . ,eiNdkN ,ei(N+1)dk1, . . . ,ei(2N)dkN , . . . ,

ei(N2−N+1)dk1, . . . ,ei(N2)dkN) (7)

=(cik1,cik2, . . . ,cikN2), for i,k = 1,2, ...,N, (8)

which gives N flocks of CC codes, each flock consisting ofN element codes

C1 = {C11,C12, . . . ,C1N} (9)

C2 = {C21,C22, . . . ,C2N} (10)

...

CN = {CN1,CN2, . . . ,CNN}, (11)

where Cik (i,k = 1,2, . . . ,N) denotes the basic elementarycode sequence of a set [13].

3.3 Cyclic Rotation Scheme for Spreading Codes

Conventional CC codes support only a limited number ofusers. Therefore, a cyclic rotation technique is used toextend the original code family size, allowing for morecodes, increased system capacity, and spectral efficiencywithout loosing performance. The periodic propertyof the code makes it possible to transmit more datasimultaneously by carrying data in each rotation of thecode, thus improving the throughput significantly. Thede-spreading or reception of the rotated spreading codescan be performed by a simplified periodic cross-correlationreceiver structure making use of fast Fourier transformalgorithms. Only the periodic cross-correlation of theoriginal non-rotated sequence needs to be taken whenusing the FFT or the circular convolution theorem methodto identify each rotated information bit (explained inSection 4.3).

For example, a CC code set with M = 4 flocks and anelementary code length of L = 16, can be defined as

C1 = {C11,C12,C13,C14} (12)

C2 = {C21,C22,C23,C24} (13)

C3 = {C31,C32,C33,C34} (14)

C4 = {C41,C42,C43,C44}, (15)

where Cik (i,k = 1,2,3,4) is the basic elementary codesequence of a set or flock.

From this, a combined un-rotated spreading sequence forflock 1 can be created by combining all the elementarycodes of the first flock C11, C12, C13, and C14. Thisresulting spreading sequence of the first flock C1 can thenbe cyclically rotated L = 16 times, creating a new set ofsequences defined as Cr

n, where r defines the rotational

index or number of cyclic rotations of the code and nstill refers to the specific flock number. The orthogonalityand perfect correlation properties of the codes are notdestroyed by the cyclic shifting operation, so the newlydefined cyclic rotated codes of the first flock (n = 1) canbe given by

Cr=11 = {C1

11,C112,C

113,C

114} (16)

Cr=21 = {C2

11,C212,C

213,C

214} (17)

. . .

Cr=L1 = {CL

11,CL12,C

L13,C

L14}, (18)

where L equals the elementary code length (16 in thisexample). Thus, L = 16 rotations can be applied to thefirst flock before cyclically repeating the sequence.

This rotation technique produces L spreading codes fromone flock and allows additional data bits to be transmittedwith each rotation of the code. The rotation of the codesin the proposed system allows 4× r additional bits to betransmitted simultaneously for r-rotations of the code inone multi-dimensional building block (or 2M× r for theentire system).

4. SYSTEM MODEL

The input information sequence of the U th user is firstconverted into 2ML parallel data sequences dU

m,r for m =1, . . . ,2M and r = 1, . . . ,L, where M defines the flock orset size and L the length of every element code sequence.

The whole set of code sequences in one flock is used tospread a symbol, thus, the processing gain is large and issometimes referred to as the congregate processing gain[14]. Every information symbol or bit dU

m,r is spread with

the corresponding spreading sequence Crn[l], n = 1, . . . ,M

as seen in (19), where the length of Crn[l] is LM (l =

1 . . .LM). Then, through the novel rotation of the CRCCcodes, the entire process is repeated L times, where r =1, . . . ,L refers to the rotational index. Leaving out the timeindex, the transmitted signal SU can be described by

SU =L

∑r=1

M2 −1

∑i=0

LM

∑l=1

[(dU

4i+1,rCr2i+1[l]+dU

4i+2,rCr2i+2[l]

)

+ j(dU

4i+3,rCr2i+1[l]+dU

4i+4,rCr2i+2[l]

)](19)

=L

∑r=1

M2

∑i=1

(ZU

i,r). (20)

For binary input symbols (BPSK) a total of 2LM symbolsare spread and summed together, which enables paralleltransmission, thereby improving spectral efficiency. Thisshows that a large number of data symbols can beprocessed in one instance. The spectral efficiency is notequal to 1/PG as in traditional CDMA systems, but insteadis equal to the theoretical unspread spectral efficiencyof the modulation method, except when using BPSK, inwhich case an improved spectral efficiency of 2 bits/s/Hzcan be achieved for one user’s building block if the set size


4L(M/2) Data bits S/P

Figure 3: The transmitter structure for one user.

equals the flock size (i.e. equal to to unspread QPSK). Thisis only possible, because of the multi-dimensionality ofthe system and the use of the created CRCC codes. Themulti-dimensional transmitter reduces the spreading codeusage and adds an imaginary dimension to the input bits.

The simplified transmitter structure of the proposed systemis portrayed in Figure 3. It describes the implementationof the U th user’s transmitter and the generated signalSU . Multiple access is then achieved by assigning theusers to different sub-carriers, as in OFDMA, to providemulti-user and frequency diversity. The proposed systemuses CDMA not to distinguish between users, which theOFDMA technique can do, but rather to improve themulti-dimensional modem design and spectral efficiencywhen spreading the data, and to improve the throughput.

4.1 Multiple Access/Carrier Implementation

A block diagram of the multiple access implementationis shown in Figure 4. It depicts how the signal SU fromFigure 3 is transmitted further via OFDM or multi-carriertechniques to produce a multi-user or multiple accesssystem. Multiple access is achieved by assigning differentOFDM sub-channels to different users by making use ofvarious sub-carrier allocation strategies. For example, agroup of adjacent sub-carriers or subbands can be assignedto each user in both frequency and time, or users can beassigned to interleaved or randomly chosen sub-carriers.

To support different types of physical channel conditions,IEEE 802.16 OFDMA systems define several waysto allocate sub-channels, three for downlink: FUSC(fully utilised subchannelisation), PUSC (partially utilisedsubchannelisation) and AMC (adaptive modulation andcoding), and two for uplink: PUSC and AMC [16] In

IFFTSubcarrier mapping

Add Cyclic Prefix (CP) / Pilot symbols

(PS)

Figure 4: Multi-carrier transmission via IFFT/FFT for multiple

access.

FUSC and PUSC a sub-channel consists of sub-carriersdistributed over the entire spectrum, providing frequencydiversity, while the AMC sub-channel consists of adjacentsub-carriers and provides for multi-user diversity [17, 18].

In the design of the novel modulation technique, the abovementioned allocation strategies of the IEEE standards canbe directly implemented. The multi-carrier aspect canbe designed in many ways to adapt to the requirementsof the system and channel conditions. The implementedmultiple access scheme allows different users to transmitover different portions of the broadband spectrum.When a broadband signal experiences frequency selectivefading, different users perceive different channel qualities(multi-user diversity). For example, a deep faded channelfor one user can still be favourable to another user. Theuse of the OFDMA technique allows for efficient use ofthe spectrum with simple FFT processing and it producesa better performing system in fading environments.

4.2 Combined System Model

A spread spectrum multi-dimensional code-divisionmultiplexed system, combined with multiple accesstechniques such as OFDMA results in the proposedmulti-layered code-division multiplexed OFDMA typesystem seen in Figure 5. As mentioned different typesof spreading techniques in different dimensions can beused, however, in this case each user is assigned to asubset of sub-carriers according to an FDMA scheme andtime spreading is not considered in this context. Thisachieves the highest throughput and spectral efficiencywithout the bandwidth efficiency loss when spreading inmultiple dimensions. The system downlink transmitterof the multiple access scheme proposed is illustrated inFigure 5, which applies OFDMA for user separation andcode-division multiplexing on the data belonging to eachindividual user. This exploits the frequency diversity byspreading over L sub-carriers. Additionally, inter-symbolinterference (ISI) and inter-carrier interference (ICI) canbe avoided, resulting in less complex detection techniques.Similarly, each sub-carrier is assigned to one user, makingthe channel estimation far less complex. It can be seen thatthe joint system makes use of the frequency, optionally thetime and code space to achieve flexible resource allocationand diversity.

Similarly to multi-carrier CDMA systems, the proposedsystem takes advantage of the combination of spreadspectrum techniques and multi-carrier modulation. Asseen in Figure 5, one user assigns LM data symbols


2LM Data bits for user 1

S/PMulti-dimensional

code-division multiplexed

Spreader for user 1

Multi-dimensional code-division multiplexed

Spreader for user U Fr

eque

ncy

Hop

ping

or

inte

rlea

ving

OFD

M

S/P

2LM Data bits for user U

Figure 5: Downlink configuration of the code-division

multiplexed OFDMA transmitter.

to one sub-system or LM sub-carriers, which are onlyused by that particular user. In the FDMA scheme,U users are transmitted over a total of Nc = U × LMsub-carriers. The spread symbols are transmitted onadjacent sub-carriers. This limits the frequency diversityof each symbol. Hence, to take full advantage of thefrequency diversity of the entire available bandwidth thesub-carrier assignment in the frequency domain can beinterleaved [19]. Various other frequency sub-carrierallocation schemes are available and these various schemesall have their tradeoffs and the system should beimplemented with the optimal scheme by regarding thechannel conditions in which it would operate.

4.3 Receiver Design

The transmitter of the proposed system performs auser-specific frequency mapping of the user’s spreadsignal SU , in which the chips are interleaved over thewhole transmission bandwidth. To perform coherent datadetection at the receiver, pilot symbols can be multiplexedinto the transmitted data, which aids in frequency and timesynchronisation.

After the transmitted signal is passed through thechannel, the inverse OFDM with user-specific frequencyde-mapping is performed. Additionally the pilot symbolsof the user are extracted and can be used for channelestimation, as they would describe the fading and noiseon the sub-carriers of user U . A variety of single-useror multi-user detection techniques can be implementedfor the detection of the data. The detection can be doneon the sub-carriers belonging to a single user, thereforerequiring less complex detection techniques. Furthermore,the estimation of LM data symbols belonging to one usercan be done simultaneously.

Multi-dimensional receivers for rotated codes: Tode-correlate the spread spectrum signal, one fast Fourier

LM Received

Data symbols

FFT METHOD

FFT METHOD

FFT METHOD

FFT METHOD

Rotational index

Data value

…

Rotation 1 –

Rotation 2 – Rotation L –

FFT METHOD

FFT METHOD

FFT METHOD

FFT METHOD

Output of example of value

Figure 6: Proposed despreading receiver using fast Fourier

transform method.

periodic cross-correlation function needs to be calculatedwith the un-rotated original spreading sequence Cr=1

n toyield a length L vector. This vector holds each rotated databit at its specific rotational index. This method making useof a fast Fourier transform algorithm, which is based on theconvolution theorem, decreases the receiver complexityand shows a huge speed improvement in the de-correlationof the received signal. Hence, the periodic correlationfunctions can be determined much faster and with far lessarithmetic complexity. The correlation of two finite lengthsequences can be found by taking the FFT of one sequenceand the complex conjugate FFT of another and point-wisemultiplying them, and then performing an inverse FFT ofthe result.

For example, a code family with a processing gain ofPG = 64, a flock size of M = 4 and an elementary codesequence length of L = 16, can transmit or combine 16data symbols using only one flock (or code sequence Cn).Each data symbol would be positioned in one rotationalposition of the de-correlated sequence when using the FFTalgorithm. When de-correlating the transmitted signal,the algorithm for de-correlating the length 64 transmitted


FFT( )

FFT( )

FFT( )

FFT( )

FFT METHOD

=FFT(.)

FFT(.)

FFT(.)

FFT(.)

IFFT(.)

ML-L+1 : ML

2L+1 : 3L

L+1 : 2L

1 : L

S/P

Array

Figure 7: Fast Fourier transform method for building block

depicted in Figure 6.

signal and all of its rotations can be found by

R = F −1(

F(S[1→ 16]

) ·F (C1

11

)+F

(S[17→ 32]]

) ·F (C1

12

)+F

(S[33→ 48]

) ·F (C1

13

)+F

(S[49→ 64]

) ·F (C1

14

)), (21)

where S[.] refers to a sub-set range of values ofthe transmitted vector. A low complexity and fasterperforming receiver algorithm using the FFT method isdepicted in Figure 6 and 7.

5. PROPERTIES AND PERFORMANCE OF SYSTEM

The basic system without any complex receiver structuresis illustrated in this paper. The simulated uncoded biterror rate performance in AWGN for the multi-user systemfollows the theoretical single-user BER performance witha much greater throughput rate and spectral efficiency. Asan example, a BPSK system can make use of a length16 elementary code (L = 16) and a flock size of M = 4.This produces a 2× 4-dimensional modems that can use16 rotations to produce 128 information bits that aretransmitted in 64 bits, yielding a spectrum efficiency of8×16/64 = 2 bits/s/Hz.

Figure 8 provides the BER performance in multipathfading channels using BPSK modulated data, where thepresented BER results are averaged over 32 users splitby frequencies. As explained above, the number of usersdepends only on the FFT size and bandwidth constraints,thus similar performance is expected for an increase innumber of users. The presented performance is thereforevalid for a fully loaded system due to the MAI-freeoperation. The multi-user system perfectly follows thetheoretical single-user performance curves in a multipathchannel. The MAI-free operation allows the system to be

0 5 10 15 2010−4

10−3

10−2

10−1

100

Eb/N0

BitErrorRate

(BER)

Rayleigh fading (Theory)

Rician fading Kr=5 dB (Simulated)



AWGN BPSK/QPSK (Theory)

AWGN BPSK (Simulated)

Figure 8: Simulated BER curves in a fading Rician channel for a

BPSK/QPSK system with different Rician K-factors.

upper-bounded by the single user theoretical performancecurve even with an increasing number of users, whereasmulti-carrier CDMA (MC-CDMA) and other CDMAtype schemes greatly decrease in performance with eachadditional user because of the present MAI.

Figure 9 illustrates the BER performance of an ordinaryBPSK OFDM system with and without a guard interval ina 6 tap Rayleigh fading channel with a maximum delayless than the channel impulse response to incur flat fadingif a guard band is to be applied. It can be seen thatthe performance without any guard band for the OFDMsystem is not consistent with that of the analytic result ina Rayleigh fading channel and the effect of ISI becomesmore pronounced as the SNR increases. However, in theproposed system, the effect of ISI and the performancedegradation is far less, considering the same systemparameters. This implies that the system is just subjectto flat fading and shows that the spreading codes can copewith some of the ISI and a smaller guard band is requiredto reduce the error floor at higher signal-to-noise ratios.A reduction in the guard band improves the bandwidthefficiency. If the system on the other hand employs a largeguard band, the BER performance of the system decreasesbelow the analytical performance curve of an ordinaryOFDM system. This shows that the system is more robustand the spreading codes enable the system to perform wellwith a smaller guard band.

In conventional MC-CDMA systems, each user isassociated with its own channel in the uplink, and thetransmitted symbols undergo their own channel distortionsrequiring complex multi-user detection schemes to restorethe orthogonality amongst users. The proposed systemhowever, improves the performance and reduces thecomplexity of detection, as the transmitted symbols thatgenerate interference are affected by the same channeldistortion, since the data symbols of the same user are


5 10 15 20 25 3010−5

10−4

10−3

10−2

10−1

100

Eb/N0

BitErrorRate

(BER)

Rayleigh FadingOFDM in multipathNo Guard bandSystem in multipathNo Guard bandSystem in multipathWith Guard band

Figure 9: Simulated BER curves showing ISI effects on the

performance of the system with guard bands and without.

(Channel Power dB=[0 -0.9 -4.9 -8 -7.8 -23.9])

transmitted on a given set of sub-carriers.

MC-CDMA systems generally have to cope with MAI,whereas the proposed simulated system only has to copewith self-interference which is caused by the contributionof signals from the same user [12]. Thus, MAI is notpresent in the system. Additionally, only a single-user lowcomplexity detection strategy is required at the receiver toachieve good performance, since the detection only needsto be applied to the sub-carriers assigned to one user.Reduced channel estimation complexity is also expected,seeing that each sub-carrier is exclusively used by oneuser. Since there is no MAI present, the same interfacecan be used for the uplink as well as for the downlink ofthe system. MC-CDMA systems can achieve their highbandwidth efficiency only in the downlink, whereas thepresented system is more suitable for the uplink.

In multi-user systems such as MC-CDMA schemes,the near-far problem places a fundamental limit on theperformance of the system, and this issue is generally notconsidered in many multi-carrier and multi-user systemdesigns and evaluations. However, the presented systemis resistant to the near-far problem due to the absenceof MAI and the fact that each user is de-correlatedindependently. Hence, very costly and complex near-farmitigation mechanisms such as power control algorithmsare unnecessary.

An MC-CDMA system spreads n data symbols over n.Lsub-carriers and is capable of exploiting more frequencydiversity; however, this makes the channel estimation andreception more difficult. On the other hand, the presentedsystem spreads 2ML data symbols over ML sub-carriersand looses some of the diversity, but facilitates simplerchannel estimation. However, this frequency diversityloss, which cannot be exploited at the de-spreadingprocess, can be made up for by employing channel coding.

Channel coding can be assigned independently to eachuser, allowing for more robustness and added redundancyfor that specific user. Inter-cell interference and resultingerrors can thus be reduced by adding fewer spreadingcodes to a user’s signal, by making use of fewer carriersor by well known forward error correcting (FEC) codes.

Additionally, the code-division or spreading of the datain the system allows for variable data rate transmissionfor each user. Thus, a wide range of multi-rate serviceswith different data rates (video, audio, image, speech,etc.) can be supported. The system would only need toalter the amount of multiplexed spreading codes at thetransmitter to change the transmission rate, without theneed for implementing adaptive coding and modulationschemes in both the transmitter and receiver.

The BER performance of the system compares toconventional OFDM if the Rayleigh fading over allchips of the spreading code is flat. If either one ortwo-dimensional spreading is applied with interleaving ofthe chips in the frequency and/or time domain, the diversityperformance curves are lower-bounded by the theoreticalBER diversity performance curves of a Rayleigh fadingchannel, where the spreading code length corresponds tothe diversity order. The performance of spreading inmultiple domains achieves a higher processing gain andthe ability to use three different dimensions adds to theflexibility of the system, as resources can be allocated inthe frequency, time, and code space. Further diversityschemes like space, angle or polarisation diversity, whichare not within the scope of this study, can additionallyincrease the overall diversity and performance of thesystem.

6. CONCLUSION

The primary objectives of next-generation wirelessnetworks for mobile and broadband services is to makeuse of the limited radio spectrum in order to achieve higherdata rates and throughput with higher bandwidth efficiencyand user-capacity. By combining OFDMA and a modifiedspread spectrum multi-dimensional modulation method ina novel manner with the use of complete complementarycodes and a cyclic rotation scheme, a unique flexible digitalbroadcasting technique, which supports high data ratesand capacities over hostile radio channels, was developed.The generic architecture of the analysed system integratesexisting techniques into a design that is adaptable andreconfigurable to different standards and technologies.This provides for scalability, easy integration into existingplatforms and also provides opportunities for new researchand development.

The system possesses several advantages over currentlyavailable 2G and 3G mobile cellular systems. It can,firstly, achieve a much higher bandwidth efficiency thanconventional CDMA systems by yielding an efficiencyper user equal to the un-spread theoretical spectralefficiency of the modulation method used, except forBPSK modulation, in which case the system can achieve


2 bits/s/Hz (double the theoretical). Secondly, the systemoffers MAI-free operation. This attributes to co-channelinterference reduction, capacity increase, resilience againstthe near-far problem and in addition, the system hasan improved throughput. Thirdly, due to its spectralefficiency, the system can make use of the additionallyavailable resources when not fully loaded, enabling itto achieve a more reliable transmission and improve theBER performance. Finally, the system achieves multipleaccess with the use of OFDMA techniques and is greatlyflexible in the way in which it spreads the data, resultingin various design alternatives with diversity improvements.The code-division or spreading of the data can offernumerous advantages such as possible data rate adaption,less complex channel estimation and diversity gains.

Many areas of this novel technology remain underexploredand this research has created a starting point or basisfor further investigation. Additionally, many questionswere uncovered and a variety of problems that requirefurther study and experimentation were highlighted.This research has provided an in-depth insight into thehigh potential of the novel integration of the proventechnologies, namely multi-dimensional spread spectrumand multi-carrier OFDMA techniques.

REFERENCES

[1] K. Zheng, G. Zeng, and W. Wang, “Perfor-mance Analysis for OFDM-CDMA With JointFrequency-Time Spreading,” IEEE Trans. Broad-cast., vol. 51, no. 1, pp. 144–148, Mar. 2005.

[2] L.-L. Yang and L. Hanzo, “Multicarrier DS-CDMA:A Multiple Access Scheme for Ubiquitous Broad-band Wireless Communications,” IEEE Commun.Mag., vol. 41, no. 10, pp. 116–124, Oct. 2003.

[3] H.-H. Chen, J.-F. Yeh, and N. Suehiro, “AMulticarrier CDMA architecture based on orthogonalcomplementary codes for new generations of wide-band wireless communications,” IEEE Commun.Mag., vol. 39, no. 10, pp. 126–135, Oct. 2001.

[4] C. Han, N. Suehiro, and T. Hashimoto, “N-ShiftCross-Orthogonal Sequences and Complete Comple-mentary Codes,” in IEEE Int. Symp. on Inf. Theory(ISIT’07), Jun. 2007, pp. 2611–2615.

[5] H.-H. Chen, D. Hank, M. E. Magana, andM. Guizani, “Design of next-generation CDMAusing orthogonal complementary codes and offsetstacked spreading,” IEEE Wireless Commun., vol. 14,no. 3, pp. 61–69, Jun. 2007.

[6] H.-H. Chen, S.-W. Chu, N. Kuroyanagi, andA. J. Han Vinck, “An algebraic approach togenerate super-set of perfect complementary codesfor interference-free CDMA,” Wirel. Commun. Mob.Comput., vol. 7, no. 5, pp. 605–622, Jun. 2007.

[7] M. E. Magana, T. Rajatasereekul, D. Hank, and H.-H.Chen, “Design of an MC-CDMA System That UsesComplete Complementary Orthogonal SpreadingCodes,” IEEE Trans. Veh. Technol., vol. 56, no. 5, pp.2976–2989, Sep. 2007.

[8] L. P. Linde, L. Staphorst, and J. D. Vlok, “Per-formance of a quasi-synchronous four-dimensionalsuper-orthogonal WCDMA modulator for nextgeneration wireless applications,” South African J. ofSci., vol. 103, no. 11-12, pp. 459–464, Dec. 2007.

[9] L. P. Linde and J. D. Vlok, “A Multi-dimensionalsuper-orthogonal modulation alternative to M-QAMWCDMA for next generation wireless applications,”in IEEE Proc. AFRICON’07, 2007.

[10] M. E. Magana and T. Rajatasereekul, “CompleteComplementary Orthogonal (CCO) Code-BasedCDMA Using Natural Mapping QAM Constella-tions,” Wireless Pers. Commun., vol. 38, no. 4, pp.435–442, Jun. 2006.

[11] H.-H. Chen, “The REAL Approach to GenerateOrthogonal Complementary Codes for Next Genera-tion CDMA Systems,” Interdisciplinary Inform. Sci.,vol. 12, no. 2, pp. 147–161, 2006.

[12] K. Fazel and S. Kaiser, Multi-carrier and spreadspectrum systems: from OFDM and MC-CDMA toLTE and WiMAX, 2nd ed. John Wiley & Sons Inc.,2008.

[13] H.-H. Chen, S.-W. Chu, and M. Guizani, “OnNext Generation CDMA Technologies: The REALApproach for Perfect Orthogonal Code Generation,”IEEE Trans. Veh. Technol., vol. 57, no. 5, pp.2822–2833, Sep. 2008.

[14] L. Lu and V. K. Dubey, “Performance of a CompleteComplementary Code-Based Spread-Time CDMASystem in a Fading Channel,” IEEE Trans. Veh.Technol., vol. 57, no. 1, pp. 250–259, Jan. 2008.

[15] H.-H. Chen, The next generation CDMA technolo-gies. Wiley Online Library, 2007.

[16] “Air Interface for Fixed and Mobile Broadband Wire-less Access Systems,” IEEE Std P802.16 (Amend-ment and Corrigendum to IEEE Std 802.16-2004),2005.

[17] T. Kwon, H. Lee, S. Choi, J. Kim, D.-H. Cho,S. Cho, S. Yun, W.-H. Park, and K. Kim, “Design andimplementation of a simulator based on a cross-layerprotocol between MAC and PHY layers in a WiBroCompatible. IEEE 802.16e OFDMA system,” IEEECommun. Mag., vol. 43, no. 12, pp. 136–146, Dec.2005.

[18] B. Makarevitch, “Adaptive resource allocation forWiMAX,” in 18th IEEE Int. Symp. on Pers., Indoorand Mobile Radio Commun. (PIMRC’07), Sep. 2007,pp. 1–6.

[19] S. Kaiser and K. Fazel, “A flexible spread-spectrummulti-carrier multiple-access system for multi-mediaapplications,” in 8th IEEE Int. Symp. on Personal,Indoor and Mobile Radio Commun. (PIMRC’97),vol. 1, 1997, pp. 100–104.

7. REFERENCES


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