IJECT Vo l . 6, Issu E 1, Jan - Mar C h 2015 Review of ... · the Rician fading channel is given...

IJECT Vol. 6, IssuE 1, Jan - MarCh 2015

w w w . i j e c t . o r g InternatIonal Journal of electronIcs & communIcatIon technology 49

ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

Review of Data Communication in Wireless Fading Channel and a Case Study

1Madhvi Soni, 2P. K. Ghosh, 3Kapil Gupta1,2Dept. of ECE, College of Engg. and Tech., Mody University, Lakshmangarh, Sikar, Rajasthan, India

3Dept. of ECE, MMEC, MM University, Mullana, Ambala, Haryana, India

AbstractThe Rotation and Component Interleaving Diversity (RCID) is an important technique used to enhance the performance of wireless digital communication system over the fading environments. RCID technique is accomplished by rotation of signal constellation and using interleaver and de-interleaver at the transmitter and at the receiver side, respectively. In this article, we study the factors causing fading in channel, and discuss the techniques to combat the fading effect. Also we review here different types of fading models and improvement of the system performance using RCID technique.

KeywordsDiversity, RCID, Symbol Error Probability, Interleaver, De-Interleaver, Fading Channels, Combining Techniques, Co-Operation

I. IntroductionWireless network provide high speed mobility for voice as well as data traffic from variety of sources [1]. There is constant increase in the use of wireless communication systems. Fading has adverse effects on wireless communication system since it affects the signal destructively leading to poor reception. Performance of wireless communication system thus degrades because fading is not a favorable condition [2-3]. Communication through these fading channels is difficult and so certain types of techniques are introduced to achieve desirable performance of the system. In wireless communication system, signal propagation mechanisms may be of reflection, diffraction, or scattering types. These mechanisms finally results in multipath propagation. Table 1 describes the concept of these propagation mechanisms [4-6].

Table 1: Various Propagation Mechanisms

A. Multipath Propagation and FadingMultipath propagation affects the wireless communication system by providing number of replicas of same signal. Signal multipath can be categorized into two types as shown in Table 2. These multiple signals have different delays and phases which appear at receiver as superposition of all the transmitted signals. It results in interference which may be constructive or destructive. This interference results in fading [5, 7]. In fact, whenever the strength of received signal varies with time then the signal is said to have faded out.

Table 2: Types of Multipath

Fading is divided broadly into two parts namely: (a) large scale fading and (b) small scale fading. In fig. 1, we depict different fading environments.

1. Large Scale FadingIt represents average signal power with respect to time over large areas. It is shown in Fig. 1 in block 2. The main causes of large scale fading are path losses due to obstructions in hills, valleys, buildings etc. Such kind of obstacles causes shadowing between transmitter and receiver. This type of fading is generally described by power law and log normal distribution about the mean.

2. Small Scale FadingIt represents change of signal power experienced over small distances of order of few wavelengths between transmitter and receiver. It is shown in block 3 of Fig. 1. There are so many factors which affect small scale fading like multipath propagation, Doppler shift etc. Small scale fading is sub categorized on the basis of two parameters namely, the time spread or time dispersion and the Doppler spread in block 4 and 5 respectively. On the basis of time spread it is classified as flat fading and frequency selective fading in block 6 and 7, respectively. Unlike frequency selective fading, flat fading occurs where coherence bandwidth is greater than the signal bandwidth. Coherence bandwidth defines the frequency interval over which two frequencies of signal are likely to experience the comparable fading. Similarly on the basis of Doppler spread, the small scale fading is classified as fast fading and slow fading in block 8 and 9 respectively. Whenever the coherence time of channel is smaller than the time period of symbol then the signal will experience fast fading and similarly if time period of symbol is smaller than coherence time of channel then it causes slow fading. Coherence time may be defined as the time duration over which impulse response is considered to be not varying.

Fig. 1: Fading Classification

II. Signal Fading StatisticsWhenever the channel characteristics are not specified then free space propagation model is used. This model assumes that there is no LOS path and no obstacles in the path of transmitter and

IJECT Vol. 6, IssuE 1, Jan - MarCh 2015 ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

w w w . i j e c t . o r g 50 InternatIonal Journal of electronIcs & communIcatIon technology

receiver then in this condition signal attenuates in free space. This type of attenuation is called free space loss. For ideal isotropic antenna, free space loss is given by:

(1) where PR and PT are received and transmitted power respectively, r is the distance between transmitter and λ receiver and is the wavelength of propagating signal [8]. To design a wireless communication system, we need to define the characteristics of channel. These channels can be divided on the basis of their distribution function. Some of the models which are widely used in this area are as follows:

A. Rician Fading ModelIf there is direct Line of Sight (LOS) path between transmitter and receiver then Rician fading model is use to characterize the fast fading. The Probability Density Function (PDF) of Rician distribution is given by:

(2)

where is the peak amplitude of the dominating signal, I0 (.) is the Bessel function of first kind with zero order and σ is the standard deviation of local power. The cumulative distribution (CDF) for the Rician fading channel is given by:

(3)

where Q(.) is the Marcum’s Q function [9-10]. Rician fading channels can also be defined in terms of variance defined as:

(4)

(5)

Rician distribution becomes the Rayleigh distribution, for the case x approaches to zero.

B. Rayleigh Fading ModelThe rapid variations (fast fading) in signal power caused by local multipath are represented by Rayleigh distribution. Rayleigh distribution describes statistical time varying nature of received envelope of flat fading signal or the envelope of an individual multipath component [6]. The Probability Density Function (PDF) of Rayleigh distribution is given by:

(6)

where r is the amplitude of received signal and σ2 is the average power of received signal.

C. Nakagami Fading ModelNakagami distribution can define both Rayleigh and Rician fading distribution with its single model [9, 11-12] and it is related to the gamma distribution. It has two parameters: shape parameter (m) and controlling parameter (Ω), where m≥0.5 and Ω>0. The PDF of Nakagami distribution is given by:

(7)

Corresponding cumulative distribution function (CDF) is given by [13]:

(8)

where p(.) is incomplete gamma function. The parameter and are given by [14-15]:

Nakagami-m distribution approximates Nakagami-q distribution which is given by:

(9)Nakagami-q distribution was introduced by Nakagami [9]. This distribution was further investigated by Hoyt so it is also called Nakagami-Hoyt distribution [16-17].

III. Technologies in Digital Wireless CommunicationSingle input single output (SISO): It is one of the simplest • MIMO configurations. In SISO transmitter operates with one antenna as does the receiver. There is no diversity so no additional processing required in it.Single input multiple outputs (SIMO): SIMO occurs where • transmitter has single antenna and receiver has multiple antennas. It is also known as receive diversity. It has been used for short wave listening / receiving stations to combat the effects of ionospheric fading and interference.Multiple input single output (MISO): MISO is also termed as • transmit diversity. In this case, the same data is transmitted redundantly from the two transmitter antennas. The receiver is then able to receive the optimum signal which it can then use to receive extract the required data.Multiple input multiple outputs (MIMO): Where there is more • than one antenna at either end of the radio link, this is termed MIMO - Multiple Input Multiple Output. MIMO can be used to provide improvements in both channel robustness as well as channel throughput. The detailed study of MIMO system can be explained as:

A. Multiple Input Multiple Output (MIMO)MIMO helps in improving the performance of wireless communication system. MIMO system provides spatial correlation between the signals at both the transmitter as well as the receiver sides without sacrificing the bandwidth by using various algorithms and techniques like precoding, spatial multiplexing, diversitycoding etc. [18-19] as explained below.

Fig. 2: MIMO Configuration




The Fig. 2 shows that there are Nt transmitting and Nr receiving antennas. All the transmitting antennas transmit the signal at a common carrier frequency on different paths which are received at receiver. If signal is transmitted from pth transmitting antenna, the received signal at qth receiving antenna yaq (t) will be summation of all the signals that are received over it from other transmitting antennas and are given by:

(10)

where the channel transitional response from the pth transmitter to the qth receiver hpq (t) is assumed to be known at receiver [18].

1. Capacity of MIMO SystemThe capacity of wireless communication system can be defined as maximal transmission rate for reliable communication. The capacity of MIMO system varies with the number of antennas [6] [20]. According to Shannon’s channel capacity formula [21]:

(11)where C is the channel capacity (bits/sec.), B is the transmission bandwidth (Hz) and S/N is signal to noise power ratio. The capacity of various configuration of MIMO is summarized in Table 3. The operation of MIMO system can be broadly divided into three main categories:

(i). Precoding In precise form precoding is multi stream beam forming scheme. Beam forming results in increased receiver gain by transmitting the same signal from each of antennas and summed up in such a way to reduce multipath fading effect. But it needs channel state information be available at both the transmitter as well as the receiver side.

(ii). Spatial MultiplexingIn spatial multiplexing high data rate signal is to be broken into lower rate streams and each of streams is transmitted over different antennas in same frequency band. If these signals arrive at the receiver with different spatial characteristics and the correct channel state information is available at receiver, it can separate these streams into parallel channels. It can improve channel capacity at higher SNR value. Spatial multiplexing is used in space division multiple accesses (SDMA) in which CSI should be known at transmitter [32].

(iii). Diversity CodingUnlike spatial multiplexing where multiple streams are transmitted, diversity coding uses a transmission scheme in which single stream is transmitted and it uses space time coding as signal coding scheme with full or near orthogonal coding. It results in improving signal diversity. This coding is used when there is no CSI is available at the transmitter side.

B. Orthogonal Frequency Division Multiplexing (OFDM):OFDM is a multicarrier modulation scheme which consists of sum of subcarriers that are modulated by using phase shift keying (PSK) or Quadrature Amplitude Modulation (QAM). Nowadays OFDM uses multi-carrier modulation also. In OFDM data are transmitted in parallel fashion over a channel at rate of R symbols per second and modulated at rate R/N symbols per second with N carriers. In this way multiple effects are reduced by factor of 1/N thus the performance of system increases [19] [23].

Table 3: Capacity of Various Wireless Link Configurations

IV. Fading Combating TechniquesWireless communication system requires signal processing to improve the link performance. Equalization, diversity and channel coding are three techniques which help in improving the performance. When the modulation bandwidth exceeds the coherence bandwidth of channel then it causes ISI (Intersymbol interference). To overcome this ISI, equalization technique can be used [11]. Channel coding improves the link performance by adding redundant data bits in transmitting message so that if some of the portion of transmitted signal is lost due to fading then it can be recovered at receiver side. Channel coding is used to correct deep fading or spectral null. The channel coding is used by receiver to detect or correct some errors introduced by the channel [24]. Diversity is another technique to mitigate fading channel impairments. Diversity can be achieved by using more than two antennas [25-27].

Fig. 3: A General Framework of Fading Effects and their Mitigation Techniques

A. DiversityDiversity plays an important role in combating the fading impairments, error bursts, and co-channel interference. In diversity technique, message signal is transmitted over two or more paths which have different statistical characteristics. By transmitting over more than one path there will be less probability that each signal will experience simultaneous deep fade. There are number of ways of achieving independent fading paths which are elaborated below.

1. Frequency DiversityThe basic concept of frequency diversity is to send message data over more than one carrier frequency. With the help of independent carrier frequencies diversity can be achieved which helps in mitigating the fading. In frequency diversity frequencies are separated by more than coherence bandwidth of channel so that it will not experience simultaneous deep fade [28].

2. Time DiversityTime diversity can be achieved by transmitting the repeated information over the time spacing that exceeds coherence time of the channel. There are many techniques which helps in achieving time diversity such as rake receiver, interleaver etc. Interleaving is a technique used to obtain time diversity. In interleaving technique the message data is spread over the time without adding any overhead bits. In this case, a pair of interleaver and de-interleaver



are used at transmitter and receiver sides, respectively. Interleaver is always used with error correcting codes. The basic function of interleaver is to protect the transmitted data from the errors. Block interleaver accepts the set of symbols and rearranges them and there is no repetition of symbols in it.Convolution interleaver is somehow similar to block interleaver except that it has memory that is, there is participation of both current symbols as well as past symbol values. This can be designed with the shift registers with M memory elements (Fig. 4). Scanning process takes place regularly. Whenever it recognizes that there are new symbol then commutator switches to next shift register and at that time new symbol comes in place of oldest symbol in shift register. This process continues till(N-1)th shift register after which again it returns to 0th shift register. This process is continuously repeating again and again. The de-interleaver rearranges the elements of its input vector without repeating or omitting any elements. The de-interleaver also uses N-shift registers, it performs the reverse mapping as that of the interleaver (Fig. 5).

Fig. 4: Block Diagram of Convolution Interleaver

Fig. 5: Block Diagram of Convolution De-interleaver

3. Space diversitySpace diversity provides independent fading path by using two or more antennas and so sometimes it is referred to as antenna diversity. Whenever there is no direct LOS path between transmitter and receiver then due to reflection, diffraction, or scattering the signal travels to multiple paths. Each path introduces different phase shifts, time delays, attenuations that cause interference. Space diversity helps in mitigating this type of multipath situation. Space diversity can be realized in several ways:

(i). Adaptive ArrayIt can be a single antenna with active elements or it can be arraying of antennas with ability to change their radiation pattern [29].

(ii). Polarization DiversityPolarization diversity is achieved by using only one dual polarized antenna. But the condition is that two polarizations must be orthogonal. Fig. 6 shows that horizontal and vertical or +45Ο and -45Ο slanted are the example of the polarization diversity by providing almost uncorrelated signals. But it has disadvantages of cross coupling between two ports [22] [30].

Fig. 6: Concept of Polarization Diversity

(iii). Transmit and Receive DiversityFor the transmission and reception in transmit and receive diversity two separate, collocated antennas are used. With transmit diversity multiple antennas create frequency selective fading at single antenna at receiver which uses equalization to obtain diversity gain against fading [31]. In receive diversity receives independent radio signals from two distinct antennas to maximize signal quality and reception. Receiver diversity results in fewer fades in the combined signal thus allowing the decoder in the baseband processor for better performance [32].

(iv). Angle Diversity (Pattern Diversity)It is diversity reception in which beyond the horizon tropospheric scattered signals are received at slightly different angles, which provide independent fading paths [33].

(v). Cooperative DiversityThe concept of cooperative diversity comes from the fact that whenever the distance between transmitter and receiver is such that the communication between them is not secure (and reliable) and the antenna deployment is not easy due to its small size consideration and power limitations then one or more relays can be used to support the communication. The concept of cooperative diversity is shown in fig. 7.

Fig. 7: Simplified Cooperation Model

The use of Relay node between source and destination results in increment in received SNR and decrement in burst of errors. The signals received at the relay input yr and the destination yd can be written as

(12)

(13)where nsd and nsr are additive white Gaussian noise and hsr and hsd are channel coefficients from source to relay and source to destination, respectively. Second operation involves two cases: (a) source transmits the data and relay recognize it and sends it to destination (signal yd1 of Eq. (14)), (b) if relay do not recognize the data from source then source continuously send data to destination ( yd2 of Eq. (15)), then received signal at destination is given by:

(14)

(15) where n1' and n1 are respective AWGN noise components. The relaying techniques involve the Decode and forward (DF), Amplify and forward (AF) and Coded cooperation. The DF is one of the most preferred methods of relaying techniques. In this approach relay firstly detect the source data, decodes it and then sends it to the destination. Error correction can also be done at the relay node [34]. The AF technique proposed in [35], simply amplify the received signal and forward it to the destination. But the major drawback of this technique is that the noise also gets amplified




with the received signal at the relay node. Coded cooperation is new type of technique proposed in [36-37]. It utilizes breaking of data stream into two segments; one segment of data is to be send by one user and the other segment is to be send by the another user. This type of cooperation takes place when there are two users. Further this coded cooperation is to be modified for the three users also.

V. A Case Study of Error Performance of M-PSK Signal Using RCID TechniqueRCID technique is applied on the Q-PSK signal constellation to analyze the performance of the communication system. We have derived the expression for Symbol Error Probability (SEP) for Q-PSK signal constellation and thus we obtained the optimum rotation angle for the same. There are many types of diversity techniques used generally such as space, time, frequency, polarization diversity etc. [38-40]. RCID technique deals with the rotation of signal constellation in such a way so that maximum number of orthogonal components can occur between any two points. RCID also concern with the use of interleaver and de-interleaver at transmitter and at receiver side so that the orthogonal components can be influenced by autonomous fading coefficients [41]. The idea of RCID was firstly introduced in [42-43]. In [2] optimum rotation angle is obtained at high SNRs for QPSK signal constellation over Rayleigh fading channels by maximizing minimum product distance and signal constellation. In [39] author find the optimum rotation angle for M-PSK over Rician fading channel by directly minimizing the union bound for SEP.

A. System ModelTo understand the rotation of signal constellation we have consider typical QPSK signal constellation as shown in Fig. 8 (a). If fading befall in channel then orthogonal components influenced simultaneously so there is no diversity so the fading cannot be combated. But as we rotate this constellation in Fig. 8 (b) then components are not simultaneously influenced by fading [2].

Fig. 8: Signal Constellation of QPSK (a) Typical QPSK (b) Rotated QPSK

Fig. 9: Block Diagram of Transmitter and Receiver of Rotated PSK

We have shown the transmitter block diagram of rotated PSK in fig. 9. The x (t) is transmitted signal. The symbol mapper generates orthogonal values which are individually interleaved by I and Q-interleaver. The interleaved components are then upconverted

and are combined to form s(t) [41]. The received signal is given by:

(16)

where h (t) is the Nakagami-m fading envelope and n(t) is zero mean additive white Gaussian noise. The received signal r (t) is given to both the correlators from where they are independently interleaved and applied to demapper. Demapper takes the orthogonal values and generates the corresponding symbols. It is assumed that ideal interleaved is used and Channel State Information (CSI) is known to the receiver so the matrix used by maximum likelihood detector is:

(17)where si is the ith symbol of rotated PSK. Here ‖.‖2 and ʘ represents Euclidean norm and component wise product respectively.

B. Performance AnalysisIf is the transmitted symbol then s→s denotes pair wise error event so conditional pair wise error probability:

(18)

where Q (.) is Gaussian tail function [2] and

(19)

(20)i, j = 1, 2,…, M and i ≠ j.θ is the angle of rotation. θi and θj are phase angle of ith and jth Symbols respectively [40].If z1=(h1

2 d12) ⁄ N0 and , using Craig’s formula [44] by:

(21)

where z = z1+z2. Now using the moment generating function (MGF) Mz (s):

(22)

MGF of z is represented by MZ (s), where

(23)i=1, 2 where m is the Nakagami-m fading parameter.

(24)where, ci = zi ⁄ 4m, i=1, 2. By [9]:

(25)

where F (.) is the Appell hypergeometric function and B (.) is beta function [45]. Let F=1 for high SNR values so,

(26)

If we consider symbols are of equal probability, union bound for SEP of M-PSK is given by [46]:



(27)

C. Simulation resultsIt is clear from the fig. 10 that optimum rotation angle occurring at about 30 degree. This result is compatible with [2], [39]. Optimum rotation angle is 31.7 degree in [2] and 29.6 degree in [39].

Fig. 10: Plot of Rotation Angle versus SEP for SNR=25dB for m=1, 2

The SEP performance at an angle 22.5 degree is shown in Fig. 11. It is clear as fading parameter, m increases, SEP performance decreases proportionally. For high SNR values, optimum rotation angle is 30 degree. At lower SNR values, optimum rotation angle changes between 30 degree and 45 degree.

Fig. 11: Plot of SNR Versus SEP for Rotation Angle 22.5 degree for m=1, 2

VII. ConclusionThere is speedily increase in the use of high data rate transmission over the fading channels. To achieve this goal rotation and component interleaving diversity (RCID) technique is to be applied over the signal constellation. RCID technique helps in enhancing the performance of wireless communication systems. It is simply the combination of rotation of signal constellation and using interleaver and de-interleaver pair at the transmitter and at the receiver side respectively. This article has been studied for Q-PSK signal constellation over the Nakagami-m fading channels. It is clear from the simulation results that the optimum rotation angle which we obtained is similar to the ones [39] because of the relation between Rician factor and Nakagami shape factor.

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P. K. Ghosh was born in Kolkata, India in 1964. He received his B. Sc (Hons in Physics), B. Tech and M. Tech degrees in 1986, 1989, and 1991, respectively from Calcutta University. He earned Ph.D. (Tech) degree in Radio Physics and Electronics in 1997 from the same University. He served National Institute of Science and Technology (Orissa), St. Xavier’s College (Kolkata), Murshidabad College of Engineering and Technology (West

Bengal), R. D. Engineering College (Uttar Pradesh) and Kalyani Government Engineering College (West Bengal) before he joins Mody University of Science and Technology (Rajasthan). To his credit, he has more than 55 research papers in Journals of repute and conference proceedings. He is a life member of Indian Society for Technical Education (ISTE), New Delhi. His research interests are in the areas of wireless communications, digital signal processing, VLSI circuits & devices.

Kapil Gupta was born in Kota (Rajasthan), India in 1980. He received his B.E. (Hons.) degree in Electronics & Communication Engineering in 2003 from RU and M.E. (Hons.) degree in Digital Communication from JNV University, Jodhpur, Rajasthan in 2008. He has more than 7 years of experience in teaching. His research interests are in Digital Communication over fading channels

and Error correction codes.

Madhvi Soni was born in Bikaner (Rajasthan), India in 1993. She has done B.Tech in Electronics and Communication from Rajasthan Technical University, Kota (Rajasthan) in 2013. At present she is doing M. Tech in Signal Processing from Mody University. Her research interests are in the field of Digital Communication and Wireless Communications.

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