Propagation Analysis for Wireless Sensor Networks Applied...

Research ArticlePropagation Analysis for Wireless Sensor NetworksApplied to Viticulture

Felipe Pinheiro Correia1 Marcelo Sampaio de Alencar2 Waslon Terllizzie Arauacutejo Lopes23

Mauro Soares de Assis4 and Brauliro Gonccedilalves Leal5

1Federal Institute of Education Science and Technology of Pernambuco Petrolina PE Brazil2PPgEE DEE CEEI Federal University of Campina Grande Campina Grande PB Brazil3Federal University of Paraıba Joao Pessoa PB Brazil4Brazilian Committee of URSI Rio de Janeiro RJ Brazil5Federal University of Sao Francisco Valley Juazeiro BA Brazil

Correspondence should be addressed to Waslon Terllizzie Araujo Lopes waslonieeeorg

Received 28 August 2016 Revised 30 November 2016 Accepted 18 December 2016 Published 30 January 2017

Academic Editor Lorenzo Luini

Copyright copy 2017 Felipe Pinheiro Correia et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Wireless sensor networks have been proposed as a solution to obtain soil and environment information in large distributed areasThemain economic activity of the Sao Francisco Valley region in theNortheast of Brazil is the irrigated fruit productionThe regionis one of themajor agricultural regions of the countryGrape plantations receive large investments andprovide goodfinancial returnHowever the region still lacks electronic sensing systems to extract adequate information from plantations Considering these factsthis paper presents a study of path loss in grape plantations for a 24GHz operating frequency In order to determine the positionof the sensor nodes the research dealt with various environmental factors that influence the intensity of the received signal It hasbeen noticed that main plantation aisles favor the guided propagation and the vegetation along the secondary plantation aislescompromises the propagation Diffraction over the grape trees is the main propagation mechanism in the diagonal propagationpath Transmission carried out above the vineyard showed that reflection on the top of the trees is the main mechanism

1 Introduction

The term Precision Agriculture (PA) refers to a set oftechnologies used to understand the changes that occurduring the plantation cycles [1] These tools should allowbetter monitoring of the stages of agricultural production Inthis context Wireless Sensors Networks (WSNs) have beenproposed as a solution to perform this monitoring [2 3]The emergence of protocols and low-cost devices enable thedeployment of the technology in those environments mainlyby allowing the supervision of large areas

This research has been developed in the Sao FranciscoValley region Northeast of Brazil The main economic activ-ity is irrigated fruit growing for export and the productionof the region reaches the foreign market especially Europewhere sanitary and quality standards are strict [4] Asmentioned WSNs are candidates to improve the production

process as they provide new ways to manage the harvestingareas along with the fact that they do not need transmissionwires Therefore the cost of deployment of WSNs may becheaper and more adequate than wired networks

One of the possible applications of this research is tocollect soilmoisture dataWith the humidity data it is possibleto develop an automatic irrigation system taking into accountareas of soil that are most in need of water avoiding theuniform irrigation of the plantation The proposed idea canbe seen in Figure 1 which represents nodes arranged in amoisture map

However before the implementation of a communicationsystem it is important to know the path loss due to differentantennas settings related to the presence of obstacles forexample Factors such as the transmission power vegetationdensity and the occurrence of line-of-sight also influence theproject [5 6]

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 7903839 10 pageshttpsdoiorg10115520177903839

2 International Journal of Antennas and Propagation

Δy

Δx

High humidity soilLow humidity soil

Ideal humidity soilSensor node

Figure 1 Representation of sensors arranged in a humiditymap thatpresents data by color

Due to the lack of specific models or parameters forthe existing models in this type of application this articlepresents an experimental study of the path loss found ingrape plantations based on a in loco measurement campaignClassical literature models were chosen and the parametersvalues were obtained empirically From these values dis-cussions regarding the results have been performed Theobjective of the research was to analyze the communicationchannel predict the path loss and evaluate the effects of thepropagation phenomena on the signal intensity

Based on the experiments performed in the same farmduring several weeks it has been noticed that the mainplantation aisles favor the guided propagation On the otherhand there was a considerable amount of vegetation alongthe secondary plantation aisles which compromised thepropagation Measurements taken following a diagonal pathin relation to the main aisle have shown that diffractionby the grape trees is the main propagation mechanismTransmission carried out above the vineyard with bothtransceivers above it has shown that reflection on the top ofthe trees is the main mechanism

This paper is organized as follows Section 2 presentsrelated works in the area of WSNs in agriculture Section 3presents theoretical concepts regarding the propagationmechanisms Section 4 shows the environment under studyThe measurements are discussed in Section 5 Conclusionsand future works are presented in Section 6

2 Wireless Sensor Networks and Agriculture

The literature presents some works that deal with WSNapplied to the agriculture which motivated this researchThe system proposed in [3] was developed for large-scaleagricultural environments using static sensor nodes withtwo goals to collect information from newborn animalsand to collect measurements of soil moisture The nodesautomatically read moisture data from the soil typically inintervals of one minute for each node Then the data isaggregated at the base to generate an updated profile for theentire pasture

In [7] software and hardware for deployment of a WSNin Washington State have been developed There are twonetworks one to measure regional temperature and oneto monitor plantation freezing In the regional network amaster node is configured with multiple repeaters to builda backbone The proposed network monitors the plantationand uses star topology The biggest problems were encoun-tered when the energy management and the switches weredamaged during storms

The Lofar Agro Project [8] has been developed tomonitormicroclimates in plantationsThe purpose ofmonitoring is tocombat the Phytophthora infestans bacteria that attack potatoThe authors comment that humidity is an important factorin the development of diseases A sensor network monitorsin addition to the humidity the temperature and whether ornot the leaves are wet which are the main factors related tothe Phytophthora infestation The communications networkhas a weather station that measures light air pressureprecipitation wind direction and strength

Studies were performed in a cornfield [9] to evaluatethe propagation characteristics with the IRIS CrossbowInc nodes The influence of antenna height the differentdirections within the planting area the weather conditions(sunny day and rainy day) and transmitted power wereconsidered All factors were evaluated for the worst caseplantation with maximum height maximum width of thestems and long thick leaves It was possible to identify theconditions for increasing the coverage area by the sensornodes

AWSNwas implemented to estimate the amount of waterin the crop from the observed signal attenuation [10] Thenodes are deployed with the objective of collecting the signalFrom the mean value of the power measured by the sensornodes the amount of water is estimated from the propagationmodel proposed by the authorsThe advantage of thismethodis that the sensors are not required to obtain data

Some studies using ZigBee are presented in [11ndash13] In[11] an irrigation control system to optimize water usageis presented In [12] a framework is proposed to monitorhumidity temperature and lighting to control water con-sumption in agricultural areas A WSN was developed in[13] using two modifications to the grid topology to improvenetwork performance

3 Theoretical Background

The WSNs suffer from various types of transmitted signaldegradation In wireless systems the signal is attenuated inthe path between the transmitter and receiver according tothe characteristics of the environment in which the elec-tromagnetic wave propagates These features include terraindeformations obstacles between the antennas and vegetationdensity In addition several propagation mechanisms influ-ence the signal propagation such as reflection scatteringrefraction and diffraction [14]

31 Classical Propagation Models The path loss is caused bythe dissipation of power radiated by the transmitter as well asby the effects of the propagation channel [15] It can be defined

International Journal of Antennas and Propagation 3

as the power loss between the transmitter and receiver in aradio communication link

There are two ways to model the path loss [16] apriori modeling and measurement-based modeling A priorimodels are appropriate for predicting path loss in placeswhere it is difficult to performmeasurementsThe path loss ispredicted using only a priori knowledge The measurement-based models are related to methods to collect data andpredict values of signal strength at locations where datacannot be collected

311 Free Space Propagation In free space it is possible todevise a model with a flexible path loss exponent [16] forideal isotropic antennas The power (in dBm) at the receptoris given by

119875119903 = 119875119905 + 119866119905 + 119866119903 + 20 log (120582) minus 10 log (161205872)minus 10120572 log (119889) minus 10 log (119871) (1)

in which 119875119905 is the transmitted power 119866119905 and 119866119903 are the trans-mitter and receiver gains respectively 120582 is the wavelength ofthe transmitted signal 119889 is the distance between transmitterand receiver and 119871 is the system loss The parameter 120572 isadjusted using the least squares or least absolute residualregression models for example [17]

312 Ground ReflectionModel Theground reflectionmodelor the plane earth model [18 19] is an a priori model Itconsiders a direct and a reflected ray with no obstaclesbetween the transmitter and the receiver The path loss isgiven by [19]

119871 = minus10 log(119866119905119866119903 ℎ2119905ℎ21199031198894 ) (2)

in which 119866119905 and 119866119903 are the transmitter and receiver gainsrespectively ℎ119905 and ℎ119903 are the heights of the antennas of thetransmitter and the receiver respectively and119889 is the distancebetween transmitter and receiver

313 Log-Distance Model The log-distance model attenu-ation parameter 119899 is obtained empirically It is used forenvironments with shadowing and the received power isgiven by [20]

119875119903 = 119875 (1198890) minus 10119899 log( 1198891198890) + 119883 (3)

in which 119875(1198890) is the average power measured at a referencedistance usually taken at 1 meter 119899 is the distance lossexponent and 119883 is a Gaussian random variable with mean120583 and variance 1205902314 Propagation between Two Parallel Planes The parallelplane guide is formed by two metal planes There is adielectric material in the middle with permittivity 120598 Theelectromagnetic wave propagates inside the structure in the119909 direction (see Figure 2)

x

y

z

d

120598

Figure 2 Waveguide diagram composed of two parallel planes

Depending on the permeability and permittivity it ispossible to have the value of the received power insideparallel planes very close to the received power in free spacefor the same distance that is the power along the parallelplanes is a function of 1198892315 Empirical FoliageModels There are somemodels basedon measurements to predict losses in different types ofvegetation and at different frequenciesThe exponential decaymodel proposed by Weissberger [21] is used when the pathbetween the transmitter and the receiver is full of densevegetation composed of trees with lowhumidityThe loss dueto vegetation is given by [21]

119871 (dB) = 13311989102841198890588 14m lt 119889 le 400m0451198910284119889 0 le 119889 lt 14m (4)

in which119891 is the frequency in GHz and 119889 is the height of thetrees in meters

An ITU-R recommendation was developed from mea-surements performed primarily in the UHF band Thedistance between the transmitter and the receiver must beshorter than 400m to allow the signal to propagate withoutthe formation of a lateral waveThe excess attenuation is givenby

119871 (dB) = 021198910311988906 (5)

in which 119891 is the frequency and 119889 is the distanceAccording to these models it is possible to verify that

the excess loss due to vegetation can be represented by theexpression [22]

119871 (dB) = 119860119891119861119889119862 (6)

From measurements taken in the environment the param-eters 119860 119861 and 119862 can be obtained using optimizationtechniques to reduce the least square error

32 Link Budget The link budget [14] is used to obtain thesignal strength at the receiver considering all path lossesbetween the transmitter and receiver The received poweraccounting for all gains and losses is given by

119875119903 = 119875119905 + 119866119905 minus 119871path + 119866119903 (7)


in which 119875119903 is the received power in dBm 119875119905 is the power ofthe transmitter 119866119905 is the transmitter gain 119871path is the totalpath loss and 119866119903 is the gain of the receptor

4 Environments

The plantation studied covers an area of approximately 10hectares and its average height is 2 meters For this structuretree trunks and wires are used to support the leaves andgrapes in order to uniformize the height of the crop Thisstructure is called a vineyard as can be seen in Figure 3

Four height and position terminal settings have beenidentified within the plantation which result in differentdominant propagation mechanisms The first case is whenthe terminals are below the vegetation top and positioned inthe type A aisle The second case occurs when the terminalsare below the vegetation top positioned in the type B aisleWhen the terminals are below the top and there are obstaclesbetween the transmitter and the receiver the third case ischaracterized Finally the fourth case occurs when bothterminals are above the crop Figure 6 presents the superiorview in which type A aisle is also used as a reference axis

The type A aisle is characterized mainly by the followingfeatures

(i) The aisle is formed by the vines and stems which areevenly spaced on both sides

(ii) The aisle is almost entirely covered by the leaves of thevines

(iii) Vegetation along the aisle has a maximum height of40 cm

(iv) There are areas where the ground vegetation has 5 cmheight

Type A aisle is presented in Figure 3 The distance betweenthe vines is around 3m and there is a larger amount ofvegetation since the vegetation along type B aisle grows toa height of 90 cm approximately (Figure 4) There are alsoground elevations along the rows Furthermore there is alarge quantity of grapes throughout the path as shown inFigure 5 There are areas where the vegetation is about 5 cmheight

The diagonal environment is similar to the environmentdescribed for the type B aisle except for the tree trunks posi-tioned between the two devices There is a lot of vegetationand there are elevations along the rows There are grapesbetween nodes and there exist areas where the vegetation isabout 5 cm high The vegetation that covers most of the areais supported by wire by trunks of vines and wooden stakes

41 Methodology The experiments described in this sectionwere performed in the Minuano farm located 70 km fromPetrolina city in the state of Pernambuco Brazil The climateis classified as tropical semiarid with low rainfall ratesthroughout the year favoring the production of grapesBesides the scarcity and irregularity of rainfall the rains occurmainly in the summer and there is strong evaporation asa result of the high temperatures The average temperatureduring the experiments was 36∘C

Figure 3 Photo of the vineyard used for the experiments

Figure 4 Photos of type B aisle vegetation in the Vineyard used forthe tests

Figure 5 Photo of grapes along type B aisle

Stem

Refe

renc

e Axi

s (Ty

pe A

aisle

)

1 2 3

4

t

Figure 6 Superior view of the plantation with the lines used toguide the measurements following the diagonals


A pair of XBee ZB Pro S2B nodes was used The deviceshave +18 dBmof output powerminus102 dBm sensitivity specifiedby the manufacturer and the operating frequency is 24GHzThe antenna is one dipole type Both devices presented thesame specifications except that one was connected to anotebook so that the data could be stored in a database Thisterminal was configured as a coordinator

One of the terminals (endpoint) was kept at the sameposition and the other one (coordinator node) was strate-gically positioned along the plantation At each point thecoordinator node requires one Received Signal StrengthIndicator (RSSI) package of the endpoint The measurementprocedure was as follows

(1) The coordinator (transmitter) is connected to a note-book and positioned at a distance of 1 meter fromendpoint

(2) The coordinator sends one package to the endpointrequiring it to calculate the RSSI

(3) The endpoint transmits the package with the com-puted value

(4) Repeat steps (3) and (4) one hundred times(5) This procedure is repeated at different distances until

the power is low enough or the plantation fence isreached

(6) Data are analyzed using Gnuplot and MATLAB(7) One propagation model is chosen and adjusted for

each case

411 Measurements The measurements taken along type Aaisle were performedwith the nodes positioned in themiddleof the aisle The receiver was installed at a height of 1m Firstthe transmitter was installed at a height of 20 cm above theground One hundred signal intensity measurements weremade at intervals of 50 meters The experiment was repeatedwith the transmitter positioned at heights of 40 cm 60 cmand 1m These measurements were taken during the ldquoinleaverdquo plantation stage

Other measurements were performed for different stagesof the plantation at a height of 1m The transmitter wasplaced along type A aisle when the plantation did not haveany leaves only the wires that supported them covered thetop of the plantation In a second round of measurementsdata were collected during the ldquoin fruitrdquo plantation stage

At a distance of 400m the end of the plantation wasreached However comparing the power value at that dis-tance with the sensitivity specified by the manufacturer it isnoticed that the range is larger than 400m Any aisles longenough to perform themeasurements beyond 400mhave notbeen found in this plantation

Along type B aisle measurements were performed withthe nodes positioned in the middle of the aisle The end-device was kept at a fixed position at a height of 1m Thetransmitter was installed at different heights such as in typeA aisle 20 cm 40 cm 60 cm and 1m It has been foundin preliminary experiments that the range in this case isabout 390m One hundred signal strength measurements

Figure 7 Diagram which represents the position of sensor nodesabove the plantation

were made at intervals of 25m instead of 50m to betterobserve the signal decay behavior

As in type A aisle measurements were limited due to thesize of the plantation to a distance of 200m Using a directcomparison between the power at the distance of 200m andthe device sensitivity (minus102 dBm) one realizes that the rangegoes beyond 200mHowever no type B aisle long enoughwasfound to perform measurements beyond 200m

For the diagonal case the measurements were performedfollowing some angles as shown in Figure 6 The end-device was kept in a fixed position with a height of 1m Thetransmitter is installed first at a height of 20 cm above theground One hundred signal strength measurements weremade following the dashed lines forming 15 30 45 and 75degrees (lines 1 2 3 and 4 of Figure 6 resp) with type A aisleThe experiment was repeated with the transmitter at heightsof 40 cm 60 cm and 1m

In some positions when the signal strength was aroundminus97 dBm the communication was not established It wasnecessary to make several attempts until the data could becollected Furthermore in this case the range is smaller thantype A and type B aisles This is an expected result becausethere are obstacles between the transmitter and the receiver

Measurements performed with the coordinator above theplantation were performed as illustrated in Figure 7 Theend-device was installed at a height of 3m positioned in themiddle of the aisle Then the coordinator was moved alongtype A aisle at a height of 3m

412 Least Absolute Residual Method The least absoluteresidual (LAR) method was used to adjust the curves Itminimizes the sum of the deviation modules The advantageof this method is that it is more robust against outliers [17]

Considering 119910119894 the power and 119909119894 the distance for theunidimensional case the method consists of determining 1205730parameter in

119910119894 = 1205730 + 120598119894 (8)

so that the absolute sum of the errors is minimized

min1205730

119899sum119894=1

10038161003816100381610038161205981198941003816100381610038161003816 = min1205730

119899sum119894=1

1003816100381610038161003816119910119894 minus 12057301003816100381610038161003816 (9)


The value of 1205730 that minimizes the sum is the sample medianwhich explains the decrease of the outliers contribution Forlinear regression

119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)

1205730 and 1205731 parameters are calculated using linear program-ming to minimize [17]

min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)

5 Interpretation of Measurements

In order to measure the goodness of the model adjustmentsthe Root Mean Square Error (RMSE) has been used [17]

RMSE = radic(sum119873119894=1 (119909119894 minus 119894)2)119873 (12)

in which119873 is the number of points in the sample and 119909119894 and119894 are the measured and predicted values respectivelyThe determination coefficient 1198772 is also used as a metric

in the study of regression and is given by [23]

1198772 = Explained VariationTotal Variation

= sum119873119894=1 (119909119894 minus 119909)2sum119873119894=1 (119894 minus 119909)2 (13)

The total variance is the sum of the squares of thedifferences between the measured value and the average ofthe measured values The explained variance is the sum ofsquares of the differences between each predicted value andthe average of the measured values This measure indicateshow good is the regression that is how much the regressionline approaches the collected dataThe coefficient 1198772 is in therange [0 1] The closer to one the better the regression linedescribes the behavior of the data

51 Type A Aisle Figure 8 shows the measurements of typeA aisle for Friis free space and plane earth models withoutcorrection factors The vertical axis represents the averagereceived power in dBm and the horizontal axis represents thedistance between antennas

The models were chosen for the first analysis becausethere are no obstacles between the terminals It is observedhowever that the signal strength decay does not follow theplane earthmodel One can verify this statement by averagingthe differences between the value predicted by the plane earthmodel and themeasured valueThus the average gain is equalto 787 dB Table 1 presents the RMSE values

From the curves and RMSE values it seems that thegeometry of the plantation favors the guided propagationof the wave This fact is evidenced mainly by the RMSEvalue for free space that is lower than the plane earthmodel Graphically it is also possible to notice this behaviorHowever a dependency on the height is identified caused bythe reflected ray at 119889 = 100m (limit of the first Fresnel zone)In addition two adjustments of the theoretical models were

0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1

hc = 20 cmhc = 40 cmhc = 60 cmhc = 1m

hc = 02

hc = 04hc = 06

Figure 8 Received power (dBm) as a function of distance and Friisfree space and plane earth models for type A aisle (linear scale fordistance)

Table 1 RMSE for Friis free space and plane earth models for typeA aisle

Model height RMSE (dBm)Friis 97914Plane earth 1 meter 256181Plane earth 60 cm 211751Plane earth 40 cm 236352Plane earth 20 cm 288378

made using the LAR method in MATLAB The exponents ofdistance for both free space and the plane earth model wereadjusted to minimize the RMSE Changing the plane earthmodel since the decay is not proportional to 119889minus4

119875119903 = 119875119905 + 119866119905 + 119866119903 + 20 log (ℎ119905) + 20 log (ℎ119903)minus 10119899 log (119889) (14)

in which 119899 is the adjusted distance exponent The valuesobtained for the exponents are presented in Table 2 with theRMSE values for each case The values of 119875119905 119866119905 and 119866119903 areprovided by the XBee manufacturer and are equal to 18 dBm21 dB and 21 dB respectively

It can be seen from Table 2 that the Friis model with theadjusted exponent has an exponent close of two with littleimprovement of the RMSE Regarding the plane earthmodelthe RMSE decreases indicating a better fit but the decay isnot proportional to the fourth power of the distance Figure 9presents the curves with the adjusted exponents

Figure 2 shows the results for measurements done fordifferent stages of the plantation at the height of 1m Both ldquoinfruitrdquo and ldquoin leaverdquo cases are characterized by the waveguideeffect although mainly because of spreading caused by the


Table 2 Friis free space and plane earthmodels RMSEwith adjustedexponents for type A aisle

Model height Exponent (119899) RMSE (dBm) 1198772Friis 187 935 095Plane earth 1 meter 329 696 098Plane earth 60 cm 325 695 099Plane earth 40 cm 325 628 096Plane earth 20 cm 325 668 094

50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

Plane earth (hr = 1m)Measurements (hr = 20 cm)Measurements (hr = 40 cm)Measurements (hr = 60 cm)Measurements (hr = 1m)

Plane earth (hr = 20 cm)Plane earth (hr = 40 cm)Plane earth (hr = 60 cm)

Figure 9 Received power (dBm) as a function of distance for Friisfree space and plane earth models with adjusted exponents for typeA aisle (linear scale for distance)

water in the fruits the attenuation is greater for the ldquoin fruitrdquocase When the wave guide is unset that is when there areno leaves on top of the plantation the signal power decaysmuch faster and the plane earth model does not fit well Asthe measurements do not have a logarithmic behavior thelinear regression was used instead the following expressionhas been obtained

119875119903 = minus3982 minus 01978119889 (15)

This result can be explained by spreading and absorptionof the electromagnetic field caused by the wires Table 3presents the exponents of the models It is important tohighlight the difference of 036 between ldquoin fruitrdquo and ldquoinleaverdquo adjustments The corresponding plot of the receivedpower (dBm) as a function of the distance is presented inFigure 10

52 Type B Aisle As type B aisle is characterized by a higherdensity of vegetation scattering and absorption cause lossesthat cancel the canalization effect In Figure 11 it can be

Table 3 RMSE of the models used for different plantation statesalong type A aisle

Model Exponent (119899) RMSE (dBm) 1198772Plane earth in fruit 365 692 095Plane earth in leave 329 696 098Linear no leaves 01978 177 099

20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450

Measurements (in fruit)Measurements (no leaves)Measurements (in leave)Plane earth (n = 367)

Plane earth (n = 4)Plane earth (n = 325)Linear (n = 01978)

Figure 10 Received power (dBm) as a function of distance fordifferent stages (in leave in fruit and no fruit) of the plantation(linear scale for distance)

seen that the decay is faster for short distances and asthe transmitter moves away from the receiver the powerdecays slowly indicating a logarithmic behavior Thereforethe log-distance model was used with some modificationsThe attenuation is given by

119860 = 10119899 log( 1198891198890) + 119883 (16)

in which 119889 is the distance 1198890 is the reference distance takenat 1 meter and 119899 is obtained from the LAR method 119883 is aGaussian random variable with zero mean

One modification is the substitution of 119875(1198890) by 119875119905 +119866119905 +119866119903119860 = 119875119905 + 119866119905 + 119866119903 minus 119875119903 = 119862 minus 119875119903 (17)

in which 119862 is given by

119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)

As this work does not address the small-scale fading the 119883termdoes not appear in the adjusted equationsTherefore thereceived power is given by

119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)

The value of 119899 is obtained from the LAR method imple-mentation provided by MATLAB and is equal to 4537 The


0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

Logarithmic adjustment

minus20

minus40

minus60

minus80

minus100

Measurements (hr = 20 cm)

Measurements (hr = 1m)Measurements (hr = 60 cm)Measurements (hr = 40 cm)

Figure 11 Received power (dBm) as a function of distance andadjusted logarithmic equation (linear scale for distance)

resulting RMSE is equal to 3567 and 1198772 equals 09399 Thecurve obtained is shown in Figure 11 with the distance in alinear scale

Another option to adjust the curves is to use an equationthat includes the height so that the model provides moreparameters and lower RMSE Start from the following expres-sion

119875119903 = (119875 (1198890) + 119891 (ℎ119903)) minus 119899119889 (20)in which 119875(1198890) is the power at the reference distance (1meter) 119891(ℎ119903) is expressed as a function of the receiverdistance 119899 is a constant and 119889 is the distance The valuesof 119875(1198890) + 119891(ℎ119903) and 119899 are obtained using the LAR methodConsidering ℎ119903 = 1m the reference height it is possible toobtain the following formula for ℎ119903 = 1

119875119903 = minus3982 minus 02115119889 (21)Therefore 119875(1198890) + 119891(ℎ119903) = minus3982 Following the same stepsfor other heights

119875 (1198890) + 119891 (ℎ119903) = minus4143 para ℎ119903 = 060119875 (1198890) + 119891 (ℎ119903) = minus4516 para ℎ119903 = 040119875 (1198890) + 119891 (ℎ119903) = minus4817 para ℎ119903 = 020

(22)

The adjusting equation chosen for 119891(ℎ119903) was119891 (ℎ119903) = 119886119890119887ℎ119903 (23)

in which 119886 and 119887 are obtained using the LARmethod and areequal to minus1207 and minus241 respectively It was possible to finda complete equation given by

119875119903 = 119875 (1198890) minus 119899119889 + 119891 (ℎ119903)119875119903 = minus3969 minus 02115119889 minus 1207119890minus241ℎ119903

(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110

Linear adjustment (hr = 1)Linear adjustment (hr = 06)Linear adjustment (hr = 04)Linear adjustment (hr = 02)

Measurements (hr =1m)Measurements (hr = 60 cm)Measurements (hr = 40 cm)Measurements (hr = 20 cm)

Figure 12 Received power (dBm) as a function of distance and theadjusted linear equation (linear scale for distance)

Table 4 RMSE and 1198772 of the adjusted linear equation

Receptor height RMSE (dBm) 1198772ℎ119903 = 1m 243 097ℎ119903 = 060 cm 220 098ℎ119903 = 040 cm 290 096ℎ119903 = 020 cm 464 090

in which 119875(1198890) is the average received power at the referencedistance The graph in linear scale for the distance is shownin Figure 12 Table 4 presents the RMSE and 1198772 values53 Diagonal First a comparison between the Weissbergermodel and the recommendation of the ITU-R for the UHFband regarding all performedmeasurements along the diago-nal has been performedThe equations for this case includingthe excess loss by vegetation are

119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)

in which 119860119890119897 is the attenuation in free space 119891 is thefrequency and119889 is the distanceTheplot of themeasurementsand the model are presented in Figure 13

Although the measurements made by Weissberger havebeen taken in different environments the proposed equationpresents a reasonable fit in this case However in order toreduce the RMSE value the parameters 119860 119861 and 119862 of theexcess attenuation were adjusted In addition the exponentof log-distance model and a linear fit have been determinedThe curves for the adjustedmodels are presented in Figure 14


20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)

Diagonal measurementsWeissberger modelITU-R recommendation

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

Figure 13 Received power (dBm) as a function of distanceWeissberger and ITU-R equations (linear scale for distance)

Table 5 Parameters RMSE values and 1198772 for Weissberger andlogarithmic and linear equations

Model Parameters RMSE (dBm) 1198772Modified Weissberger

119860 = 0081098 067119861 = 196119862 = 083

Logarithmic 119899 = 506 269 098Linear 119899 = 036 764 083

Table 5 presents the exponents the RMSE and 1198772 valuesobtained

54 Terminals above the Vineyard When the two terminalsare above the plantation the electromagnetic field is reflectedon the top of the plantation structure formed by the metallicwires and leaves Thus the plane earth model is usedconsidering the heights of the nodes equal to 1m insteadof 3m (3m for the total height from the ground minus 2mheight of the piles) In this situation until a distance of 100meters is reached the propagation occurs in free space sincethe clearance of the route is larger than 06119877 in which119877 is theradius of the first Fresnel zone

For measurements taken up to a 100 meters the gaprelative to the top structure is approximately 06119877 that isthe plane earth and free space model leads to the sameattenuation value For this distance the main propagationmechanism is the plane earth with the reflected ray on thetop of the plantation The RMSE for the plane earth modelwith the adjusted exponent equals 564 The value of theexponent is equal to 4017 The graph of Figure 15 showsthe measurements collected with the terminals above theplantation following type A aisle and Friis and plane earthmodels

0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)

Diagonal measurementsWeissberger model modifiedLogarithmic adjustmentLinear adjustment

minus20

minus40

minus60

minus80

minus100

minus120

Figure 14 Received power (dBm) as a function of distance mod-ified Weissberger model and linear and log-distance adjustments(linear scale for distance)

0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)

Friis modelPlane earth model

minus20

minus40

minus60

minus80

minus100

Measurements (h1 = 3m h2 = 3m)

Figure 15 Received power (dBm) as a function of distance Friis freespace and plane earthmodels for the case in which the terminals areabove the plantation (linear scale for distance)

6 Conclusions and Future Works

This paper presents a study of path loss in grape plantationsfor a 24GHz operating frequencyThemain contributions ofthis research are the identification and interpretation of thepropagation phenomena in the studied environment as wellas the methodology adopted to obtain the data parametersThe researched environment has characteristics that favorcertain propagation mechanisms depending on the situation

The region was divided into four areas characterized bydifferent dominant propagation mechanisms Type A aisle


is free of obstacles and forms a structure that favors thepropagation as a parallel plate waveguide although thereis a dependence of height In type B aisle scattering andabsorption caused by vegetation which is denser increase thesignal attenuation compared with the propagation along typeA aisle

The diagonal propagation is affected by multiple diffrac-tion around the trunks of vines which raises the distanceexponent When the two transmitters are above the planta-tion the top structure reflects the signal

It can be noticed that for this case the simplest clas-sical literature models present a good fit and give a goodexplanation of what happens in this type of environmentOn the other hand based on the results future directionsfor the research were identified For example it is importantto obtain a mathematical model for propagation throughvegetation in situations in which canalization occurs and todevelop amathematicalmodel for propagation in agriculturalenvironments with obstacles considering as a parameter theradius of the tree trunks and their disposal on the plantation

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Copele CAPES CNPq andIecom for supporting this research

References

[1] W Maohua ldquoPossible adoption of precision agriculture fordeveloping countries at the threshold of the new millenniumrdquoComputers and Electronics in Agriculture vol 30 no 1ndash3 pp45ndash50 2001

[2] Aqeel-Ur-Rehman A Z Abbasi N Islam and Z A ShaikhldquoA review of wireless sensors and networksrsquo applications inagriculturerdquo Computer Standards and Interfaces vol 36 no 2pp 263ndash270 2014

[3] T Wark P Corke P Sikka et al ldquoTransforming agriculturethrough pervasive wireless sensor networksrdquo IEEE PervasiveComputing vol 6 no 2 pp 50ndash57 2007

[4] J P R Lima and E A AMiranda ldquoFruticultura irrigada no valedo Sao Francisco incorporacao tecnologica competitividade esustentabilidaderdquo Revista Economica do Nordeste vol 32 pp611ndash632 2001

[5] M S Alencar and V C Rocha Jr Communication SystemsSpringer 2005

[6] M D Yacoub Foundations of Mobile Radio Engineering CRCPress Boca Raton Fla USA 1st edition 1993

[7] F J Pierce and T V Elliott ldquoRegional and on-farmwireless sen-sor networks for agricultural systems in Eastern WashingtonrdquoComputers and Electronics in Agriculture vol 61 no 1 pp 32ndash43 2008

[8] A Baggio ldquoWireless sensor networks in precision agriculturerdquoTech Rep Delft University of Technology Delft The Neder-land 2009

[9] S Li and H Gao ldquoPropagation characteristics of 24GHzwireless channel in cornfieldsrdquo in Proceedings of the IEEE 13thInternational Conference on Communication Technology (ICCTrsquo11) pp 136ndash140 IEEE Jinan China September 2011

[10] J C Giacomin F H Vasconcelos and E J D Silva ldquoEstimatingvegetation water content with wireless sensor network com-munication signalsrdquo in Proceedings of the IEEE Instrumentationand Measurement Technology (IMTC rsquo07)mdashSynergy of Scienceand Technology in Instrumentation and Measurement WarsawPoland May 2007

[11] Aqeel-ur-Rehman Z A Shaikh H Yousuf F Nawaz MKirmani and S Kiran ldquoCrop irrigation control using wirelesssensor and actuator network (WSAN)rdquo in Proceedings of the2nd International Conference on Information and EmergingTechnologies (ICIET rsquo10) pp 1ndash5 Karachi Pakistan June 2010

[12] G Ali A W Shaikh Aqeel-ur-Rehman and Z A Shaikh ldquoAframework for development of cost-effective irrigation con-trol system based on Wireless Sensor and Actuator Network(WSAN) for efficient water managementrdquo in Proceedings ofthe 2nd International Conference on Mechanical and ElectronicsEngineering (ICMEE rsquo10) vol 2 pp 378ndash381 IEEE Kyoto JapanAugust 2010

[13] M Keshtgari andADeljoo ldquoAwireless sensor network solutionfor precision agriculture based on zigbee technologyrdquo WirelessSensor Network vol 4 no 1 pp 25ndash30 2012

[14] J S Seybold Introduction toRFPropagation JohnWileyampSonsHoboken NJ USA 2005

[15] A GoldsmithWireless Communications CambridgeUniversityPress New York NY USA 1st edition 2005

[16] C Phillips D Sicker and D Grunwald ldquoA survey of wirelesspath loss prediction and coverage mapping methodsrdquo IEEECommunications Surveys amp Tutorials vol 15 no 1 pp 255ndash2702013

[17] Y Dodge The Concise Encyclopedia of Statistics Springer NewYork NY USA 1st edition 2008

[18] W C Y Lee Mobile Communications Engineering McGraw-Hill New York NY USA 1st edition 1982

[19] W C Y Lee Mobile Communications Design FundamentalsJohn Wiley amp Sons Hoboken NJ USA 2nd edition 1993

[20] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall Upper Saddle River NJ USA 2nd edition2002

[21] M A Weissberger ldquoAn initial critical summary of models forpredicting the attenuation of radio waves by foliagerdquo TechRep ECAC-TR-81-101 Eletromagnetic Compatibility AnalysisCenter Annapolis Md USA 1981

[22] Y S Meng Y H Lee and B C Ng ldquoEmpirical near groundpath loss modeling in a forest at VHF and UHF bandsrdquo IEEETransactions on Antennas and Propagation vol 57 no 5 pp1461ndash1468 2009

[23] F Larson Estatıstica Aplicada Pearson Prentice Hall Sao PauloBrazil 4th edition 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Δy

Δx

High humidity soilLow humidity soil

Ideal humidity soilSensor node

Figure 1 Representation of sensors arranged in a humiditymap thatpresents data by color

Due to the lack of specific models or parameters forthe existing models in this type of application this articlepresents an experimental study of the path loss found ingrape plantations based on a in loco measurement campaignClassical literature models were chosen and the parametersvalues were obtained empirically From these values dis-cussions regarding the results have been performed Theobjective of the research was to analyze the communicationchannel predict the path loss and evaluate the effects of thepropagation phenomena on the signal intensity

Based on the experiments performed in the same farmduring several weeks it has been noticed that the mainplantation aisles favor the guided propagation On the otherhand there was a considerable amount of vegetation alongthe secondary plantation aisles which compromised thepropagation Measurements taken following a diagonal pathin relation to the main aisle have shown that diffractionby the grape trees is the main propagation mechanismTransmission carried out above the vineyard with bothtransceivers above it has shown that reflection on the top ofthe trees is the main mechanism

This paper is organized as follows Section 2 presentsrelated works in the area of WSNs in agriculture Section 3presents theoretical concepts regarding the propagationmechanisms Section 4 shows the environment under studyThe measurements are discussed in Section 5 Conclusionsand future works are presented in Section 6

2 Wireless Sensor Networks and Agriculture

The literature presents some works that deal with WSNapplied to the agriculture which motivated this researchThe system proposed in [3] was developed for large-scaleagricultural environments using static sensor nodes withtwo goals to collect information from newborn animalsand to collect measurements of soil moisture The nodesautomatically read moisture data from the soil typically inintervals of one minute for each node Then the data isaggregated at the base to generate an updated profile for theentire pasture

In [7] software and hardware for deployment of a WSNin Washington State have been developed There are twonetworks one to measure regional temperature and oneto monitor plantation freezing In the regional network amaster node is configured with multiple repeaters to builda backbone The proposed network monitors the plantationand uses star topology The biggest problems were encoun-tered when the energy management and the switches weredamaged during storms

The Lofar Agro Project [8] has been developed tomonitormicroclimates in plantationsThe purpose ofmonitoring is tocombat the Phytophthora infestans bacteria that attack potatoThe authors comment that humidity is an important factorin the development of diseases A sensor network monitorsin addition to the humidity the temperature and whether ornot the leaves are wet which are the main factors related tothe Phytophthora infestation The communications networkhas a weather station that measures light air pressureprecipitation wind direction and strength

Studies were performed in a cornfield [9] to evaluatethe propagation characteristics with the IRIS CrossbowInc nodes The influence of antenna height the differentdirections within the planting area the weather conditions(sunny day and rainy day) and transmitted power wereconsidered All factors were evaluated for the worst caseplantation with maximum height maximum width of thestems and long thick leaves It was possible to identify theconditions for increasing the coverage area by the sensornodes

AWSNwas implemented to estimate the amount of waterin the crop from the observed signal attenuation [10] Thenodes are deployed with the objective of collecting the signalFrom the mean value of the power measured by the sensornodes the amount of water is estimated from the propagationmodel proposed by the authorsThe advantage of thismethodis that the sensors are not required to obtain data

Some studies using ZigBee are presented in [11ndash13] In[11] an irrigation control system to optimize water usageis presented In [12] a framework is proposed to monitorhumidity temperature and lighting to control water con-sumption in agricultural areas A WSN was developed in[13] using two modifications to the grid topology to improvenetwork performance

3 Theoretical Background

The WSNs suffer from various types of transmitted signaldegradation In wireless systems the signal is attenuated inthe path between the transmitter and receiver according tothe characteristics of the environment in which the elec-tromagnetic wave propagates These features include terraindeformations obstacles between the antennas and vegetationdensity In addition several propagation mechanisms influ-ence the signal propagation such as reflection scatteringrefraction and diffraction [14]

31 Classical Propagation Models The path loss is caused bythe dissipation of power radiated by the transmitter as well asby the effects of the propagation channel [15] It can be defined








119871 = minus10 log(119866119905119866119903 ℎ2119905ℎ21199031198894 ) (2)



119875119903 = 119875 (1198890) minus 10119899 log( 1198891198890) + 119883 (3)


x

y

z

d

120598



119871 (dB) = 13311989102841198890588 14m lt 119889 le 400m0451198910284119889 0 le 119889 lt 14m (4)



119871 (dB) = 021198910311988906 (5)



119871 (dB) = 119860119891119861119889119862 (6)



119875119903 = 119875119905 + 119866119905 minus 119871path + 119866119903 (7)



4 Environments














Stem

Refe

renc

e Axi

s (Ty

pe A

aisle

)

1 2 3

4

t











each case













119910119894 = 1205730 + 120598119894 (8)


min1205730

119899sum119894=1

10038161003816100381610038161205981198941003816100381610038161003816 = min1205730

119899sum119894=1

1003816100381610038161003816119910119894 minus 12057301003816100381610038161003816 (9)



119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)


min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)












0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1


hc = 02

hc = 04hc = 06












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119871 = minus10 log(119866119905119866119903 ℎ2119905ℎ21199031198894 ) (2)



119875119903 = 119875 (1198890) minus 10119899 log( 1198891198890) + 119883 (3)


x

y

z

d

120598



119871 (dB) = 13311989102841198890588 14m lt 119889 le 400m0451198910284119889 0 le 119889 lt 14m (4)



119871 (dB) = 021198910311988906 (5)



119871 (dB) = 119860119891119861119889119862 (6)



119875119903 = 119875119905 + 119866119905 minus 119871path + 119866119903 (7)



4 Environments














Stem

Refe

renc

e Axi

s (Ty

pe A

aisle

)

1 2 3

4

t











each case













119910119894 = 1205730 + 120598119894 (8)


min1205730

119899sum119894=1

10038161003816100381610038161205981198941003816100381610038161003816 = min1205730

119899sum119894=1

1003816100381610038161003816119910119894 minus 12057301003816100381610038161003816 (9)



119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)


min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)












0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1


hc = 02

hc = 04hc = 06












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











4 Environments














Stem

Refe

renc

e Axi

s (Ty

pe A

aisle

)

1 2 3

4

t











each case













119910119894 = 1205730 + 120598119894 (8)


min1205730

119899sum119894=1

10038161003816100381610038161205981198941003816100381610038161003816 = min1205730

119899sum119894=1

1003816100381610038161003816119910119894 minus 12057301003816100381610038161003816 (9)



119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)


min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)












0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1


hc = 02

hc = 04hc = 06












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















each case













119910119894 = 1205730 + 120598119894 (8)


min1205730

119899sum119894=1

10038161003816100381610038161205981198941003816100381610038161003816 = min1205730

119899sum119894=1

1003816100381610038161003816119910119894 minus 12057301003816100381610038161003816 (9)



119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)


min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)












0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1


hc = 02

hc = 04hc = 06












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119910119894 = 1205730 + 1205731119909119894 + 120598119894 (10)


min119899sum119894=1

1003816100381610038161003816119910119894 minus 1205730 minus 12057311199091198941003816100381610038161003816 (11)












0

20

40

50 100 150 200 250 300 350 400 450

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80

minus100

hc = 1


hc = 02

hc = 04hc = 06












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












50 100 150 200 250 300 350 400 450

0

20

40

Sign

al p

ower

(dBm

)

Distance (meters)

Friis model

minus20

minus40

minus60

minus80





119875119903 = minus3982 minus 01978119889 (15)





20

40

Sign

al p

ower

(dBm

)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0

Distance (meters)50 100 150 200 250 300 350 400 450





119860 = 10119899 log( 1198891198890) + 119883 (16)




119862 = 119875119905 + 119866119905 + 119866119903 = 222 dBm (18)


119875119903 = 119875119905 + 119866119905 + 119866119903 minus 10119899 log (119889) dBm (19)



0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)


minus20

minus40

minus60

minus80

minus100









(22)




(24)

50 100 150 200 250

Sign

al p

ower

(dBm

)

Distance (metros)

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100

minus110







119875119903 = 119860119890119897 minus 13311989102841198890588119875119903 = 119860119890119897 minus 021198910311988906 (25)




20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

minus100




119860 = 0081098 067119861 = 196119862 = 083





0

20

40

20 40 60 80 100 120 140 160 180 200

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100

minus120


0

20

40

100 200 300 400 500

Sign

al p

ower

(dBm

)

Distance (meters)


minus20

minus40

minus60

minus80

minus100










Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Propagation Analysis for Wireless Sensor Networks Applied...

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