research article research on maritime radio wave multipath...

Research ArticleResearch on Maritime Radio Wave Multipath PropagationBased on Stochastic Ray Method

Han Wang1 and Wencai Du12

1College of Information Science amp Technology Hainan University 58 Renmin Avenue Haikou Hainan 570228 China2FITM City University of Macau Choi Kai Yan Building Taipa Macau

Correspondence should be addressed to Wencai Du wencaihainueducn

Received 24 January 2016 Revised 8 May 2016 Accepted 22 May 2016

Academic Editor Yuri Vladimirovich Mikhlin

Copyright copy 2016 H Wang and W DuThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Multipath effect in vessel communication is caused by a combination of reflections from the sea surface and vessels This paperproposes employing stochastic ray method to analyze maritime multipath propagation properties The paper begins by modelingmaritime propagation environment of radio waves as random lattice grid by utilizing maximum entropy principle to calculatethe probability of stochastic ray undergoing k time(s) reflection(s) and by using stochastic process to produce the basic randomvariables Then the paper constructs the multipath channel characteristic parameters including amplitude gain time delay andimpulse response based on the basic random variables Finally the paper carries out a digital simulation in two-dimensionalspecific fishery fleet model environment The statistical properties of parameters including amplitude response probability delaydistribution and power delay profiles are obtained Using these parameters the paper calculates the root-mean-squared (rms)delay spread value with the amount of 964120583s It is a good reference for the research of maritime wireless transmission rate of thevessels It contributes to a better understanding of the causes and effects of multipath effect in vessel communication

1 Introduction

As we know that about 70 of the Earth surface is coveredby the ocean waters and over 90 of the worldrsquos goods aretransported by merchant fleet over sea Maritime commu-nication plays an important role in many marine activitiessuch as offshore oil exploitation maritime transportationand marine fishery The current maritime communicationsystems mainly include signal sideband (SSB) short-waveradio system VHF radiotelephone coast cellular mobilecommunication network and maritime satellite communi-cation network Maritime VHF radio telephone is mainlyused for ship-to-shore and ship-to-ship voice communicationscenario The transmission distance of the maritime VHFradio is limited to 20 nautical miles Another drawbackof the maritime VHF radio is its lack of support of dataservices Maritime satellite communication systems [1 2]such as the Inmarsat-F systemandFleet-Broadbandmaritimedata service are suitable for ocean sea ship communicationsHowever the satellite communication system is relativelyexpensive due to the high cost of the terminal equipment

and high maintenance and upgrade costs Although theservice fee is high the data transmission rate is far from theuser requirements Consequently maritime communicationswhich can deliver voice and higher data transmission rates arehot topic in current and future research

Generally the approaches to modeling wireless channelpropagation can be divided into two categories statisticalmeasurement and electromagnetic field prediction The for-mer is a mainstream channel modeling methodology whichincludes parametric statisticalmodelingmethod and physicalpropagation modeling method The latter is an approachwhich includes ray method finite difference time domainmethod and moment method Maritime communicationchannel modeling based on statistical measurements ofempirical models has been widely studied The majority ofscholars have utilized measurement and estimation data topredict a particular path loss in mobile channel modelingover sea [3ndash8] In [8] authors have extended the ITU-RP1546-5 as a radio over sea propagation model for investi-gating the path loss curve

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 5178136 7 pageshttpdxdoiorg10115520165178136

2 Mathematical Problems in Engineering

However the analysis of large-scale fading in vesselcommunication environment or ship to shore communi-cation environment cannot reflect the multipath channelcharacteristics where multipath effect should be consideredThe vast majority of small-scale multipath analyses are basedon field measurements [9ndash12] Measurements are carriedout in different sea areas but the conclusions have regionallimitations The finite difference time domain method is alsoadopted in maritime channel modeling [7 13] However thismethod has high calculation costs and requires well-definedcommunication environment

The paper will contribute to technique in modelingwireless channel propagation in the sea The sea surfacereflections and other ships reflections are considered inexploring the multipath rms delay spread in fishery fleetcommunication environment by employing the stochasticray method to measure maritime wireless radio multipathpropagation properties by utilizing lattice grid to describethe maritime fishery fleet propagation scenario and usingBrownian bridge process to construct the basic statisticalproperties of random variables and by numerical simulationto obtain the rms delay spread value This study providesstochastic ray channel modeling method that can effectivelyevaluate the maritime multipath propagation channel

The rest of this paper is organized as follows Section 2describes the stochastic ray theory and its probability distri-bution Maritime random radio wave propagation multipathstatistical characteristics are given in Section 3 The simu-lation and analysis are presented in Section 4 Finally theconclusion is presented in Section 5

2 Stochastic Ray Theory andIts Probability Distribution

In the analysis of wireless channel propagation themultipatheffect under the unknown environment should be taken intoconsideration Due to the complexity and sensitivity of thewireless propagation environment and the requirements ofa stochastic channel model no-wave approach is utilizedin the practical electromagnetic engineering [14] In [1516] the propagation environment is modeled as a randomdistribution of point scatters Stochastic ray method is usedto analyze the propagation process Researches [14ndash17] showthat stochastic ray method is an effective method to studythe characteristics of urban wireless multipath propagationchannel

21 Stochastic Bridge Process The process where a numberof rays emitted from the source after a multihop randomwalk reach the destination is called beammultipath diffusionprocessThe formal mathematical definition of this process isgiven with Definition 1

Definition 1 For all 0 le 119905 le 119879 if the trajectory of stochasticprocess 119884(119905 120596) passing through two fixed points 119903

0 1199031

where 119884(119905 120596) | 119884(0 120596) = 1199030 119884(119879 120596) = 119903

1 1199030 1199031isin 119877 0 le

100

200

300

400

500

600

700

800

900

1000

Tx

Rx

Y(m

)

100 200 300 400 6000 700 800 900 1000500X (m)

Figure 1Themaritime stochastic rays propagation in lattice whereTx is a transmitter and Rx is a receiver

119905 le 119879 the process is called stochastic bridge process denotedby 119884119879119903101199030

(119905 120596) It can be formulated as

1198841198791199031

01199030

(119905 120596) = 1199030+ 119883 (119905 120596) minus

119905

119879[119883 (119879 120596) minus 119903

1+ 1199030] (1)

where 119883(119905 120596) is a stochastic process with the starting pointat the source point

22 Random Lattice Channel The authors in [14] proposedan idea for modeling of the urban propagation environmentas a random lattice The percolation theory was exploited inthe domain of channel modeling for the first time Consider afinite array (see Figure 1)made of square sites with side of unitlengthThe status (occupied or empty) of a cell is independentof the status of all other cells in the lattice and assume thatempty probability is 119901 and the occupancy probability is 119902 =

1 minus 119901 Given a very large lattice randomly occupied withprobability 119902 percolation theory deals with the quantitativeanalysis of groups of neighboring empty sites (clusters) formaverage size number and so forth For modest values of 119901(say 119901 near zero) the average dimension of clusters is smallwhile for 119901 near unity the lattice looks like a single clusterwith sporadic holes As 119901 grows the dimension of the emptyclusters grows as well Clearly for 119901 = 1 the whole latticeis empty There exists a threshold level 119901

119888asymp 059275 at

which the lattice appearance suddenly changes for 119901 gt 119901119888

a single empty cluster that spans the whole lattice formswhile for 119901 lt 119901

119888all empty clusters are of finite size Near

the percolating threshold the characteristics of the 119901-latticechange qualitatively the system exhibits a phase transitionThere exists an average distance among the closed clusters inthe site percolation with given 119901 denoted by 119889 = 119886radic1 minus 119901where 119886 is the cell side length of lattice

Mathematical Problems in Engineering 3

In [14ndash16] percolation lattices are used for description ofthe propagation in urban areas The conclusion is supportedby field measurements in literatures In this paper we cannotdirectly use the original lattice channel theory Therefore weadapt it to comply withmaritime propagation channelmodel

Let us consider the following example In May 2013 afleet of 30 fishery vessels departs from Hainan provinceDanzhou city carrying out fishing activities in China SpratlyIslands The weight of each fishery vessel is above 100 tonsTaking this example into consideration we create a two-dimensionalmaritime propagationmodelMaritime stochas-tic ray propagation in lattice is presented in Figure 1Maritimefishing fleet environment is assumed in two-dimensionalequally spaced square gridTheblack irregular grids representfishery vessels There are 30 irregular grids which gives theoccupancy probability of the lattice The entire fishing fleet isin the scale of 1000m times 1000m

23 The Probability Distribution of Stochastic Rays at Two-Dimensional Propagation Space after Undergoing 119896 Time(s)Reflection(s) Since the propagation environment is modeledas a random grid channel let us assume that the transmitter isplaced at (0 0) and after 119896 time(s) reflection(s) the receiveris placed at (119909 119910) the arriving ray undergoing 119896 time(s)reflection(s) among all the rays has a probability we denoteit by 119891(119909 119910) Under certain constraints using the maximumentropy principle we can get the probability expression

A probability density function 119875(119909 119910) Shannon entropyis defined as below

119867(119875) = minus∬119909119910

119875 (119909 119910) log10

1003816100381610038161003816119875 (119909 119910)1003816100381610038161003816 119889119909 119889119910 (2)

where 119875(119909 119910) satisfies (denoted by C1) (i) 119875(119909 119910) ge 0119909 119910 isin 119877 (ii) ∬

119909119910119875(119909 119910)119889119909 119889119910 = 1 and (iii) ∬

119909119910120588(119909

119910)119875(119909 119910)119889119909 119889119910 = 119863119896 In (iii) 120588(119909 119910) is the Euclidean

distancemetric119863119896is the average distance associatedwith the

reflections

Proposition 2 The Shannon maximum entropy 119891(119909 119910)which is described by formula (2) and satisfies condition C1can be expressed as

119891 (119909 119910) = 119888119890120578120588(119909119910)

(3)

where 119888 and 120578 are constants Proposition 2 has been proved in[18]

Proposition 3 In the two-dimensional Euclidean distancemetric under the constraint ∬

119909119910radic1199092 + 1199102119875(119909 119910)119889119909 119889119910 =

119863119896 the probability of arrival of the stochastic rays at a special

spatial location after 119896 time(s) reflection(s) 119891(119903 120579) satisfies

119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

) (4)

where 119903 = radic1199092 + 1199102 120579 is the azimuth angle The averagedistance of reflections is

119863119896= 119889119896120573 (5)

where 119889 is the average distance between obstacles We considerwave propagation process as diffusion process When 120573 = 05it indicates normal diffusion process when 120573 lt 05 it indicatesanomalous diffusion process

Proof of Proposition 3 Let 120582 = 119890120578 we have 119888119890120578120588(119909119910) = 119888120582

120588(119909119910)and let 119891(119909 119910) = 119891

0120582radic1199092+1199102

Since∬119909119910119891(119909 119910)119889119909 119889119910 = 1 we

have

∬119909119910

1198910120582radic1199092+1199102

119889119909 119889119910 = ∬119903120579

1198910120582119903119903 119889119903 119889120579

= 1198910int

2120587

0

119889120579int

infin

0

119903120582119903119889119903

= 21205871198910int

infin

0

119903120582119903119889119903

(6)

Let 120594 = intinfin

0119903120582119903119889119903 we have 120594 = 1(ln 120582)2 2120587119891

0(ln 120582)2 = 1

and 120582 = exp(minusradic21205871198910) Since 120582 lt 1

119891 (119903) = 1198910exp(minusradic2120587119891

0119903)

int

2120587

0

int

infin

0

1199031198910exp(minusradic2120587119891

0119903) 119903 119889119903 119889120579 = int

2120587

0

1198910119889120579

sdot int

infin

0

1199032 exp(minusradic2120587119891

0119903) 119889119903

= 21205871198910int

infin

0

1199032 exp (minusradic2120587119891

0119903) 119889119903 = minus

1

radic21205871198910

sdot int

infin

0

(radic21205871198910119903)

2

exp (minusradic21205871198910119903) 119889 (radic2120587119891

0119903)

=1

radic21205871198910

int

infin

0

1199112119890minus119911119889119911 = minus

1

radic21205871198910

Γ (3) =2

radic21205871198910

= 119863119896

1198910=

2

1205871198632119896

119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

)

(7)

In three-dimensional environment we set the Euclideandistance 119903 = radic1199092 + 1199102 + 1199112 In this case the average distancetraveled by a ray in 119896 time(s) reflection(s)119863

119896 is

119863119896= ∭

119909119910119911

radic1199092 + 1199102 + 1199112119891 (119909 119910 119911) 119889119909 119889119910 119889119911 (8)

Then we have a corollaryIn the three-dimensional Euclidean distance metric

under the constraint of (8) the probability of arrival of thestochastic rays at a special spatial location after 119896 time(s)reflection(s) 119891(119903 120579 120593) satisfies

119891 (119903 120579 120593) =27

412058721198633

119896

exp(minus 3119903

119863119896

) (9)

The proof of this corollary is similar to Proposition 3


100 200 300 400 500 600 700 8000Distance between Tx and Rx (m)

k = 1

k = 2

k = 3

times10minus5

0

02

04

f(r)

06

08

1

12

Figure 2 The arrival probability density curve after 119896 time(s)reflection(s)

By (4) and (5) we can draw the two-dimensional stochas-tic ray probability distribution Figure 2 shows the arrivalprobability density curve after 119896 time(s) reflection(s) where119903 = 800m 119889 asymp 200m and 120573 = 05 It can be seenthat 119891(119903) decreases with the increase of the distance Morereflections can cause lower arrival probability When thedistance changes to a certain value the ray arrival probabilitybecomes very small In fact when 119896 is more than threethe reflected ray arrival rate is negligible In the followinganalysis we consider the case where the maximum numberof reflections is two

3 Maritime Random Radio Wave PropagationMultipath Statistical Characteristics

31 Brownian Bridge Process Constructsthe Basic Random Variables

Definition 4 119882(119905 120596) is standard Brownian motion if thestochastic process 119884(119905 120596) satisfies

1198841198791199091

01199090

= 1199090+119882(119905 120596) minus

119905

119879[119882 (119879 120596) minus 119909

1+ 1199090]

forall0 le 119905 le 119879

(10)

then we call it as Brownian bridge process which travelsthrough two fixed points 119909

0 1199091

Thus the Euclidean distance of 119894 hops Brownian bridgesamples in 119871-dimensional space can be expressed as

119885119894=

119894

sum

119896=0

119871

sum

119897=1

[119884119897(119905119896+1

120596) minus 119884119897(119905119896 120596)]2

12

(11)

To simplify the analysis we omit 120596 the Euclidean dis-tance of each hop in 119871-dimensional space can be expressedas

Δ119885119896=

119871

sum

119897=1

[119884119897(119905119896+1

) minus 119884119897(119905119896)]2

12

=

119871

sum

119897=1

[119882119897(119905119896+1

) minus 119882119897(119905119896) minus

119882119897(119894)

119894+ 1199091minus 1199090]

2

12

=

119871

sum

119897=1

[1198850+ 1199091minus 1199090]2

12

(12)

where 1198850= 1198851minus1198852 1198851 1198852sim 119873(0 120590

2) (12) can be rewritten

as

Δ119885119896=

119871

sum

119897=1

1198852

12

(13)

where 119885 sim 119873(1199091minus 1199090 21205902) distribution function 119873 means

the normal distribution We define 119885119894as the Euclidean

distance of 119894 hops in 119871-dimensional space

119885119894=

119894

sum

119896=1

Δ119885119896 (14)

32 Amplitude Gain of Multipath We define the amplitudegain of the 119894119895multipath component as below [14]

119886119894119895= exp(

minus1198952120587119885119894119895

120582) 10minus(120)[sum

119894

119896=0119871119894119895119896+(1minus120575(119894))119871

119886]119885minus1198992

119894119895

119885119894119895gt 1

(15)

where 119894 is the reflection number of themultipath componentsduring its propagation process 119894 = 0 1 119895 is the 119895thmultipath component undergoing 119894 time(s) reflection(s) 119896is the 119896 time(s) reflection(s) 119896 = 0 1 119894 120582 is the carriedfrequency 119899 is path loss parameter 119871

119894119895119896is the loss caused by

119896 time(s) reflection(s) from the 119894119895 multipath component andscatterer random variable (dB) 119871

119894119895119896sim 119873(119871

111 (11987111110)2)

119871119886is the loss due to the direction of antennas 120575(119894) is Dirac

delta function 119885119894119895is the path length of the 119894119895 multipath

component

33Multipath TimeDelay Themultipath time delay of 119895pathreflected 119894 time(s) is

120591119894119895=119885119894119895

119888 (16)

where 119885119894119895is the path length of the 119894119895 multipath component

and 119888 is the propagation speed of electromagnetic wave

34 The Impulse Response of Stochastic Multipath ChannelThe small-scale variations of a radio signal can be directly


related to the impulse response of the radio channel Theimpulse response is a channel characterization and containsall information necessary to simulate or analyze any type ofradio transmission through the channel

In (15) and (16) we give the amplitude gain of themultipath 119886

119894119895 and the time delay 120591

119894119895 A channel impulse

response is given as follows which can be used to calculatepower delay profile of the channel

ℎ (119905 120591) =

119873

sum

119894=0

119872119894

sum

119895=1

119886119894119895120575 (119905 minus 120591

119894119895) (17)

where 119873 is the reflection time and 119872119894is the number of 119894

time(s) reflection(s) multipathsUsing the stochastic ray method to establish maritime

multipath channel model is described through a flow chartFigure 3 shows the flow chart of establishing maritimemultipath channel model The process includes 6 main steps

4 Simulation Results and Analysis

A thorough literature search has been performed on thedistributions of multipath delay and amplitude gain ofmultipath The main conclusions are that the multipathdelay distribution meets Poisson distribution and that theamplitude gain of multipath satisfies classical distributionssuch as Rayleigh and Rice distribution In this paper weutilize stochastic raymethod to study themaritimemultipathdelay distribution and other maritime multipath statisticalcharacteristics

In order to develop some general design guidelines forwireless systems main quantifying parameters of the multi-path channel are used such as the mean excess delay and rmsdelay spread They are regarded as important factors for thedesign of the radio communication links Moreover they areused for measurement of system performance degradationdue to intersymbol interference In this paper we firstlyanalyze the impulse response of the maritime multipathchannel ℎ(119905 120591) the power delay profile of the channel is foundby taking the spatial average of |ℎ(119905 120591)|2 then the two channelparameters (mean excess delay and rms delay spread) can bedetermined from a power delay profile

The simulation parameters are given as below the trans-mitter is located at (300 800) the receiver is located at(800 200) and the distance 119909

1minus 1199090

asymp 800m as shownin Figure 1 Assuming that there are maximum two timesreflections and a total number of 50 multipaths where 119896 = 2119872119894= 50 In 119885 sim 119873(119909

1minus 1199090 21205902) we set 120590 = 30 the

purpose of this 120590 value is to make sure that the randomray reflection trace length is slightly greater than 800mThisparameter choice would comply to the physical propagationenvironment depicted in Figure 1

Figure 4 shows the probability density curve of multipathdelay time It can be found that the distribution is similar tononcentral Laplace bilateral distribution The magnitude ofthe multipath delay is in microsecond range The maximumprobability has occurred in 120591 = 75 120583s Obtained resultscomply with measurements results given in [11 12] the

Establishing a two-dimensional maritime propagationenvironment model (geometric description and obstaclereflection information) locating the transmitterreceiverlocation

Selecting a stochastic bridge process (such as Brownian

Generating stochastic rays selecting the maximumreflection times and the total number of effective rays

Calculating the time delay of multipaths calculating theamplitude gain of multipaths

Calculating the impulse response of maritime stochasticmultipath channel obtaining its power delay profiles

Getting the time dispersive properties of maritime multipathchannels

bridge process) to produce a suitable sample function ofthe trajectory of the maritime multipath components

Figure 3The flow chart of establishingmaritimemultipath channelmodel

multipath delay magnitude is consistent with the experiencevalue

In the simulation of the amplitude gain we assume thatsignal propagates in sea-free space 120582 = 950MHz 119871

119894119895119896sim

119873(3 (03)2) 119871119886= 0 dB and 119899 = 2 The probability density

function of the amplitude gain of the multipath fading isshown in Figure 5

Figure 6 shows the impulse response of the stochasticmultipath channel We can find that the trend of multipathintensity is decreasing With the delay time increase themultipath intensity becomesweaker In the range of 0 to 20 120583sthe multipath signals have stronger intensity

For small-scale channel modeling power delay profile isdefined as the power at the given time delayThe power delayprofile of the channel 119875(120591) is found by taking the spatialaverage of |ℎ(119905 120591)|2 over a local area By this method we canbuild an ensemble of power delay profiles Figure 7 gives thepower delay profiles of the stochastic multipath channel


0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)

Figure 4 The probability density curve of multipath delay time

0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij

Figure 5 The probability density curve of amplitude gain ofmultipath

Channel impulse response

10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de

Figure 6 The impulse response of stochastic multipath channel

Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)

Figure 7 The power delay profiles of stochastic multipath channel

The time dispersive properties of multipath channels aremost commonly quantified by their mean excess delay (120591)and rms delay spread (120590

120591) The mean excess delay is the

first moment of the power delay profiles and describes thedegree of dispersion of the multipath signal It is definedwith 120591 = sum

119872119875(120591119872)120591119872sum119872119875(120591119872) The rms delay spread is

the square root of the second central moment of the powerdelay profiles It describes the additional delay of the standard

deviation and is defined to be 120590120591= radic1205912 minus (120591)

2 where 1205912 =sum119872119875(120591119872)1205912

119872sum119872119875(120591119872) These two parameters are of great

significant for designing the communication system data rateand receiver By calculation we get the two parameters valueswhere 120591 = 895 120583s and 120590

120591= 964 120583s A common rule of

thumb in a communication system design is to employ aproper symbol duration much larger than the average rmsdelay spread to avoid performance degradation due to theintersymbol interference

5 Conclusion

The present study provides the application of stochastic raymethod to measure maritime radio wave propagation multi-path statistical characteristics taking Hainan fishery fleet asa reference We establish a two-dimensional maritime prop-agation environment model the fishery vessels are modeledas irregular obstacles We draw the flow chart of establishingmaritime multipath channel model Through analyzing ofthe probability of the amplitude gain of multipath and timedelay we obtain the impulse response of stochastic multipathchannel Then the time dispersive properties of multipathchannels mean excess delay (120591) and rms delay spread (120590

120591)

are calculated Mean excess delay and rms delay spread arethe two significant maritime multipath channel parametersFinally we get the conclusion that the values of rms delayspread are on the order of microseconds in maritime fisheryfleet radio wave channels


Competing Interests

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

Acknowledgments

This work is supported by Hainan University ExcellentPaper Cultivation Plan and the International Science andTechnology Corporation Plan organized by the Ministry ofScience and Technology of China Grant no 2015DFR10510the National Natural Science Foundation of China Grant no61561017 and Hainan Province Natural Science Foundationof China Grant no 20166217

References

[1] L E Braten M Rytir and P A Grotthing ldquoOne year of20GHz satellite measurement data from a nordic maritimeenvironmentrdquo in Proceeding of the 9th European Conference onAntennas and Propagation pp 1ndash5 Lisbon Portugal April 2015

[2] F Clazzer A Munari M Berioli et al ldquoOn the characterizationof AIS traffic at the satelliterdquo in Proceeding of OCEANS Confer-enceOceanic Engineering Society andMarine Technology Societypp 1ndash9 Taipei Taiwan April 2014

[3] K Maliatsos P Constantinou P Dallas and M IkonomouldquoMeasuring and modeling the wideband mobile channel forabove the sea propagation pathsrdquo in Proceedings of the 1stEuropean Conference on Antennas and Propagation (EuCAPrsquo06) pp 1ndash6 Nice France November 2006

[4] I J Timmins and S OrsquoYoung ldquoMarine communications chan-nel modeling using the finite-difference time domain methodrdquoIEEE Transactions on Vehicular Technology vol 58 no 6 pp2626ndash2637 2009

[5] K Yang T Roslashste F Bekkadal and T Ekman ldquoChannelcharacterization including path loss and Doppler effects withsea reflections for mobile radio propagation over sea at 2GHzrdquo in Proceedings of the International Conference onWirelessCommunications and Signal Processing (WCSP rsquo10) pp 1ndash6IEEE Suzhou China October 2010

[6] W Hubert Y-M Le Roux M Ney and A Flamand ldquoImpact ofship motions on maritime radio linksrdquo International Journal ofAntennas and Propagation vol 2012 Article ID 507094 6 pages2012

[7] F Huang Y Bai and W Du ldquoMaritime radio propagation withthe effects of ship motionsrdquo Journal of Communications vol 10no 5 pp 345ndash351 2015

[8] H Wang W Du and X Chen ldquoEvaluation of radio over seapropagation based ITU-R recommendation P1546-5rdquo Journalof Communications vol 10 no 4 pp 231ndash237 2015

[9] K Maliatsos P Loulis M Chronopoulos P Constantinou PDallas and M Ikonomou ldquoExperimental small scale fadingresults for mobile channels over the seardquo in Proceedings of theIEEE 17th International Symposium on Personal Indoor andMobile Radio Communications (PIMRC rsquo06) pp 1ndash5 HelsinkiFinland September 2006

[10] J C Reyes-Guerrero and L A Mariscal ldquoExperimental timedispersion parameters of wireless channels over sea at 58 GHzrdquoin Proceedings of the 54th International Symposium (ELMARrsquo12) pp 89ndash92 Zadar Croatia September 2012

[11] K Yang T Roste F Bekkadal and T Ekman ldquoExperimentalmultipath delay profile of mobile radio channels over seaat 2GHzrdquo in Proceedings of the Loughborough Antennas andPropagation Conference (LAPC rsquo12) pp 1ndash4 LoughboroughUK November 2012

[12] K-B Kim J-H Lee S-O Park and M Ali ldquoExperimentalstudy of propagation characteristic for maritime wireless com-municationrdquo in Proceedings of the 17th International Symposiumon Antennas and Propagation (ISAP rsquo12) pp 1481ndash1484 IEEENagoys Japan November 2012

[13] JMansukhani and S Chakrabarti ldquoSmall scale characterizationof marine channel using the finite-difference time domainmethodrdquo in Proceedings of the 3rd International Conferenceon Computing Communication and Networking Technologies(ICCCNT rsquo12) pp 1ndash7 Coimbatore India July 2012

[14] G Franceschetti S Marano and F Palmieri ldquoPropagationwithout wave equation toward an urban area modelrdquo IEEETransactions on Antennas and Propagation vol 47 no 9 pp1393ndash1404 1999

[15] S Marano andM Franceschetti ldquoRay propagation in a randomlattice amaximumentropy anomalous diffusion processrdquo IEEETransactions on Antennas and Propagation vol 53 no 6 pp1888ndash1896 2005

[16] A Martini M Franceschetti and A Massa ldquoStochastic raypropagation in stratified random latticesrdquo IEEE Antennas andWireless Propagation Letters vol 6 pp 232ndash235 2007

[17] L-QHu Z-BWang andH-B Zhu ldquoApplications of stochasticbridge processes tomodeling space-time characteristics of shortrange wireless propagation channelsrdquo Journal of Electronics andInformation Technology vol 29 no 8 pp 1934ndash1937 2007

[18] T M Cover and J A Thomas Elements of Information Theorychapter 11 Wiley New York NY USA 1991

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Algebra

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


However the analysis of large-scale fading in vesselcommunication environment or ship to shore communi-cation environment cannot reflect the multipath channelcharacteristics where multipath effect should be consideredThe vast majority of small-scale multipath analyses are basedon field measurements [9ndash12] Measurements are carriedout in different sea areas but the conclusions have regionallimitations The finite difference time domain method is alsoadopted in maritime channel modeling [7 13] However thismethod has high calculation costs and requires well-definedcommunication environment

The paper will contribute to technique in modelingwireless channel propagation in the sea The sea surfacereflections and other ships reflections are considered inexploring the multipath rms delay spread in fishery fleetcommunication environment by employing the stochasticray method to measure maritime wireless radio multipathpropagation properties by utilizing lattice grid to describethe maritime fishery fleet propagation scenario and usingBrownian bridge process to construct the basic statisticalproperties of random variables and by numerical simulationto obtain the rms delay spread value This study providesstochastic ray channel modeling method that can effectivelyevaluate the maritime multipath propagation channel

The rest of this paper is organized as follows Section 2describes the stochastic ray theory and its probability distri-bution Maritime random radio wave propagation multipathstatistical characteristics are given in Section 3 The simu-lation and analysis are presented in Section 4 Finally theconclusion is presented in Section 5

2 Stochastic Ray Theory andIts Probability Distribution

In the analysis of wireless channel propagation themultipatheffect under the unknown environment should be taken intoconsideration Due to the complexity and sensitivity of thewireless propagation environment and the requirements ofa stochastic channel model no-wave approach is utilizedin the practical electromagnetic engineering [14] In [1516] the propagation environment is modeled as a randomdistribution of point scatters Stochastic ray method is usedto analyze the propagation process Researches [14ndash17] showthat stochastic ray method is an effective method to studythe characteristics of urban wireless multipath propagationchannel

21 Stochastic Bridge Process The process where a numberof rays emitted from the source after a multihop randomwalk reach the destination is called beammultipath diffusionprocessThe formal mathematical definition of this process isgiven with Definition 1

Definition 1 For all 0 le 119905 le 119879 if the trajectory of stochasticprocess 119884(119905 120596) passing through two fixed points 119903

0 1199031

where 119884(119905 120596) | 119884(0 120596) = 1199030 119884(119879 120596) = 119903

1 1199030 1199031isin 119877 0 le

100

200

300

400

500

600

700

800

900

1000

Tx

Rx

Y(m

)

100 200 300 400 6000 700 800 900 1000500X (m)

Figure 1Themaritime stochastic rays propagation in lattice whereTx is a transmitter and Rx is a receiver

119905 le 119879 the process is called stochastic bridge process denotedby 119884119879119903101199030

(119905 120596) It can be formulated as

1198841198791199031

01199030

(119905 120596) = 1199030+ 119883 (119905 120596) minus

119905

119879[119883 (119879 120596) minus 119903

1+ 1199030] (1)

where 119883(119905 120596) is a stochastic process with the starting pointat the source point

22 Random Lattice Channel The authors in [14] proposedan idea for modeling of the urban propagation environmentas a random lattice The percolation theory was exploited inthe domain of channel modeling for the first time Consider afinite array (see Figure 1)made of square sites with side of unitlengthThe status (occupied or empty) of a cell is independentof the status of all other cells in the lattice and assume thatempty probability is 119901 and the occupancy probability is 119902 =

1 minus 119901 Given a very large lattice randomly occupied withprobability 119902 percolation theory deals with the quantitativeanalysis of groups of neighboring empty sites (clusters) formaverage size number and so forth For modest values of 119901(say 119901 near zero) the average dimension of clusters is smallwhile for 119901 near unity the lattice looks like a single clusterwith sporadic holes As 119901 grows the dimension of the emptyclusters grows as well Clearly for 119901 = 1 the whole latticeis empty There exists a threshold level 119901

119888asymp 059275 at

which the lattice appearance suddenly changes for 119901 gt 119901119888

a single empty cluster that spans the whole lattice formswhile for 119901 lt 119901

119888all empty clusters are of finite size Near

the percolating threshold the characteristics of the 119901-latticechange qualitatively the system exhibits a phase transitionThere exists an average distance among the closed clusters inthe site percolation with given 119901 denoted by 119889 = 119886radic1 minus 119901where 119886 is the cell side length of lattice






119867(119875) = minus∬119909119910

119875 (119909 119910) log10

1003816100381610038161003816119875 (119909 119910)1003816100381610038161003816 119889119909 119889119910 (2)


119909119910119875(119909 119910)119889119909 119889119910 = 1 and (iii) ∬

119909119910120588(119909



reflections


119891 (119909 119910) = 119888119890120578120588(119909119910)

(3)



119909119910radic1199092 + 1199102119875(119909 119910)119889119909 119889119910 =



119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

) (4)


119863119896= 119889119896120573 (5)



120588(119909119910)and let 119891(119909 119910) = 119891

0120582radic1199092+1199102

Since∬119909119910119891(119909 119910)119889119909 119889119910 = 1 we

have

∬119909119910

1198910120582radic1199092+1199102

119889119909 119889119910 = ∬119903120579

1198910120582119903119903 119889119903 119889120579

= 1198910int

2120587

0

119889120579int

infin

0

119903120582119903119889119903

= 21205871198910int

infin

0

119903120582119903119889119903

(6)


0119903120582119903119889119903 we have 120594 = 1(ln 120582)2 2120587119891

0(ln 120582)2 = 1


119891 (119903) = 1198910exp(minusradic2120587119891

0119903)

int

2120587

0

int

infin

0

1199031198910exp(minusradic2120587119891

0119903) 119903 119889119903 119889120579 = int

2120587

0

1198910119889120579

sdot int

infin

0

1199032 exp(minusradic2120587119891

0119903) 119889119903

= 21205871198910int

infin

0

1199032 exp (minusradic2120587119891

0119903) 119889119903 = minus

1

radic21205871198910

sdot int

infin

0

(radic21205871198910119903)

2


0119903)

=1

radic21205871198910

int

infin

0

1199112119890minus119911119889119911 = minus

1

radic21205871198910

Γ (3) =2

radic21205871198910

= 119863119896

1198910=

2

1205871198632119896

119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

)

(7)


119896 is

119863119896= ∭

119909119910119911

radic1199092 + 1199102 + 1199112119891 (119909 119910 119911) 119889119909 119889119910 119889119911 (8)



119891 (119903 120579 120593) =27

412058721198633

119896

exp(minus 3119903

119863119896

) (9)




k = 1

k = 2

k = 3

times10minus5

0

02

04

f(r)

06

08

1

12






1198841198791199091

01199090

= 1199090+119882(119905 120596) minus

119905

119879[119882 (119879 120596) minus 119909

1+ 1199090]

forall0 le 119905 le 119879

(10)


0 1199091


119885119894=

119894

sum

119896=0

119871

sum

119897=1

[119884119897(119905119896+1

120596) minus 119884119897(119905119896 120596)]2

12

(11)


Δ119885119896=

119871

sum

119897=1

[119884119897(119905119896+1

) minus 119884119897(119905119896)]2

12

=

119871

sum

119897=1

[119882119897(119905119896+1

) minus 119882119897(119905119896) minus

119882119897(119894)

119894+ 1199091minus 1199090]

2

12

=

119871

sum

119897=1

[1198850+ 1199091minus 1199090]2

12

(12)

where 1198850= 1198851minus1198852 1198851 1198852sim 119873(0 120590


as

Δ119885119896=

119871

sum

119897=1

1198852

12

(13)




119885119894=

119894

sum

119896=1

Δ119885119896 (14)


119886119894119895= exp(

minus1198952120587119885119894119895

120582) 10minus(120)[sum

119894

119896=0119871119894119895119896+(1minus120575(119894))119871

119886]119885minus1198992

119894119895

119885119894119895gt 1

(15)




119894119895119896sim 119873(119871

111 (11987111110)2)



component


120591119894119895=119885119894119895

119888 (16)










ℎ (119905 120591) =

119873

sum

119894=0

119872119894

sum

119895=1

119886119894119895120575 (119905 minus 120591

119894119895) (17)








1minus 1199090


1minus 1199090 21205902) we set 120590 = 30 the













119894119895119896sim






0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)


0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij



10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de


Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)








2 where 1205912 =sum119872119875(120591119872)1205912



120591= 964 120583s A common rule of


5 Conclusion


120591)



Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119867(119875) = minus∬119909119910

119875 (119909 119910) log10

1003816100381610038161003816119875 (119909 119910)1003816100381610038161003816 119889119909 119889119910 (2)


119909119910119875(119909 119910)119889119909 119889119910 = 1 and (iii) ∬

119909119910120588(119909



reflections


119891 (119909 119910) = 119888119890120578120588(119909119910)

(3)



119909119910radic1199092 + 1199102119875(119909 119910)119889119909 119889119910 =



119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

) (4)


119863119896= 119889119896120573 (5)



120588(119909119910)and let 119891(119909 119910) = 119891

0120582radic1199092+1199102

Since∬119909119910119891(119909 119910)119889119909 119889119910 = 1 we

have

∬119909119910

1198910120582radic1199092+1199102

119889119909 119889119910 = ∬119903120579

1198910120582119903119903 119889119903 119889120579

= 1198910int

2120587

0

119889120579int

infin

0

119903120582119903119889119903

= 21205871198910int

infin

0

119903120582119903119889119903

(6)


0119903120582119903119889119903 we have 120594 = 1(ln 120582)2 2120587119891

0(ln 120582)2 = 1


119891 (119903) = 1198910exp(minusradic2120587119891

0119903)

int

2120587

0

int

infin

0

1199031198910exp(minusradic2120587119891

0119903) 119903 119889119903 119889120579 = int

2120587

0

1198910119889120579

sdot int

infin

0

1199032 exp(minusradic2120587119891

0119903) 119889119903

= 21205871198910int

infin

0

1199032 exp (minusradic2120587119891

0119903) 119889119903 = minus

1

radic21205871198910

sdot int

infin

0

(radic21205871198910119903)

2


0119903)

=1

radic21205871198910

int

infin

0

1199112119890minus119911119889119911 = minus

1

radic21205871198910

Γ (3) =2

radic21205871198910

= 119863119896

1198910=

2

1205871198632119896

119891 (119903 120579) =2

1205871198632119896

exp(minus 2119903

119863119896

)

(7)


119896 is

119863119896= ∭

119909119910119911

radic1199092 + 1199102 + 1199112119891 (119909 119910 119911) 119889119909 119889119910 119889119911 (8)



119891 (119903 120579 120593) =27

412058721198633

119896

exp(minus 3119903

119863119896

) (9)




k = 1

k = 2

k = 3

times10minus5

0

02

04

f(r)

06

08

1

12






1198841198791199091

01199090

= 1199090+119882(119905 120596) minus

119905

119879[119882 (119879 120596) minus 119909

1+ 1199090]

forall0 le 119905 le 119879

(10)


0 1199091


119885119894=

119894

sum

119896=0

119871

sum

119897=1

[119884119897(119905119896+1

120596) minus 119884119897(119905119896 120596)]2

12

(11)


Δ119885119896=

119871

sum

119897=1

[119884119897(119905119896+1

) minus 119884119897(119905119896)]2

12

=

119871

sum

119897=1

[119882119897(119905119896+1

) minus 119882119897(119905119896) minus

119882119897(119894)

119894+ 1199091minus 1199090]

2

12

=

119871

sum

119897=1

[1198850+ 1199091minus 1199090]2

12

(12)

where 1198850= 1198851minus1198852 1198851 1198852sim 119873(0 120590


as

Δ119885119896=

119871

sum

119897=1

1198852

12

(13)




119885119894=

119894

sum

119896=1

Δ119885119896 (14)


119886119894119895= exp(

minus1198952120587119885119894119895

120582) 10minus(120)[sum

119894

119896=0119871119894119895119896+(1minus120575(119894))119871

119886]119885minus1198992

119894119895

119885119894119895gt 1

(15)




119894119895119896sim 119873(119871

111 (11987111110)2)



component


120591119894119895=119885119894119895

119888 (16)










ℎ (119905 120591) =

119873

sum

119894=0

119872119894

sum

119895=1

119886119894119895120575 (119905 minus 120591

119894119895) (17)








1minus 1199090


1minus 1199090 21205902) we set 120590 = 30 the













119894119895119896sim






0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)


0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij



10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de


Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)








2 where 1205912 =sum119872119875(120591119872)1205912



120591= 964 120583s A common rule of


5 Conclusion


120591)



Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











k = 1

k = 2

k = 3

times10minus5

0

02

04

f(r)

06

08

1

12






1198841198791199091

01199090

= 1199090+119882(119905 120596) minus

119905

119879[119882 (119879 120596) minus 119909

1+ 1199090]

forall0 le 119905 le 119879

(10)


0 1199091


119885119894=

119894

sum

119896=0

119871

sum

119897=1

[119884119897(119905119896+1

120596) minus 119884119897(119905119896 120596)]2

12

(11)


Δ119885119896=

119871

sum

119897=1

[119884119897(119905119896+1

) minus 119884119897(119905119896)]2

12

=

119871

sum

119897=1

[119882119897(119905119896+1

) minus 119882119897(119905119896) minus

119882119897(119894)

119894+ 1199091minus 1199090]

2

12

=

119871

sum

119897=1

[1198850+ 1199091minus 1199090]2

12

(12)

where 1198850= 1198851minus1198852 1198851 1198852sim 119873(0 120590


as

Δ119885119896=

119871

sum

119897=1

1198852

12

(13)




119885119894=

119894

sum

119896=1

Δ119885119896 (14)


119886119894119895= exp(

minus1198952120587119885119894119895

120582) 10minus(120)[sum

119894

119896=0119871119894119895119896+(1minus120575(119894))119871

119886]119885minus1198992

119894119895

119885119894119895gt 1

(15)




119894119895119896sim 119873(119871

111 (11987111110)2)



component


120591119894119895=119885119894119895

119888 (16)










ℎ (119905 120591) =

119873

sum

119894=0

119872119894

sum

119895=1

119886119894119895120575 (119905 minus 120591

119894119895) (17)








1minus 1199090


1minus 1199090 21205902) we set 120590 = 30 the













119894119895119896sim






0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)


0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij



10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de


Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)








2 where 1205912 =sum119872119875(120591119872)1205912



120591= 964 120583s A common rule of


5 Conclusion


120591)



Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















ℎ (119905 120591) =

119873

sum

119894=0

119872119894

sum

119895=1

119886119894119895120575 (119905 minus 120591

119894119895) (17)








1minus 1199090


1minus 1199090 21205902) we set 120590 = 30 the













119894119895119896sim






0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)


0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij



10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de


Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)








2 where 1205912 =sum119872119875(120591119872)1205912



120591= 964 120583s A common rule of


5 Conclusion


120591)



Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

005

01

015

02

025

03

035

04

045

Prob

abili

ty

times10minus665 7 75 8 85 9 95 106

120591 (s)


0

002

004

006

008

01

012

014

016

018

02

Prob

abili

ty

times10minus41 12 14 16 18 2 22 2408

aij



10 20 30 40 50 60 700Delay (120583s)

0

01

02

03

04

05

06

07

Mag

nitu

de


Power delay profile

minus120

minus100

minus80

minus60

minus40

minus20

0

Nor

mal

ized

pow

er (d

Bm)

10 20 30 40 50 60 700Delay (120583s)








2 where 1205912 =sum119872119875(120591119872)1205912



120591= 964 120583s A common rule of


5 Conclusion


120591)



Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Competing Interests


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article research on maritime radio wave multipath...

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