Analysis and simulation of nakagami fading channel with ... - faraday

Analysis and Simulation of Nakagami Fading Channel withMATLAB*Li Tang Zhu Hongbo(Dept. of Communication Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210003,CHINA, Email: litango1 @sina.com)Abstract: The paper simulated and analyzed thestatistical perfomances of the Nakagami fadingchannel in wireless communication with MATLAB,including the complex envelop of received signal, theLevel Crossing Rates and Average Fade Durations onthe Maximal-Ratio Combining diversity.Key words: Multipath channel, Nakagami fading,MATLAB Simulation, Combining diversity1. IntroductionThe first work to researching and developing ofdigital mobile communication engineering isunderstanding mobile channel characteristics itself. Inthe propagation environment of digital mobilecommunication, the signal received by the mobilemay consist of a large number of multipath componentdue to reflection, diffkaction and scattering betweenthe transmitter and the receiver. The randomlydistributed phase, amplitudes, and angles of arrival ofmultipath component combine at the receiver give aresultant signal strength which can changes rapid overa small travel distance and be named fast fading.When there is no LOS component between mobileand BS, received signal consist of reflection andscattering wave from different directions and followRayleigh distribution. When there is a dominantstationary signal component present, the small-scalefading envelop distribution is Ricean. Rayleigh fadingmodels are frequently utilized in simulating highfrequency signals propogating in an ionosphericchannel. However, Rayleigh fading falls short indescribing long-distance fading effects with sufficientaccuracy. This fact was first observed by Nakagami,who then formulated a parametric gammadistribution-based density function, to describe theexperimental data he obtained. It was then showed bymany researchers using real-life data that the modelproposed by Nakagami provides a better explanationto less and more severe conditions than the Rayleighand Ricean model and provides a better fit to themobile communication channel data['].Because Nakagami fading could representvarious fading condition in wireless channel, sosimulation and analysis of the statistical characters ofthe Nakagami fading channel are very important. Thispaper made use of MATLAB to simulate and analyzeThis work was supported by the National Natural ScienceFoundation of China (No. 6993 1030)490the complex envelop of received signal, theLevel Crossing Rates arid Average Fade Durations onthe Maximal-Ratio Combining diversity. Theimportant issue in this paper is to develope a methodto simulation fading channel using MATLAB andcomprehend the statistical performances of Nakagamichannel.2. Simulating the statistical charactersof Nakagami fading channel modelwith MATLAB;2.1 Multipath Fading Channel ModelsWe first give the theoretic PDF of Rayleigh andhcean fading and their relations to Nakagamiprobability distribution parameters in order to analyzeand compare both states. Assuming that the receiver ismoving relative to the transmitter, and there is no LOScomponent, then the received signal can be expressedsr,y ('1 =Ni=lai ~ ~ ~ ( + u~ cd t t + , #i) (1)Where W, is carrier fiequency, ai and #; are theamplitude and phase of ith arrival path, phase #iareuniformly distributed over [072z] .W Vw,, = C COS viis the Doppler shift of ith reflectedCof scattering wave, where vi is the angle relative tothe direction of motion of the antenna and assumedare uniformly distributed over [O72z],when N isvilarge, the probability density function of the receivedsignal envelope can be shown to be Rayleigh, whenthere exist a line-of-sight(L0S) component betweenthe transmitter and the receiver, the received signalcan be expressed as random multipath componentssuperimposed on a domnant signal., i.e.[21.+ p COS(W,t 4- W,t]where the constant p is the strength of the directcomponent, W, is the Doppler shift along the LOSpath, the envelope, in this case, has a kcian densityfunction. When there not exist a direct signal,

Typical simdated nakagami lading of me camer Receiver speed=80!un%I0.5 1 1.5Vsecfig.2 Simulating received signal envelop when m=1.5(corresponding to Rician distribution) ,a 7 r,/dtI)fig.6 Normalized LCR f!)r m=0.6 ( m=1.5, with diversityorders L= 1,2,3,4,10Twical simulated nakagami lading of me canier Receiver s peed=M3020-20.I4 05 1 15Vsecfig.3 Simulated received signal envelop when m=10(light shadow fading)C F rJdB)fig.7 Normalized AFD for m=0.6 with diversiy ordersL=l,2,3,4,5fig.4 Normalized LCR for m=0.6 with diversity ordersL=l,2,3,4,10fig.8 Normalized AFD for m=l with diversiy ordersL==l,2,3,4,5IO''E3fig.5IT rJdtI)Normalized LCR for m=lwith diversity ordersL=l,2,3,4,10fig.9Normalized AFD for m=l.5 with diversity ordersLa= 1,2,3,4494