A WIDEBAND RADIO CHANNEL MODEL FOR SIMULATION OF CHAOTIC COMMUNICATION SYSTEMS

Transcription

1 A WIDEBAND RADIO CHANNEL MODEL FOR SIMULATION OF CHAOTIC COMMUNICATION SYSTEMS Kalle Rui, Mauri Honanen, Michael Hall, Timo Korhonen, Veio Porra Insiue of Radio Communicaions, Helsini Universiy of Technology P.O.Box 3, FIN-5 HUT, Finland, E:mail: Absrac - A general purpose wideband radio channel model implemened in MATLAB has been designed specifically for esing he performance of wideband chaoic communicaion sysems uilising a radio inerface. The heoreical basis of he model is presened in he paper, as well as a shor descripion of he MATLAB program and some illusraive examples of he oupu signal under given inpu signal and channel condiions. The channel model is based on a number of imevarying aps modelling he signal dispersion in a mulipah environmen. Generaion of he ap fading process is implemened using a novel mehod based on summaion of a number of complex phasors. I. INTRODUCTION A wideband channel model has been designed in MATLAB a he Helsini Universiy of Technology, based on he experience gained in channel modelling acquired during he years wihin he projec SARF (New Radio Communicaion Sysems and heir RF-echnology) sponsored by he Finnish Academy. The model uses a novel ap generaion mehod, and uilises subrouines wrien in C language in order o imise he speed of he program. This model was originally developed for esing chaoic communicaion sysems, bu conains all he essenial feaures for general purpose wideband channel modeling and simulaion. The chaoic communicaion wideband channel model is based on he apped delay line or FIR (Finie Impulse Response) filer srucure presened in Secion II, which has been used exensively for simulaion of mobile communicaion sysems, regardless he differen radio environmens (indoor, urban, rural, mobile saellie), differen bi raes (several bi/s o several Mbi/s) and differen sysem echnologies (TDMA, CDMA, FDMA) or sysem conceps (GSM, DECT, IS-54, IS-95, UMTS) exising or conceived. Since he channel modeling is performed in equivalen low-pass (ELP) signal domain, processing of complex signals is required. The heoreical bacground of he model is given in Secions II and III. A general ouline of he MATLAB program and some illusraive MATLAB displays of he oupu signal under given inpu signal and channel condiions are presened in Secion IV. Deails of he MATLAB implemenaion are no considered in his paper. II. THE FIR FILTER CHANNEL MODEL A wideband (dispersive) mulipah radio channel is generally characerised in complex equivalen low-pass signal domain by a ime-varian FIR filer, implemened as a apped delay line wih K complex ime-varian ap coefficiens h (), =,,..., K, as shown in Figure. x() T T T h () h () h () h K- () SUMMATION y() Figure : Tapped delay line presenaion of a wideband mulipah radio channel. The channel inpu and oupu signals are x() and y(), respecively. For some modulaion schemes (e.g. binary phase-shif eying, BPSK), x() can be chosen real, whereas he ap coefficiens h () and hus y() are generally complex. The uni ap delay of he model is

2 denoed τ, which mus be an ineger muliple of he sampling inerval T s of he simulaion sysem (ofen τ = T s ). The number of aps K should be chosen such ha ( K ) τ is equal o or larger han he imum anicipaed delay spread of he radio channel o be simulaed. The ap delays need no necessarily be uniformly spaced. For example, in he GSM TU (Typical Urban) six ap channel model he sampling inerval is. µs and he ap delays are a,.,.5,.6,.3 and 5. µs []. A ap delay model wih non-uniform ap delay spacing corresponds o he uniformly spaced ap delay model shown in Figure where a number of aps are simply se o zero. According o he heory of communicaions, he following imporan relaionship mus be saisfied in order o avoid aliasing and unrecoverable signal disorion in he A/D and D/A conversion processes [] τ B where B is he bandwidh of he equivalen low-pass signal x(). To conclude, he signal or sysem bandwidh and imum delay spread ogeher deermine he number of aps required in he channel model. I should be noed ha he ime-varian ap coefficiens (ap gains) h () are complex. The relaionship beween a real rf signal s() and he corresponding complex equivalen low-pass signal (also called he complex envelope) u() is [] () s () = Re u ()exp( jπ f) () c III. MODELLING THE TIME-VARIANT TAP GAIN ( TAP FADING ) In discree ime simulaion programs, he ap coefficiens h () are no ime coninuous, bu are insead sequences of complex samples h i, h() = h, iδ ( its) (4) i= where δ() denoes he Dirac impulse funcion. Since he ime consan characerising he channel variaion in ime domain is orders of magniude larger han he channel ime spread in delay domain (even in highspeed erresrial mobile radio sysems), he ap coefficien samples h i, need o be updaed very infrequenly in erms of T s. Beween successive calculaed updaes, spaced by T, he ap coefficien samples may be inerpolaed uilising some suiable inerpolaion algorihm. The upper limi of T is se by he imum Doppler shif expeced in he channel (see below). Lie all ime or frequency variables, T mus be specified in erms of T s in he MATLAB simulaion model. The Doppler frequency of a propagaion pah, ν, is relaed o he linear velociy of moion of he mobile saion V, he rf wavelengh λ, and he angle α beween he direcion of moion and he received pah, in he following way (see Figure ) ν = V cos α (5) λ reflecor where f c is he rf carrier frequency. If x() is he ELP inpu signal, he corresponding ELP oupu signal y() from he wideband radio channel characerised by is imevarian ELP impulse response h( τ, ) is obained hrough convoluion ] K y ( ) = h( τ, x ) ( τ ) d τ = h ( x ) ( τ ) (3) = base saion α mobile saion V where he expression on he righ hand side can be inerpreed as he sum of delayed and ime-varyingly weighed replicas of he signal x(). Figure : Example for calculaing Doppler frequency of a propagaion pah.

3 According o he Nyquis sampling crierion, he inerval beween updaes T should be less han he inverse of he oal Doppler spread λ T < = ν V (6) where he random variables A m and φ m are he phasor ampliudes and iniial phasor phases, respecively. The iniial phasor phases are essenial in order o avoid complee phase alignmen beween he roaing phasors a ime insan =, and can be randomly chosen from he uniform disribuion (... π ). The choice of disribuion(s) for A m, however, is a nonrivial maer. In he MATLAB simulaions presened a he end of he paper, he ampliudes of he :h ap are chosen equal, which o a close approximaion resuls in a Rayleigh envelope disribuion of he composie ap fading process when is larger han, say, 6. On he oher hand, a specular (or Rician) ap, for insance in case of a line-ofsigh (LOS) channel he ap a =, is obained by choosing A much larger han he remaining phasors A m, m. This ap model is versaile since also oher ap disribuions can be generaed, if required. The mean power of he :h ap is equal o he sum of he square of he phasor ampliudes where ν is he imum possible Doppler shif, equal o V λ. When here are several unresolved pahs conribuing o he acual fading of a ap, here are several Doppler frequencies involved. Since hese Doppler shifs can no be observed direcly, we have o resor o he Doppler spread funcion s ( ν ), which is obained hrough Fourier ransform of h () T s( ν) = ] h( )exp( jπν) d (7) In sofware simulaion, he ime dependen fading process of he :h ap (or he corresponding ime domain samples h i, ) can be generaed in several ways. In his model, a novel approach is used. A number of phasors are generaed, where each phasor (represening a propagaion pah) is roaing in complex plane a a Doppler frequency ν m drawn from a specified Doppler disribuion confined o he range V λ... V λ. The ap fading as a funcion of ime is simply he complex sum of hese phasors, h () = A expj πν + φ E J (8) m m m P = A m where, in a ypical wideband radio channel, i can be assumed ha he mean power decreases exponenially wih increasing ap number. The mean ap powers of he six aps in he GSM TU channel model menioned in Secion II are -3,, -, -6, -8 and - db, respecively. The Doppler specrum of he :h ap simply consiss of he power localised a he Doppler frequencies allocaed o he phasors m m (9) S ( ν) = s ( ν) = A δ( ν ν ). () Ofen, however, he Doppler specrum is assumed o be of he form [3] S ( ν) = πν P ) + *,. - ν ν () for ν < ν < ν and zero oherwise. This specrum is based on he assumpion ha he delayed and refleced or scaered signals arrive a he mobile receiver from all direcions wih equal probabiliy. Theoreically, he Doppler shifs of he unresolvable propagaion pahs of he :h ap should be randomly chosen from he U-formed disribuion of (), o be exac, bu are chosen in he MATLAB simulaion program for simpliciy from he uniform disribuion E V λ... V λj wihou causing significan changes in he average fading behaviour. The assumpion leading o () is, in pracice, rarely fulfilled anyway. Finally, he phasor ampliudes of he :h ap are obained from (9) once he mean ap powers and ampliude disribuion(s) are specified. In case of equal ampliudes we simply obain

4 A = P M. () m IV. THE MATLAB CHANNEL MODEL In he MATLAB channel model, he compuaional rouines in he model are wrien in C programming language in order o speed up he compuaions. The builin capabiliy of MATLAB o exploi C language rouines is uilised in form of he mexfuncion inerface beween MATLAB and C code. The channel model comprises wo separae MATLAB mex-files. The file apse.mex ses he iniial values for he ampliudes A m, iniial phases φ m and Doppler frequencies ν m of he phasors employed for generaing he ap coefficiens. These values are used a he beginning of he simulaion. The file wchannel.mex aes care of he acual channel modelling. Samples are aen from he inpu signal x(), hese samples are hen processed uilising he ap coefficiens afer he predeermined updae inerval. Since he processing is performed in blocs of a specific lengh, a signal spli up ino a se of blocs may conain disconinuiies a he bloc boundaries, due o he memory of he channel. The program is consruced in such a way ha his is avoided. To demonsrae he operaion of he MATLAB channel model, he GSM TU (Typical Urban) six ap channel model menioned in Secion II was employed in a es simulaion. In his model, he ap delays are a,.,.5,.6,.3 and 5. µs [], which leads o a reasonable choice for sampling inerval of T s =. µs. The corresponding ap mean powers are -3,, -, -6, -8 and - db. In order o obain approximaely Rayleigh fading, 5 phasors were chosen for each ap. In his example, for illusraive purpose, a very high relaive imum Doppler frequency of. T s was chosen, requiring a small ap updaing inerval, in his case 3T s. In Figure 3, he complex oupu signal y(), in form of real and imaginary pars, is displayed for he case when he inpu signal x() is a consan, real signal of uni ampliude. Figure 4 shows he impulse response of he simulaed channel as a funcion of ime. Each ap fades independenly wih an approximaely Rayleigh disribued envelope. A (narrowband) complex summaion of he ap coefficiens wihou aing ino accoun he (wideband) signal dispersion in form of ap delays resuls in a similar waveform as ha shown in Figure 3. REFERENCES [] GSM specificaion 5.5 Annex C, ETSI 993 [] J.G.Proais: Digial communicaions, McGraw- Hill, 983 [3] W.C.Jaes: Microwave mobile communicaions, Wiley, 974 Ampliude [arbirary uni] Real par Imaginary par Time [samples] Figure 3: GSM channel simulaion oupu wih consan inpu signal. Power [arbirary uni] Delay [µs] Time

5 Figure 4: Impulse response of he simulaed GSM channel as a funcion of ime (in unis of 8 sample inervals).