Simulation of Wideband Wireless Multipath Channel

Physical wireless multipath phenomena Analytical model representation

Model of Comm channel  Channel model: representation of input-output relationship of the channel in mathematical or algorithmic form.  May be derived from measurements or based on theory of physical propagation phenomena  Measurement-based model: empirical characterization of the channel in the time or frequency domain, often involve statistical descriptions in the form of random variables or random processes- unwieldy &difficult to generalize.  Mathematical model that represent the physical perspective need to be simplify and converted to convenient form to be used in simulation such as transfer function or impulse response.

Simulation  Assumptions and approximation  Tradeoffs between accuracy, complexity, and computational requirements  Monte Carlo method: pass large number of symbols through a communication system, calculate the error at the receiver output  MATLAB  Two categories of channel models:  Transfer function models for time-invariant channels : (wires, free space, optical fibers). Channel is assumed to be static. Particular frequency response due to fixed delay. Transfer function is “flat” if mesg source has bandwidth for which channel has constant gain response. “Frequency selective” if mesg source has bandwidth over which the channel has a significant gain variation. Usually simulated using FIR technique (measured / synthesized impulse or freq response) & IIR (analytical)  Tapped delay line models for time-varying channels (mobile radio channel): Channel vary over time. “Fast fading” if channel changes during the smallest time interval of interest of an applied signal. “Slow fading” if channel remain static for large number of consecutive symbols of applied source and channel can be treated as above (time- invariant) for the particular span of time. Simulation using Tapped Delay Line with tap gains and delays that are random processes. ------

Modeling Wireless Channel Fading [3]  The most popular model describes fading as complex Gaussian Process. [1],[2]

Clarke’s Model  For frequency non-selective fading (flat), the channel can be modeled as y(t)=c(t)x(t) + n(t)  Y(t): received signal  Most popular models assumes c(t) and n(t) are complex stationary zero-mean Gaussian processes with independent and identical distributed real and imaginary parts.  Different models of fading channels are based on different assumptions about the fading power spectral density S(f) Rayleigh fading channel [4]  If each multipath component in the received signal is independent then the PDF of its envelope is Rayleigh  Impulse response of flat Rayleigh fading mobile channel consists of a single delta function whose weight has a Rayleigh PDF. 

Jakes Model  approximate the Rayleigh fading process by summing a set of complex sinusoids  the sinusoids are weighted so as to produce an accurate approximation of desired channel Doppler spectrum  Jakes shows that the theoretical Doppler spectrum for the isotropic scattering mobile radio channel can be well approximated by a summation of relatively small number of sinusoids with frequencies and relative phases of the sinusoids set according to a specific formulation 

Deterministic Channel Modeling [5]  Modeling of the classical Rayleigh and Rice processes requires the realization of two real-valued coloured Gaussian random processes.  Modeling of frequency selective channels using finite impulse response (FIR) filters with L time- variant complex valued coefficients. 

REFERENCES

[1] W.C. Jakes, Microwave Mobile Communications, Wiley, 1974, New York

[2] Theodore S. Rappaport, Wireless Communications Principle and Practice, Prentice Hall, 2002, New Jersey

[3] William Turin, Rittwik Jana, Carol Martin, Jack Winters, Modeling Wireless Channel Fading, IEEE , 2001

[4] R. Steele, Lajos Hanzo, Mobile Radio Communications, Wiley, West Sussex, 1999

[5] Matthias Patzold, Mobile Fading Channels, John Wiley, West Sussex, 2002