Analytical Results on the Statistical Distribution of the Zeros of Mobile Channels

In this paper, the distribution of zeros of mobile channels is investigated and the results obtained are applied to the GSM (Global System for Mobile Communications) /EDGE (Enhanced Data Rates for GSM Evolution) system. The taps of the discrete-time overall impulse response can be modeled as correlated complex Gaussian random variables, where the correlations depend on the transmit filter, the power delay profile of the channel, and the receiver input filter. For calculation of the density of zeros of the overall transfer function a result from the mathematical literature on the zeros of polynomials with correlated Gaussian coecients is used. From this density two cumulative distributions which are relevant for the design of suboptimum receivers are derived and specialized to the case of uncorrelated taps. Finally, practical equalizer design rules for the GSM/EDGE system are deduced from the calculated statistical distributions