The statistics of the zeros of mobile channels: results and implications for equalizer design

In this paper, the distribution of zeros of mobile channels is investigated and the results obtained are applied to the channel models standardized for 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 with zero or nonzero mean, 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 results from the mathematical literature on the zeros of random polynomials are used. From this density two cumulative distributions which are relevant for the design of suboptimum receivers for intersymbol interference (ISI) channels are derived for the case of uncorrelated taps with exponential distribution of the tap variances. Finally, practical equalizer design rules for the GSM/EDGE system are deduced from the calculated statistical distributions.