On the distribution of zeros of mobile channels with application to GSM/EDGE

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 lter, the power delay pro le of the channel, and the receiver input lter. For calculation of the density of zeros of the overall transfer function a result from the mathematical literature is used. From this density two cumulative distributions which are relevant for the design of suboptimum receivers are derived. Our investigations show that for the power delay pro les speci ed for GSM/EDGE, an allpass pre lter which transforms the impulse response in its minimum phase equivalent should be employed if decision{feedback equalization (DFE) or reduced{state sequence estimation (RSSE) are used at the receiver. On the other hand, if impulse response truncation using a linear pre lter is applied, the truncated impulse response should have a length of 3 as will be shown. This paper is also presented in part at PIMRC, London, September 2000 and ICC, Helsinki, June 2001. R. Schober et al.: On the Distribution of Zeros of Mobile Channels 2