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

The distribution of zeros of mobile channels is investigated and the results obtained are applied to the GSM/EDGE 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 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 profiles specified for GSM/EDGE, an allpass prefilter 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 prefilter is applied, the truncated impulse response should have a length of three as shown.