Delay-spread considerations of same-frequency repeaters in wideband channels

In current analog cellular systems, same-frequency repeaters are very often used as gap fillers. With digital wideband systems, the use of a repeater, with its inherent group delay added to the differential propagation delay, may yield a degradation in the performance in view of the resulting delay spread. An approach to estimate the statistics of the delay spread when each link is subjected to lognormal shadowing and each channel's power-delay profile follows an exponential decay is presented. Expressions for the cumulative density function (CDF), mean value, mean-square value, and standard deviation for the RMS delay spread are derived, and their accuracy is verified through simulation.