Matched filter bounds for wireless communication over Rayleigh fading dispersive channels

This letter extends the theory of the matched filter bound for fading dispersive channels. We generalize to arbitrary fading, as well as delay, properties of the channel. The channel model is a standard time varying linear filter and the calculation of the matched filter bound is based on a Karhunen-Loeve expansion of the received pulse spectrum when an isolated pulse is transmitted. Results are presented illustrating the various diversity effects. We conclude that in addition to the effect on probability of bit error of implicit delay diversity there is the less well known effect of implicit Doppler diversity in fast fading. The effect on probability of bit error of pulse shaping and explicit diversity is also illustrated