Matched filter performance of receive antenna arrays in dispersive Rayleigh fading channels

The matched filter bound for binary signaling in continuous Gaussian WSSUS channels with receive diversity is derived. The treatment is quite general as the case of discrete multipath channels with correlated fading is a special case of our results. Furthermore, we impose no constraints with regard to the selectivity of the channel, i.e. the channel may or may not be time, frequency, and space selective. It is assumed that a statistical characterization of the channel is available through its direction-delay-Doppler power spectral density. The derivation is based on using a discrete representation of the received signal obtained by the Karhunen-Loeve-expansion. Arbitrary propagation directions of the waves impinging at the antenna array can be taken into account. The behavior of the matched filter bound is analyzed with respect to the parameters characterizing the mobile radio channel and the properties of the antenna array, i.e. the number of sensors, the antenna pattern, and the array geometry.