Performance of optimum and suboptimum combining diversity reception for binary DPSK over independent, nonidentical Rayleigh fading channels

This paper is concerned with the error performance analysis of binary differential phase shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. Space antenna diversity reception is assumed. The diversity branches are independent, but have nonidentically distributed statistics. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of first and second-order diversity. Our results are more general in that the order of diversity is arbitrary. Moreover, the bit error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-bit-interval fading correlation coefficient at the matched filter output, the mean signal-to-noise ratio per bit per branch and the order of diversity. A simple, more easily computable Chernoff bound to the BEP of the optimum diversity detector is also derived.