Performance of Optimum and Suboptimum Combining Diversity Reception for Binary DPSK over Independent, Nonidentical Rayleigh Fading Channels

TL;DR

This paper analyzes the error performance of binary DPSK with diversity reception over nonidentical Rayleigh fading channels, providing exact and bound expressions for arbitrary diversity order and channel conditions.

Contribution

It generalizes previous results by deriving exact BEP expressions and bounds for arbitrary diversity order and nonidentical fading channels in binary DPSK systems.

Findings

Exact closed-form BEP expressions for arbitrary diversity order.

Chernoff bound for the BEP of the optimum diversity detector.

Behavior of BEP as a function of fading correlation and SNR.

Abstract

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 explict 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.