Performance of equal gain combining for quantized estimates of Rayleigh fading channels

Recently radio frequency (RF) level antenna diversity combining has been proposed as a low cost and power efficient alternative to conventional antenna diversity combining. In RF level diversity combining the diversity weights are implemented in the hardware by making use of circuit elements such as phase shifters and variable gain amplifiers, while channel estimation is performed in the digital baseband domain. In this paper, we analyze the performance of an RF level equal gain combiner. Two alternative but numerically equivalent representations of the probability density function and characteristic function of the combined signal amplitude for binary phase shift keying signals (BPSK) over Rayleigh fading channels are derived. The newly derived characteristic function is then used to evaluate the error probability. Finally, we compare the performance with binary frequency shift keying (BFSK) and differential binary phase shift keying (DBPSK) schemes with diversity reception. It is shown that for only 3 level phase compensation, BPSK exhibits superior performance to both BFSK and DBPSK.