Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers