Optimum selection diversity for BPSK signals in Rayleigh fading channels

We propose a new selection diversity scheme, called -selection diversity, that selects the branch providing the largest magnitude of log-likelihood ratio (LLR). The LLR for BPSK signals in fading channels is found to be proportional to the product of the fading amplitude and the matched filter output after phase compensation. The proposed -selection diversity scheme is shown to be optimal in the sense of minimizing the bit error rate (BER), and outperform existing selection diversity schemes. We also propose a suboptimal selection diversity scheme, called -selection diversity, that does not require a phase compensation in the selection process, thereby significantly reducing implementation complexity. We show that the proposed -selection and -selection diversity schemes exhibit significant power gains over existing selection diversity schemes in Rayleigh fading channels.