Performance analysis of a (3, L) selection combining scheme for binary NCFSK signals on Rayleigh fading channels

In a previous paper, we derived the optimum selection combining (OSC) scheme for binary noncoherent FSK (NCFSK) signals on independent (but not necessarily identically distributed) Rayleigh fading channels with L-antenna diversity reception. In the OSC scheme, the diversity branch having the largest magnitude of the logarithm of the ratio of the a posteriori probabilities (log-APP ratio - LAPPR) of the transmitted information bit is chosen. In this paper, we derive the bit error performance of a (3, L) selection combining scheme for binary NCFSK signals which combines the three branches whose LAPPR magnitudes are the largest among the available L branches in i.i.d Rayleigh fading. Numerical results for this (3, L) selection scheme show that, for L=5, combining the three branches with the largest LAPPR magnitudes yields almost the full performance of the square-law combining of all the L=5 branches. For L=7, the performance of combining the three branches with the largest LAPPR magnitudes is just about 0.2 dB worse from the performance of square-law combining of all the L=7 branches. We also compare the performance of the proposed (3, L) selection scheme with the (3, L) selection combining scheme of Chyi et al. (1989).