Capacity of BPSK signaling in fading channels with generalized selection combining

We calculate the capacity for binary phase shift keying (BPSK) signaling in Rayleigh fading channels with generalized selection combining (GSC). In GSC, the K diversity branches with largest fading amplitudes among L available diversity branches are combined. We also calculate the capacity of BPSK signaling in Nakagami-m fading channel when there is no diversity available, i.e. L is equal to one. Based on the capacity, the minimum required signal-to-noise ratio (SNR) per information bit for reliable communication is found as a function of code rate with both hard decision and soft decision. We find that the minimum required SNR per information bit increases monotonically as code rate increases. The channel dispersion induced by fading is found to be more harmful than the information loss by hard decision for large available SNR per bit. Also, we find that the gain provided by increasing diversity order is larger than the loss by hard decision for large available SNR per bit.