Analysis of signal-to-noise ratio distributions and bit error rates for equal gain diversity systems on generalized fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L-branch equal-gain (EG) diversity combiners in Nakagami fading channels is derived. The bit error rate for a matched-filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase-shift keying (CPSK) and differential coherent phase-shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit-error-rate results are also obtained for coherent and noncoherent reception of frequency-shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. It is shown that, even with -20-dB (k = 0.01) gain unbalance between the branches of a dual EG combiner, there is still a considerable improvement over the nondiversity case for the generalized fading model (m = 1).