Bit error variances of DPSK and NCFSK in Nakagami-m channels

There has been an intensive interest in exactly evaluating the average bit error rate (BER) of different modulation techniques in fading environments. However, it is less well known how the variance of BER behaves. In this paper, we derive the closed-form variance formulas for binary DPSK and NCFSK in the Nakagami-m fading environment. One of the striking results is that, unlike their BER average, the BER variance is non-monotonic with the average received SNR/bit ratio rho. We show that the variances reach the maximum at a particular rho and the corresponding standard deviation is as high as 15%. The other important result is, when rho becomes sufficiently large, DPSK is 1.5 dB better than NCFSK, FSK is 2.2 dB better than NCFSK, and PSK is 3.7 dB better than NCFSK