A connection between Rayleigh fading and worst-case partial band interference

For FH/BFSK (frequency hopping/binary frequency-shift keying) on a worst-case partial-band Gaussian interference channel, the bit error probability results are well known for the extreme cases in which the signal is either nonfading or Rayleigh fading. In the present work the author fills in the region between these extremes by considering the general Nakagami-m fading model. Here the worst-case partial-band Gaussian interference results are given by a one-parameter family, which for m→∞ gives the Viterbi-Jacobs (1975) nonfading result and for m=1 gives the Rayleigh fading result. In the latter case a broadband interference strategy is optimal. Thus the Nakagami-m solutions provide a smooth one-parameter bridge between the Viterbi-Jacobs channel and the Rayleigh fading channel. The results show that the worst-case interference fraction ρ increases as the fading variance increases, up to Rayleigh fading. Any fading less severe than Rayleigh, however slight the departure from Rayleigh, requires a partial-band strategy for sufficiently large E _b/N_I