Strategies for FH/MFSK signaling with diversity in worst-case partial-band noise

Optimum diversity and worst-case partial-band noise jamming conditions have been derived for noncoherent energy detection of frequency-hopped (FH) M-ary frequency-shift keyed (MFSK) signals using a soft-chip decision suboptimum linear combining metric with perfect jamming-state side information. However, the assumption implicit in previous publications is that the error is first maximized over the jammer's partial-band duty factor for arbitrary diversity, and the result is then minimized over the amount of diversity. This paper shows that if the order of optimization is reversed, different conditions and performance are produced; that is, the previous solution is not a saddlepoint. This introduces some game-theoretic considerations for the communicator and the jammer, the risks and advantages of which are explored.