t have P1 = 1. Now consider the general choice for p under a minimax criterion. We assume the transmitter has no prior knowledge of the jammer noise power distribution J and SO the probability vector p does not depend on J. Consider here the choice of p that minimizes the maximum error probabil- ity. Specifically we choose p = p* = to minimize max P (p, ) (2.298) under the constraint that p is a probability vector. The maximization of Psp Worst Noise Jammer Distribution-Slow Fading Non-Uniform Channel J) with respect to J is under the constraints of (2.242) and J have non-neg- ative components. Here the minimax error probability is given by = min max P (p,J) (2.299) Necessary and sufficient conditions for (p,J) to be the minimax point (p*, J*) have been found and analyzed by Avidor [25]. The minimax solution cor- responds to the jammer noise power distribution resulting in the sub-band symbol error probabilities = = . . . = PL(IE) <...< Pq(0) (2.300) for some L where (2.301) For the minimax solution the jammer distributes its power SO that the strongest sub-bands without jammer noise receive the most jammer power, thus reducing all the better sub-bands to the same level of performance. Here the effective signal-to-noise ratios for the L sub-bands are No + BaJa (2.302) q=1,2,...,L and for the remaining sub-bands =L+1,L+2,...,Q. (2.303) Note that the minimax jammer noise power distribution is q=1,2,...,L (2.304) q=L+1,L+2,...,Q and from the constraint (2.242) (2.305) Non-Coherent Frequency-Hopped Systems (2.306) Thus, in terms of the total power J the smallest L is found to satisfy (2.304) and (2.306). Only these L sub-bands are jammed by the noise jammer. The minimax choice of p* has the form aq/Bq q=1,2,...,L (2.307) q=L+1,...,Q. with resulting minimax bit error probability (2.308) where 8 and J* satisfies (2.302) and (2.304) and L is the smallest integer sat- isfying (2.306). 2.6.2 Diversity and Coding Following the discussion leading to (2.270), with coding and diversity the soft decision ML metric is aqEex (2.