309) when the chip hops into the q-th sub-band. This ideal receiver assumes knowledge of A1, A2, ao; B1,B2, Bo; and J, the jammer noise power distribution. Here aqE is the average chip energy at the receiver when the signal hops into the q-th sub-band. In this case the coding parameter is D(p,J) (2.310) whre any coded bit error bound has the form Pb = G(D(p,J)) (2.311) and G(.) is determined by the code used. This follows from generalizing the Worst Noise Jammer Distribution-Slow Fading Non-Uniform Channel discussion leading to (2.275). For the coded FH/MFSK system with the ML metric, the minimax point (p*,J") satisfies D* = D(p*,,**) = = min max D(p,J). (2.312) This is similar to the uncoded case and in fact, the minimax point (p*,J") is exactly the same. This is because D(p,J) is a concave function of J and the unique minimax point gives the condition Allainy q=1,2,...,L (2.313) 4(1+%) =L+1,L+2,...,Q. (2.314) This implies J* satisfies (2.304) where 8 is given by (2.302) and L is the small- est integer where (2.306) is true. For the hard decision case assume a hard M-ary decision is made for each FH/MFSK chip. If the FH/MFSK signal is hopped into the q-th sub-band, then the coding channel has M inputs and M outputs with conditional chan- nel probabilities (2.315) y x x where Pq(Jq) is given by (2.291) and , {1, ,2,...,M}. For a sequence of symbols x and y and hop sequence q we have the conditional probability p(yxq) (2.316) Non-Coherent Frequency-Hopped Systems Here the ML hard decision metric is (2.317) With this metric the coding parameter is (2.318) Again D(p,J) is a concave function of J and thus there is a unique minimax solution where the minimax point (p*, J*) satisfies (2.302), (2.303), and (2.304) where L is the minimum integer where (2.306) is satisfied. For the special case of the uniform channel where (2.319) q=1,2,...,Q for the soft decision ML metric, broadband jamming is the worst case when jammer state information, J, is assumed. This was shown in Section 2.5.2 and also follows directly from the 