dition specified in [10] and Appendix 2A. Conditioned on Hj,e1j and e2j have the following probability distributions: Pr{e1j=1|H}= (2.84) SO that (2.85) Since (2.83) (or common sense) says that (e2j - e1j) must have a non-zero probability of being greater than zero for a symbol error to occur, (2.85) shows that this requires that a <1. Using the familiar relationship of (2.20a) between bit and symbol error rates, and combining (2.81)-(2.83) and (2.85), we have, for arbitrary m and a, PrsM Fm (2.86) Coding Countermeasures where Performing the minimization by setting aFlax to zero yields (2.87) provided M > 2, and a 1/(M 1) SO that 0. For worst case jamming, we want to choose a E (0, 1) to maximize F. Although it is not immediately obvious from the form of (2.87), Figure 2.38 demonstrates that F has a unique maximum for each value of K 2 over this range of a. Denote the maximizing value of a by ao, and define (2.88) where B and ao are given in Table 2.7 below. The constraint <1 must also be satisfied: using (2.74) with n = 1, this translates into (2.89) Consequently, the performance in worst case n = 1 band multitone jamming Figure 2.38. Demonstration that Pb bound for FH/MFSK signals with arbitrary diversity m and SNR EIN, in n = 1 band multitone jamming has unique maximum over jammer parameter a (refer to (2.86)-(2.88)). Non-Coherent Frequency-Hopped Systems with diversity m is upperbounded by (2.90) K(M mM Eb where S = ao MIK is also computed in Table 2.7. Although (2.90) is an upperbound, it is relatively simple and easy to eval- uate, and many behavioral performance characteristics can be deduced from it. It is plotted in two different formats for several values of K > 2 in Figures 2.39-2.41. Unlike the K = 1 curves in Figure 2.35, the P upper- bounds for fixed m in Figures 2.39 and 2.40 have no slope discontinuities; this does not rule out such behavior in the exact bit error rate. The arguments in Section 2.3.1.2 discussing the saturation effect imposed by the constraints of band multitone jamming are valid 