se linear region than the same jammer with awc = 1. The advantage of using a > 1 does not only apply to the limiting case of n = M band multitone jamming where all errors are attributed to the ran- dom phase effect. (2.46e) shows that awc peaks at 2.52 for large enough Eb/N, whenever n .84M: interestingly, in this region, the asymptotic Pb is inde- pendent of n. By contrast, had we restricted a to be less than 1, the worst case asymptotic Pb would have been that of (2.46d). The jamming advantage realized by permitting awc 1 is the ratio of these two Pb expressions (2.48) For example, at M = 16 that advantage is 0.4 dB at n = 14 and 1.2 dB at n = 15, as well as the previously mentioned 2.0 dB at n = M = 16. A final observation from Figure 2.17 is that unlike n = 1 band multitone jamming (refer to Figure 2.12), when n = M the performance improves with increasing K or M, just as it does for broadband or worst case par- tial-band noise. Actually, (2.46e) shows that this effect occurs over the range .84M < n V M for large enough Eb/N, since MIK(M - 1) increases with K > 1. For K = 1 and 4, Figure 2.18 illustrates the relative effectiveness of band multitone jamming for n = 2 and M. Figure 2.19 shows the variation in per- formance with n for K = 4. The implication of these two graphs is that the performance improves with n for fixed K, and degrades with K for fixed n. In fact, these conclusions are essentially correct. Consider the large EIN, asymptotic expressions for Pb in (2.41), (2.46d), and (2.46e): these all have the form (2.49) Worst Case Jamming (a WC <4) (awc s ) ED/Nj. dB Figure 2.15. Optimum power allocation for n = M band multitone jammer. Eb/Nj, dB Figure 2.16. The probability p that a given FH slot is jammed, and the probability that a given M-ary band is jammed, for worst case n = M band multitone jamming. Non-Coherent Frequency-Hopped Systems M=n=2 10.10 Eb/N,,BB Figure 2.17. Performance of uncoded FH/MFSK system with n = M band multi- tone interference when jamming tone powers are optimized (solid line