 Rc, which causes the number of M-ary bands to decrease (refer to Figure 2.10). Eventually, the number of M-ary bands equals J/S, and the saturation condition = 1 is reached. In this region, under the assumption of perfect receiver jamming state side information, Pb is sim- ply the probability 2-m that the incorrect binary symbol is hit on all m diver- sity transmissions. This surprising behavior is better illustrated in Figure 2.36, which demon- strates the variation in performance with diversity for several SNR's. There is an initial minimum Pb in the region <1 or m < E/2Nj; from (2.76), this occurs at where (2.77) awc==1 Non-Coherent Frequency-Hopped Systems MOPT=7 Eb/N = 14 dB MOPT=9 MOPT=12 m*=17 DIVERSITY m, CHIPS/BIT Figure 2.36. Variation in performance of FH/BFSK signals in worst case n = 1 band multitone jamming with diversity. Note that Pb decreases as 2-m for large m, inde- pendent of E/N. For fixed EbIN the initial minimum occurs at m = Mopt; however, lower Pb's are later achieved for m > m* (refer to (2.79)). provided For smaller values of EIN Mopt = 1 and the performance is given by (2.40) and (2.41): (2.78) However, in the saturation region, P falls below that defined in (2.77) for m > m*, where (2.79) and Ph becomes arbitrarily small for larger values of m. If it is important to use minimal diversity, Mopt is a good choice. However, since m* is only mod- erately larger, better performance can be achieved without resorting to impractically large amounts of diversity. Figure 2.37 illustrates the extreme effectiveness of diversity for FH/BFSK signals in worst case n = 1 band multitone jamming. Even at the local min- Coding Countermeasures BROADBAND WORST CASE n = l NOISE, NO BAND MULTITONE DIVERSITY JAMMING M=MOPT 13.35 dB Eb/Nj.c 14.95 dB Figure 2.37. Effectiveness of diversity against worst case n = 1 band multitone jamming for FH/BFSK signalling. Improvement is 35 dB relative to m = 1 system, and performance is only 1.6 dB worse than in broadband noise, with m = = Mopt at imum, m = Mopt, the impr