that B decreases with n. Because 8 is inversely proportional to B, the performance with opti- Coding Countermeasures m = MOPT Eb/N, dB Figure 2.55. Variation in performance of FH/8-ary FSK signals with optimum diversity Mopt in worst case band multitone jamming as a function of the number n of jamming tones per jammed band. Jamming effectiveness deteriorates monotoni- cally with n. mum diversity also improves with n for a given K, as shown in Figure 2.55. Recall also that Figure 2.53 suggested that with optimum diversity and worst case band multitone jamming, the best performance for n = 2 is achieved with K = 3 over some range of EINj; Figure 2.56 supports this observation and shows that it is valid for EIN V 11 dB. (2.113) says that the exponen- tial component in the Pb bound, which determines the asymptotic perfor- mance for large Eb/N,, decreases with 8 for a given SNR. Table 2.8 shows that 8 is in fact maximized at K = 3 when n = 2, as well as when n = 3 or 4 (but not for n = 5). So 8-ary FSK does have an advantage against the more effective band multitone jammers (except for the n = 1 case where 4-ary FSK is better) for low bit error rates (i.e., large E/N. Finally, for the spe- cial case n = M, Table 2.8 shows that 8 increases with K SO that the perfor- mance improves with K as illustrated in Figure 2.57. 2.3.1.3 Independent Multitone Jamming As effective as band multitone jamming is against FH/MFSK signals, espe- cially the n = 1 case, this strategy loses most of its potency if the M-ary band structure is removed. For example, a sophisticated anti-jam system might elect to use M frequency synthesizers to independently hop each transmit- ted symbol as a way of defeating band multitone or repeat-back jamming Non-Coherent Frequency-Hopped Systems m=mOPT Eb/Nj, dB Figure 2.56. Superiority of FH/8-ary FSK signals with optimum diversity in worst case n = 2 band multitone jamming, for E/N, VN 11 dB. n = M m =MOPT Eb/Nj, dB Figure 2.57. Performance of FH/MFSK signals with optimum diversity in worst case n = M ban