ining the worst case a for the other multitone strategies. Worst Case Jamming From Table 2.2 and the discussion above, a symbol error can only occur if the M-ary band containing the transmitted data is jammed, and then only if the data symbol itself is not hit and a < 1: (2.36) Since we know that (2.37) (2.3), (2.4), (2.28), and (2.31) allow us to rewrite u in the form (2.38) for multitone band jamming with arbitrary N. Recallling the relation between Ps and Pb (see (2.20a)), and setting n = 1, the performance for a given a is specified by (2.39) The worst case performance is achieved by maximizing a. But, in addition to the constraint a <1, there is the requirement that the number of jam- ming tones not exceed the number of M-ary bands, i.e., u < 1. Therefore, the worst case n = 1 band multitone jammer sets a equal to (2.40) for which (2.39) reduces to (2.41) since M = 2k. Under the worst case partial-band noise scenario, the relationship between Pb and Eb/N, became inverse linear for P6's below a threshold that depended on K (see (2.25)); here that same type of relationship arises for all Pb < 1/2, independent of K. Both worst case jammers are significantly more effective than broadband noise against uncoded FH/MFSK signals with non-coher- ent detection, especially for large EIN, as shown in Figure 2.12. However, of the two, it is clear that the multitone structure is a better jamming Non-Coherent Frequency-Hopped Systems WORST CASE n = I BAND MULTITONE WORST CASE PARTIAL BAND NOISE BROADBAND NOISE Eb/Nj,dB Figure 2.12. Advantage of n = 1 band multitone strategy over partial-band noise and broadband noise jamming of uncoded FH/MFSK signals. p: K= 4 Eb/N, dB Figure 2.13. Parameters characterizing worst case n = 1 band multitone jamming of uncoded FH/MFSK signals. Worst Case Jamming strategy, particularly for larger values of K. The performance in additive noise improves with K due to the block orthogonal coding gain implicit in the MFSK modulation; for multitone jamming the performance degrades with K since the 