ing tone coincides exactly in frequency with one of the N available FH slots, with at most one tone per slot. Furthermore, while the multitone jammer may periodically rearrange the loca- tion of its tones to thwart any FH avoidance measures, it is assumed that such changes coincide with hop transitions. While these artificial constraints could never be achieved in practice, like the earlier partial-band jamming assumptions, they simplify the analysis and yield somewhat pessimistic performance results. For example, if a jamming tone is offset in frequency from an FH slot, less energy gets into the adjacent MFSK detector reducing the jamming effectiveness, and the performance must be averaged over the frequency offset distribution. Worst Case Jamming EXAMPLE M= 4 INDEPENDENT n=2 BAND X (JAMMING TONE) NOT JAMMED NOT JAMMED NOT JAMMED NOT JAMMED Figure 2.10. Multitone jamming strategies: independent multitone jamming dis- tributes the tones pseudorandomly over all N FH frequencies; band multitone jam- ming places n E [1, M] tones in each jammed M-ary band. We denote the fraction of the FH slots jammed by (2.26) analogous to the fraction of the SS bandwidth jammed in the partial-band noise case. However, there was a uniformity in the partial-band jamming scheme that does not generally carry over to the multitone case. In the for- mer, an entire M-ary band was assumed to be evenly degraded by Gaussian noise if it was jammed at all. Under the various multitone scenarios, the num- ber of symbols in an M-ary band that can be hit by jamming tones can range anywhere between zero and all M. A single jamming tone hitting any of the M - 1 untransmitted symbols can produce an error, provided that the jam- ming tone power J/Q is slightly greater than the signal power S, in the absence of additive noise. Since the jammer is presumed to not know the hopping sequence, it is to its advantage to place its tones in as many M-ary bands as possible, even if most of these jammed bands contain a single jam- ming tone. Consequently, with r