s), or are con- strained to always exceed the received signal power (dotted lines). Eb/Nj, dB Figure 2.18. Relative effectiveness of band multitone jamming for several values of M and N. Worst Case Jamming 10210 Eb/Nj, dB Figure 2.19. Performance improves with n for band multitone jamming, for a given K. where S is given by missing < n < .84M (provided K 2) (2.50) M - 1' .84M<nsM. (2.49) and (2.50) reveal a singular exception to our premature conjectures: for n = 2 the asymptotic Pb is minimized at K = 2. With this one anomaly, the relative effectiveness of band multitone jamming for large Eb/N, can be summarized as follows: (i) for a given K, the performance improves with n; (ii) for a given n, the performance degrades with K; (iii) for a given n/m .84, the performance improves with K. From the jammer's point of view, the n = 1 band multitone strategy is pre- ferred, while the n = M case is relatively ineffective. 2.2.2.3 Independent Multitone Jamming As we noted in our introduction to multitone jamming, the particular appeal of the so-called independent category is its simplicity. Its effectiveness is not contingent on the jammer knowing the location of the tone frequencies in Non-Coherent Frequency-Hopped Systems each M-ary band, which could be independently hopped over the entire spread-spectrum bandwidth, and there is no need to regulate the number of jamming tones on each band. Utilizing a seemingly inelegant strategy, the Q jamming tones are distributed uniformly over the N available frequen- cies. If Q >> M - 1 (see (2.29)), each of the FH slots that comprise a given M-ary band are independently jammed with probability p, which reduces to (2.51) based on (2.5), (2.26), (2.31), and (2.37). We will now analyze the effective- ness of independent multitone jamming, and compare it with the other jam- ming schemes. Referring to Table 2.1, a symbol error can occur only if at least one of the M - 1 untransmitted symbols in the M-ary band containing the data is jammed. Then, conditioned on this event, a symbol err