(2.52) Applying (2.20a) and (2.51), with the restriction that p < 1, the bit error rate in worst case jamming is specified by (2.53) where p is a function of a defined by (2.51). For Eb/N, <y (tabulated below), Figure 2.20 shows that awc <1, but the maximization in (2.53) must be computed separately for each combination of K and E/N. However, Table 2.3 shows that this computationally difficult region corresponds to Pb > .37 for any K, SO it is not of practical interest. 1 AK, and (2.53) reduces to (2.54) Note that when a = awc and KEIN >> 1, (2.51) says that p <<1 (see Figure 2.20 as well): then (2.54) reduces to (2.55) Worst Case Jamming Eb/Nu,dB Figure 2.20. Worst case independent multitone jamming parameters: awc is ratio of signal-to-jamming tone powers, p is probability that a given FH slot is jammed, and is probability that at least one slot in an M-ary band is jammed. which is identical to (2.41) for n = 1 band multitone jamming. So, as illus- trated in Figure 2.21, for the low error rates that typify most practical com- munication systems, these two jamming strategies are equally effective against uncoded non-coherent FH/MFSK signals. Recall that we suggested this hypothesis at the beginning of this section based on identical expressions for u when p is small (refer to (2.30) and the discussion that follows). A summary of the relative effectiveness of all of the worst case partial- band noise and multitone jammers is shown in Figure 2.22 for K = 4. The n = 1 band and independent multitone strategies are the most effective in the absence of coding; partial-band noise is as effective as band multitone jam- ming for n ~ M/2; and n = M band multitone jamming is the least effective Table 2.3 Parameters associated with performance of uncoded FH/MFSK signals in worst case independent multitone jamming. y, dB Po Ky 1 Pblp=po Non-Coherent Frequency-Hopped Systems WORST CASE n=1 BAND MULTITONE JAMMING WORST CASE INDEPENDENT MULTITONE JAMMING Eb/Nj,dB Figure 2.21. Worst case independent and n = 1 band multitone jamm