he Pb curve in the selected region. (The results below indicate that the worst performance for these parameters occurs at p = .16, for which Pb=3.0 X = 10-2.) Figure 2.8 illustrates the performance of an FH/BFSK system in partial- band noise for several partial-band jamming factors p. For small enough Eb/N,, it is evident that broadband noise jamming (p = 1) is the most effec- tive. In general, for any value of Eb/N, there is an optimum value of pe (0, 1] from the jammer's viewpoint which maximizes Pb, and this is denoted by Pwc (for worst case jamming). The performance in worst case partial-band noise is the upper envelope (or supremum) of the family of Pb curves for fixed values of p: as shown in Figure 2.8, when Eb/N1 exceeds a threshold level, Pwc < 1 indicating a partial-band jamming advantage, and the perfor- mance curve is a straight line. Of course, in practice, it may be difficult for the jammer to match p to the actual Eb/N, The worst case partial-band noise jammer chooses p to maximize the Pb for a given M and Eb/N From (2.20b) and (2.23), the resulting average p=Pwc P =.1 Eb/Nj,dB Figure 2.8. Performance of FH/BFSK system in partial-band noise for several fixed values of p. The performance in worst case partial-band noise is realized when the jammer chooses p = Pwc to maximize P for a given EIN Note that Pwc decreases as EIN, gets larger. Worst Case Jamming performance can be expressed as For M = 2, this maximation is a simple mathematical calculation; for larger values of M, it must be evaluated numerically. The results have the form [5, (15) and (16)] (2.25) where the parameters B and Y are tabulated for 1 < K < S below and Pwc denotes the jammer's optimum p. (2.25) demonstrates that SO long as Eb/N, is not unusually small, worst case partial-band jamming converts the exponential relationship between Pb and Eb/N1 in (2.20) into an inverse linear dependence. As shown in Figure 2.9, the resulting degradation can be severe for small P's: for example, the loss is 14.7 dB at Pb = 10-3 for K = 1, and incr