 (2.111) where B and S aM/nK are also given in Table 2.8 for various values of K and n. Unfortunately, in the saturation region EbIN1 < im (or u = 1), awc = (nK/mM)E,/N, and F must be minimized numerically over l > 0 for each value of EIN, (this is not typically a region of practical interest unless there is some additional channel coding since the M-ary error rate is rel- atively high). As usual, the easiest way to observe the variation in performance with the parameters implicit in (2.111) is to examine different graphical representa- tions. However, since a given two-dimensional parametric plot can only illus- trate the relationship between three of the independent variables Pb, E/N, K, m, and n, there are many graphs to choose from; the few selected below provide some valuable insights. Figure 2.52 is representative of the behav- ior of Pb as a function of m and n for fixed K and Eb/N We see that there is an optimum diversity Mopt which increases with N. And the performance appears to improve with n for a given m, which Table 2.8 indicates is due to the fact that B decreases with n for fixed K. This suggests that it is to the jam- mer's advantage to keep n small SO as to place a jammer tone in as many M-ary bands as possible: this is a direct consequence of the assumption that the receiver has perfect jamming state side information. Figure 2.53 fixes n and EbIN1 and illustrates the variation in Pb with m and K. Here we discover Non-Coherent Frequency-Hopped Systems DIVERSITY m CHIP/SYMBOL Figure 2.52. Performance of FH/8-ary FSK signals with m diversity chips/symbol in worst case band multitone jamming with n jamming tones per 8-ary band. These curves demonstrate the existence of an optimum diversity Mopt, and the decreased jamming effectiveness for larger n. n =2 JAMMING TONES/M-ARY BAND E6/N =13db = DIVERSITY m CHIPS/SYMBOL Figure 2.53. Variation in performance of FH/MFSK signals in worst case n = 2 band multitone jamming with alphabet size M = 2K and diversity m. Note the supremacy of the K = 3 case. Codin