e see that the exact Pb does indeed decrease for sufficiently large m, SO this characteristic is not simply a bound anom- aly. The piecewise linear nature of the exact curves is due to the real world constraint that m and the maximizing parameter k take on only integer values, SO the worst case performance variation with diversity is not as smooth as the bounds suggest. As a matter of interest, the exact perfor- mance of K = 1 is superimposed on Figure 2.44. Before the saturation con- dition u = 1 is reached, for the selected SNR, we see that the K = 1 performance is only marginally better than for K = 4 and worse than for K = 2 (or K = 3, which was not plotted). However, because the K = 1 performance improves SO rapidly for m Eb/2N1 where = 1 (refer to Coding Countermeasures 2.01 dB .50 dB Eb/Nj, dB Figure 2.42. Comparison of exact and upperbound Pb formulas for FH/4-ary FSK signalling with diversity m chips per symbol in worst case n = 1 band multitone jam- ming. Accuracy of bound improves with m, and is moderately tighter than for worst case partial-band noise (Figures 2.24 and 2.25). 2.97 dB 58 dB Eb/Nj, dB Figure 2.43. Same as Figure 2.42, except K = 4. Accuracy degrades significantly with K for small m ~ 2, but increases only slightly with K for large m VN 10. Non-Coherent Frequency-Hopped Systems Eo/Nj=19 = dB K = 2 BOUND K = 2 EXACT DIVERSIT Y m CHIPS/SYMBOL Figure 2.44. Accuracy of upperbound performance variation with diversity for FH/MFSK signals in worst case n=1 band multitone jamming (refer to Figure 2.41). Performance for K = 1 is slightly better than K = 4 for small m, but improves dras- tically as 2-m in the saturation region m Eb/2N where = 1 (see (2.76)). E6/N = 14 dB EXACT ao = .683 BASED ON UPPERBOUND EXACT =.427 BASED ON UPPERBOUND DIVERSITY m CHIPS/SYMROI Figure 2.45. Comparison of "quasi-worst case" jamming parameter awc derived from Pb upperbound of (2.86) and (2.87) with actual worst case parameter based on (2.97)- (2.99) and (2.102) describing exact performance of FH/MFSK signals with d