 we assume a desired P of 10-5 , (2.126) and (2.128) suggest that we use EbIN1 = 14.58 dB and m = Mopt = 13. Using previously derived bounds on P for worst case jamming with arbitrary diversity, curves of performance versus diversity are drawn in Figure 2.65 for n = 1 band multitone, independent multitone, and partial- band noise jamming with the selected K and E/N. Although Mopt = 24 and 22 respectively for the last two jammers, we see that the bound onPb for these jammers at m = 13 does not exceed the desired bit error rate, SO we do indeed have a viable system design. Non-Coherent Frequency-Hopped Systems WC n=1 BAND MULTITONE JAMMING MOPT = 13 WC INDEPENDENT MULTITONE JAMMING WC PARTIAL-BAND NOISE MOPT 22 E , IN = 14.58 dE DIVERSITY, m Figure 2.65. Variation in performance of FH/8-ary FSK systems with diversity for several kinds of worst case jamming when EIN, = 14.58 dB, which was selected to achieve a P of 10-5 or better under any jamming conditions with m = 13. 2.3.2 Coding without Diversity We have seen in the previous sections that time diversity techniques can sig- nificantly reduce the effectiveness of worst case noise and multitone jam- mers against FH/MFSK signals. In particular, optimum diversity restores the exponential relationship between Pb and Eb/N1 from the inverse linear dependence characterizing worst case jamming without any coding redun- dancy. Yet, diversity transmission corresponds to a simple repetition code. And there are many block and convolutional codes that are much more power- ful than repetition codes, based on experience with classical additive Gaussian noise channels. It remains to be seen how effective these codes are in a non-stationary, non-Gaussian jamming environment. In fact, it would probably be valuable to derive codes and detection metrics specifically matched to the more insidious pulsed, partial-band, or tone jamming chan- nels characteristic of the electronic warfare era. Several papers in the open literature have investigated the effectiveness of various block, con