ovement relative to m = 1 is 35 dB at Pb = 10-5, and the performance at that Pb is only 1.6 dB worse than in broadband noise. And for m > m*, the performance is even better; in fact, for large enough values of m, Pb is lower than in broadband noise (it is not plotted since Pb becomes arbitrarily small for large m). If the m = Mopt performance here is compared with the worst case partial-band noise/optimum diversity curve in Figure 2.32, which was 3 dB worse than the broadband noise case for small Pb's, recall that the latter curve is an upperbound while the for- mer is exact. Turning now to larger size alphabets (K > 1) but still considering only n = 1 band multitone interference, the performance with m-diversity and the suboptimum linear sum metric with perfect side information will now be ana- lyzed using the union/Chernoff bounding techniques of Section 2.3.1.1. Because of the side information, it is convenient to introduce the event Hi that the j-th chip is jammed, as in the partial-band noise case. Adopting the convention of Section 2.3.1 which declares that a particular chip is jammed when two or more energy detector outputs are high on a given transmission, for n = 1 band multitone jamming. (2.80) Non-Coherent Frequency-Hopped Systems Under the assumption that the receiver has error-free information about which of the m diversity transmissions are jammed, an M-ary symbol error requires the occurrence of H = (H,H, Hm), where (2.81) using (2.74). Let lij denote the energy detected for the i-th M-ary symbol on the j-th diversity transmission, normalized by the chip signal energy Ec, and suppose symbol 1 is sent. Then, as in (2.60) and (2.61), the M-ary detection problem is reduced to a binary one by employing the union bound: (2.82) Next, the m-ary statistics are simplified to those for a single chip transmis- sion by applying the Chernoff bound: (2.83) The factor of 1/2 that appeared in the partial-band noise bound of (2.61) is absent here because the discrete-valued eij's do not satisfy the sufficient con- 