ting exponentially tight upperbounds. Still, the accuracy of these bounds remains a source of concern and raises issues of credibility. In the partial-band noise case we were able to use some exact calculations derived by Trumpis as a benchmark (recall Figures 2.25 and 2.26). Here, for n = 1 band multitone jamming and a soft decision non-coherent combining metric with perfect jamming state information, we can use combinatorial techniques to again compute the exact performance. However, the results are much more complex, particu- larly for large amounts of diversity, and they do not yield insights as readily as the closed form expression of (2.90). Suppose symbol 1 is sent and event H occurs, which is a necessary condi- tion for a symbol error in the perfect side information case. Then, for a given jammer parameter a, the normalized conditional soft decision symbol met- rics of (2.57) are (2.93) where li denotes the number of times the i-th symbol is hit by a jamming tone over the m diversity transmissions. Note that conditioned on H, each of the m hops contains only one jamming tone, which is equally likely to hit any of the M - 1 untransmitted symbols on that hop. This is the situation pic- tured in the grid at the beginning of Appendix 2B (I M - 1,. m). The conditional symbol error rate is given by =Pr{{max>ma|H} (2.94) Coding Countermeasures where (2.95) The probability of any particular pattern of m jamming tones conditioned on H is (M - 1)-m. Appendix 2B computes the number of these patterns satisfying the constraint on lmax in (2.94); in the notation of Appendix 2B, k = ma (2.96) where is the smallest integer greater than or equal to X. Using (2.81) and (2B.8), we have ()M()(-3 where k 1 < ma : < k, and provided (2.97) where X denotes the integer part of X, and we are adopting the convention that the special case of k = 1 or 2, (2B.6) and (2B.7) yield simpler expressions for Pb: and 0<ma< 1 (2.98) m<M - m>M - 1 provided k = 2 and 1 < ma < 2. (2.99) So for m < 8, we can compute the exact performance for any 