bound in (2.19) is the leading (i.e., i = 2) term in the summation of (2.14), and is sat- isfied with equality for M = 2. When a symbol error occurs, the decision is equally likely to favor any of the M - 1 incorrect orthogonal symbols. Since M/2 of these incorrect binary K-tuples will produce an error in a given bit, the probability of a bit error is given by [3, (8.14)] (2.20a) (2.20b) V 2K-2e KEB/2N (2.20c) where (2.20c) is satisfied with equality when K = 1. The performance results above are illustrated in Figure 2.5. It is evident that as Eb/N, becomes large enough for a given K or M, the union bound approaches arbitrarily close to the exact bit error probability, reflecting the dominance of the leading term in the summation of (2.20b). Also, the per- formance improves as K increases, which is to be expected since MFSK mod- ulation is equivalent to using an (M, K) binary block orthogonal code (i.e., a code which maps blocks of K bits into M = 2K symbol codewords). The Worst Case Jamming UNION UPPERBOUND Eb/N,,BB Figure 2.5. Performance of conventional MFSK (M = system over AWGN channel, with bit energy Eb and noise power density N. broadband noise jamming results of (2.20) will be used as a reference point for comparing the performance of more sophisticated jammers and FH schemes in the sections that follow. 2.2 WORST CASE JAMMING In this section we will examine the degradation in performance of uncoded SFH/MFSK systems that occurs when a smart jammer has a priori knowl- edge of all FH system parameters except for the PN code (the jammer can even know which PN code is being used provided that it cannot achieve real time PN synchronization), and devises an optimum strategy to exploit this. We will consider the two most effective jamming strategies against FH sys- items: partial-band noise and multitone jamming. In the multitone category, we will analyze several distinct approaches, and identify the best of these. Much of the credit for the initial work in this area belongs to Houston [5], and we will refer fr