hannels, one would expect that they would be useful against partial-band noise jamming as well. This is indeed true and will be shown next. Define diversity of order m as the case where each M-ary symbol is trans- mitted m times over the channels described in the previous sesctions. Thus, if E is the energy for each transmission then each M-ary symbol requires a total energy of Es=mEc (4.98) The transmitted symbol for each single use of the channel is now referred to as a "chip." Thus, with diversity of order m, each M-ary symbol consists of the transmission of m chips. Each transmitted chip consists of a frequency-hopped MFSK tone over the partial-band noise jammed channel described in the previous section. If symbol x = i is to be transmitted, then the i-th MFSK tone is transmitted 5We take the high signal-to-noise ratio to be infinite for one level. General Analysis of Anti-Jam Communication Systems m times where each tone is independently hopped (ideal interleaving assumption is used for slower hop rates) resulting in independent jamming conditions for each chip or transmitted tone. The output corresponding to symbol X = i consists of the m chip outputs k=1,2,...,m (4.99) with the channel input Xk =xfork=1,2,...,mwhere ekj is the detected energy at the j-th tone frequency during the k-th chip interval or k-th use of the channel. Thus, when symbols Xk = x, k = 1,2, m are transmitted the m channel outputs are (4.100) For the conventional additive white Gaussian noise channel, the natural choice for the metric is . + emx (4.101) x =1,2,...,M. = That is, the decision is based on the non-coherent com- bining (or sum) of the energies of each of the m chips corresponding to each of the MFSK tones. With the partial-band jammer and jammer state knowl- edge available a more general metric is m(y,x;)=c(21)e1x+c(22)e2x+ = + c(Zm)emx (4.102) where (4.103) represents the jammer state information for the m uses of the channel. A new extended channel is obtained where each input symbol results in m uses of the channel consid