g on the availability of the side infor- mation sequence Z. The metric is used by the decoder to make decisions as to which sequence was transmitted given the corresponding channel output sequences. The additivity property is important in reducing the decoder pro- cessing complexity. In general in a jamming environment the receiver would most likely have incomplete knowledge of the channel conditional probabilities¹ p(yx, z). Thus, the maximum-likelihood metric (y,x; z) = log p(y\x,z) (4.11) when side information is available or m(y,x) = log p(y)x) (4.12) 1In a jamming environment, it is unrealistic to assume the jamming signal statistical character- istics are known. This is also true of many other cases and, thus, the receiver design is often "mismatched" to the actual channel. General Analysis of Anti-Jam Communication Systems when no side information is available, is not necessarily used in the decoder. Instead, an arbitrary metric denoted m(y,x;z) when side information is avail- able and m(y, x) when it is not available is assumed in the following. (The case where no side information is available can be regarded as a special case where the metric m(y, x; z) does not depend on z.) 4.2 CODED BIT ERROR RATE BOUND Assume for the moment that there are only two possible coded sequences of length N given by (4.6) and (4.13) When the channel output sequence is (4.7) and side information is (4.8) the decoder decides X is the transmitted sequence if (4.14) Otherwise, it decides X is the transmitted sequence. Assuming X is the actual transmitted coded sequence, the probability that the decoder incorrectly decides X is given by This is called a pairwise error probability. Applying the Chernoff bound (see Appendix 4A) (4.15) has the follow- ing bound: (4.16) for any l > 0. For X = Xn it is clear that (4.17) Coded Bit Error Rate Bound Antipodal and orthogonal waveforms commonly used in anti-jam commu- nication systems and all metrics of interest have the important property, - = (4.18) where D(A) is independent of Xn and X