cation systems where there are no optimum detectors and maximum-likelihood decoding decision rules are not known at the receiver. Here, we are generally interested in robust detectors that are effective with all types of jammers and easy to compute decoding metrics. Under intentional jamming, it is unrealistic to assume that the receiver has complete knowledge of the jamming signal's statistical characteristics. With channel measurements, the receiver may have some side informa- tion which can aid the decoding process. For example, the receiver may have knowledge of when a jammer signal is present or not during the transmis- sion of a coded symbol. Side information may also include time-varying channel parameter values such as propagation conditions at HF frequencies General Analysis of Anti-Jam Communication Systems measured with channel sounder equipment or the number of other active transmitters in a spread-spectrum multiple access environment. Such side information is included in the general formulation of the expression for upper bounds to coded bit error probabilities. In summary, because for anti-jam communication systems exact bit error probabilities are difficult or impossible to evaluate, we derive general upper bounds to these probabilities that are tight and can be numerically evalu- ated. These bounds allow for receivers that have incomplete knowledge of the channel using any of several types of detectors and arbitrary decoding metrics. Channel measurements that provide additional side information can be included in the decision metrics and the impact of such side information can be evaluated with these upper bounds. Ideal signal acquisition and syn- chronization is assumed here. 4.1 SYSTEM MODEL Consider the general anti-jam communication system illustrated in Figure 4.1. Here the channel can include noise, jamming, and possibly channel dis- tortions such as fading and dispersion. The modulator is assumed to be mem- oryless in that any given modulation waveform depends only on one input coded symbol