Worst-case power-constrained noise for binary-input channels with varying amplitude signals

We consider the problem of communicating in the presence of an additive jammer. The transmitted binary signal amplitude is allowed to vary according to a pseudorandom pattern known at the receiver. We obtain criteria as to what the optimal (communicator) amplitude distributions and (jammer) noise distributions should look like, and some comparative results on the performance in general. We present specific results for the special case where the performance measure is probability of error with maximum-likelihood detection. For this performance measure we also obtain precise results when the amplitude distributions are limited to those with at most two different amplitude levels.<>