Considers the problem of deciding between M signals that are observed through an unknown FIR system (channel). The authors suggest a generalized likelihood ratio test, and develop an upper bound on the detection performance under the worst possible channel. They then suggest a signal design strategy that is immune to the unknown channel effect in which they construct the transmitted signals using an autoregressive mechanism. The signals in this class are distinguished only by the location of their poles. The authors show that in some cases these signal designs achieve the bound.>