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A particular type of communications detection problem is considered: the problem of specifying a detector to decide which one of two sure signals is being transmitted when the signals are perturbed randomly both by Gaussian noise and multipath transmission. If the delays in the various channels are known, but the strengths are random, a maximum likelihood detector may be specified by methods which are a simple extension of known methods. If the delays are random, the problem is more difficult. One possible solution is first to estimate certain channel parameters from the received signal and then to use these estimates in a likelihood test. It is shown how to make consistent unbiased estimates for appropriate channel parameters under certain assumptions on the nature of the signal.