Performance of a suboptimal multisample decision rule against known signals with additive unknown-mean amplitude-bounded random interference

The robust single-sample randomized decision rule for known signals in independent, unknown-mean, amplitude-bounded, additive noise ([1], [2]) is extended to a two-stage suboptimal multisample decision rule for independent finite sample size (M) measurement sequence (x1,.... .,xM). The first stage is the robust single-sample decision rule of [2] using N random thresholds; The second stage is essentially the M-sample sign detector. Performance is evaluated both analytically and via simulations in terms of the probability-of-error Pe. Comparisons are made with the sign detector for a variety of noise models. The optimum second-stage threshold ??0 = (M+2)/2, and Pe is shown to improve rapidly with increasing M and decreasing N.