A random-threshold decision rule for known signals with additive amplitude-bounded nonstationary random interference

The robust single-sample randomized decision rule for known signals in independent, unknown-mean, amplitude-bounded, additive noise is extended to a two-stage suboptimal multisample decision rule for independent finite-sample-size (M) nonstationary measurement sequences (x₁, . . ., x_M). The first stage is a robust single-sample decision rule using N random thresholds; the second stage is the M-sample sign detector with N randomly chosen sample thresholds. This random-threshold detector, for a given number of thresholds N, is shown to be an equalizer decision rule for a class of nonstationary symmetrical noise; moreover, the equalizer rule P_e performance is a lower bound on independent, asymmetrical noise performance. The set of random-threshold detectors (N>1), when combined with the modified sign detector (N=1), forms a family of equalizer-rule multisample detectors for known signals in nonstationary bounded-amplitude noise where the choice of N and corresponding performance depend only on the ratio of bounded noise range to signal separation S₁-S₀