Optimal probability-of-error thresholds and performance for two versions of the sign detector
Joel M. Morris · IEEE Transactions on Communications · 1991
Expressions are obtained for specifying the optimal error probability (minimum P/sub e/) thresholds lambda /sub 01/ and lambda /sub 02/ for the traditional and modified sign detectors, respectively. These thresholds are shown to depend on the parameters p, P/sub 1/, and M where: M is the number of observations z/sub i/ used in the test statistic; P/sub 1/=P(H/sub 1/) is the prior probability for hypothesis H/sub 1/ that signal s/sub 1/ is present and 1-P/sub 1/=P(H/sub 0/) corresponds to the hypothesis H/sub 0/ that signal s/sub 0/ is present; and p=Pr(z/sub i/>or=0 mod H/sub 1/) with s/sub 0/=0 for the traditional sign detector and p=Pr(z/sub i/>or= lambda mod H/sub 1/)=Pr(z/sub i/>