On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference--II: The randomized decision rule solution (Corresp.)

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solution uses an equaUy likely mixed strategy to chose one of Bayesian single-threshold decision rules having been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability density , where is a picket fence function with pickets on its domain. Thee pair is shown to satisfy the saddlepoint condition for probability of error, i.e., holds for all and . The decision rule is also shown to be an eqoaliir rule, i.e., , for all , with . Thus nature can force the communicator to use an {em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.