Bias analysis of the forced choice detection test for Rayleigh/Rician statistics

For Rayleigh/Rician statistics at the decision device, the probability of correct decision in the forced choice (FC) hypothesis test is given in terms of a closed-form finite series. This leads naturally, via the Gaussian approximation to the binomial distribution, to an explicit confidence interval on the correct decision probability in a FC detection performance test. The analysis is verified by comparison with the results of a Monte Carlo trial. A compact expression is also derived for the conventional receiver operating characteristic (ROC). The two analytical expressions are used to obtain an exact characterisation of the bias in the estimated probability of detection from the FC and the conventional likelihood ratio test. It is shown that at high probabilities of false alarm the forced choice test overestimates the actual detection probability at moderate SNRs.