.263), i.e., (1.277) and thus, with Albert's approach, one can study the effect of bias variations on the resulting performance measures. On the other hand, although not pre- viously stated, Wald's result for false alarm probability as applied to the square-law biased detector implies the optimum bias of (1.263) and fur- thermore is independent of Y [see (1.254)]. Figure 1.47 contains three sets of plots of false alarm probability versus the upper threshold n'1 with pre-detection signal-to-noise ratio Y as a para- meter. The first set of plots corresponds to Wald's result of (1.254). The remaining two sets are obtained from Albert's exact result, i.e., (1.269) with two different biases, namely, the optimum choice of (1.277) and b' = y. Perhaps the most striking feature of the exact results is their extreme sen- sitivity to small variations in bias. For example, when y = .01, then from (1.277) we would have an optimum bias b' = .01005, which only differs from b' = y = .01 by an amount equal to .00005. Nevertheless, the false alarm probabilities for these two bias values are markedly different. A similar sit- uation occurs in Figure 1.48 where the average sample number M1(0) is plot- ted versus Y with lower threshold n'2 as a parameter and the same three situations as in Figure 1.47. Here, Wald's result for the average sample num- ber of a sequential test corresponds to evaluating (1.256) with the In I func- tion in (1.257) approximated, as previously discussed, by (1.258). Performing the expectation with the aid of (1.76) gives (1.278) which when substituted in (1.256) results in (1.279) where PFA is given by (1.254). Unfortunately, a similar analysis for the case of signal present is difficult and has not been made available in the open literature. Thus, the relation- ship among detection probability, pre-detection signal-to-noise ratio, bias, and the two-decision thresholds has not been obtained and, as a result, a complete analytical characterization of the moments of the system acquisi- tion time is not possib