le. Another unfortunate situation occurs in regard to the application of Albert's approach to the time-out type of sequential detection system (see Figure 1.43) where the upper threshold is replaced by a maximum time fea- ture. Even in the case of signal absent, there appears to be no valid modifi- cation of the basic approach to apply to this situation. In view of the foregoing limitations and analytical difficulties, one PN Synchronization Using Sequential Detection Y = .01 WALD'S RESULTS b' I = r b = r (1+ y12) 1 = LOWER THRESHOLD = -2 7 = SIGNAL-TO-NOISE RATIO & = 5 UPPER THRESHOLD, 7 Figure 1.47. Probability of alarm for the biased square-law detector when the sig- nal is not present (reprinted from [29]). b'=y y/2) WALD'S RESULTS = UPPER THRESHOLD = 5 LOWER THRESHOLD SIGNAL - TO - NOISE RATIO, Figure 1.48. Average test duration for the biased square-law detector when the signal is not present (reprinted from [29]). PN Synchronization Using Sequential Detection normally, at this point, turns to a simulation approach. The salient features of such an approach along with typical numerical illustrative results are pre- sented in the next section. Before completely abandoning the analytical approach, however, we recall that Wald's approximate analysis does indeed provide us with a relationship among false alarm probability, detection probability, and the upper and lower detection thresholds [see (1.254) and (1.255)]. Thus, in the region of validity of his approach, i.e., small values of y and the bias of (1.263), one can combine (1.254) and (1.255) with (1.276) and (1.279) and obtain an expression for the average dismissal time (aver- age test duration for a noise only cell). This relation can then be compared with the fixed dwell time determined from (1.81) for the single dwell sys- tem to establish the degree of superiority of the sequential detector. Thus, we conclude this section with a comparison of the mean search times of the single dwell and sequential detection systems using Wald's approach to analytical