the false alarm penalty time Tp = AMT of the coincidence detector with KTd = KT/N, gives K = ANM. From (1.180), we observe that H1(1) = 1 - PFAPFA = 1 - PFA < and thus from (1.154), (1.157), and (1.180), P11,(1181) Rapid Acquisition Using Matched Filter Techniques which is also implied by the presence here of an absorbing false alarm state. Such an absorbing false alarm state comes about when the correlation detector produces a threshold exceedance under H and the coincidence detector verifies it with a B out of A majority logic decision producing a ter- mination of the search. For the uniform and worst case a priori probability distributions, (1.181) reduces to PFA)" (uniform) 1.182) PFA)2 (worst case) 1 - (1 PD)(1 PFA) and the mean acquisition time under these same conditions becomes 1)PFA(1 (uniform) (worst case) (1.183) where To and TM are defined as To = (1 - PFA) + (K + 1)PFA,(1 - PFA) TM = (1 - PD) + (K + 1)PD6(1 - PD). (1.184) When the H region contains more than one cell, the flow graph of this region expands as in Figure 1.28, which is drawn for the special case of N = 1 (two cells, namely Q1 and Q2). Under these circumstances, H(z) and HM(z) of (1.180) are modified to become HD(Z) = {PD(Q1) + PD(Q2)[(1 - PD,(Q1))z + PD(Q1)(1 (1.185a) HM(Z) = PD(Qi))z + PD(Qi)(1 (1.185b) = MATCHED FILTER (CORRELATION) DETECTOR = COINCIDENCE DETECTOR 11-cale P001912 PD06212 [1-PD0(02)] Figure 1.28. Flow graph of the H region for the matched filter acquisition system. Rapid Acquisition Using Matched Filter Techniques 1.5.2 Evaluation of Detection and False Alarm Probabilities for Correlation and Coincidence Detectors In order to apply the results for PACQ and TACQ of the rapid acquisition non-coherent receiver as per (1.182) and (1.183), one needs to calculate the detection and false alarm probabilities for both the non-coherent correla- tion detector (Pdo, , PFA0) and the coincidence detector (Pd, PFA) . Computations of this nature were previously performed in Section 1.2.4 for the non-coherent detector associated with t