 Code Acquisition in Direct-Sequence Receivers detector (CD) whose operation is as follows. Upon a tentative decision of an "in-sync" condition (corresponding to hypothesis H1), the local PN seg- ment used for code weighting in Figure 1.27a or stored in the holding reg- ister of Figure 1.27b is now updated by the local PN generator SO that for a specified interval of time, say Tp, the input code and local code segment remain at a fixed relative time offset. During this time interval, the non- coherent correlator/detector continues to make threshold tests; however, to strengthen the reliability of the verification operation performed by the CD these tests are now conducted over disjoint MT sec time intervals of the received waveform and are thus statistically independent. If A of these tests are performed in the time interval Tp, i.e., Tp = AMT then the rule used by the CD for final acceptance of the H hypothesis is that B out of A of these correspond to threshold crossings. Upon successful completion of this major- ity logic decision, the tracking loop is activated, whereas upon unsuccessful completion (fewer than B out of A threshold crossings), the local code seg- ment again is held fixed and the search continues. 1.5.1 Markov Chain Acquisition Model and Acquisition Time Performance The flow diagram for the matched filter acquisiton system is a special case of Figure 1.23 where, for the simple case of only one cell leading to the acqui- sition state ACQ, Hp(z) = 0 Ho(z) = = HD(z) = (1.180) In the above P Do and PFA0 denote the detection and false alarm probabil- ities of the correlation detector (probability of threshold exceedance under H and H, respectively) and PD and PFA are the analogous probabilities of the coincidence detector (probability of B threshold exceedances out of A tests under H and H, respectively). Furthermore, since the effective dwell time Td (i.e., the time spent in examining each cell under hypothesis H in the absence of a false alarm) in the matched filter system is TJN, then equat- ing 