P1 = PFA1,91=1- - PFA1,P2 = PFA2, and q2 = 1 - PFA2 where PFA1 and PFA2 are, respectively, the false alarm proba- bilities in the search and lock modes. Before proceeding to an evaluation of PL and Td for the SLS of Figure 1.59, we draw attention to the similarity of (1.288) and (1.4), the latter being the mean acquisition time for the single dwell acquisition acting alone (i.e., in the absence of the SLS). Clearly without any hit verification, the proba- bility of lock would simply be equal to the detection probability of the detec- tor in the search mode of operation, i.e., PL=PD. (1.290) Furthermore, the average dwell time for an incorrect cell without an SLS is the average of the dwell time for a miss (which occurs with probability 1 -PFA) and the dwell time for a hit (which occurs with probability PFA) includ- ing the penalty of K dwell time units to discover the false alarm. Thus, TdTd(1-PFA)+(Td+Ktd)PFA = Td(1+ KPFA). (1.291) Finally, substituting (1.290) and (1.291) in (1.288) results in (1.4), as it natu- rally should. Pseudonoise Code Acquisition in Direct-Sequence Receivers 1.8.1.1 Evaluation of Probability of Lock The events contributing to an entering of the lock mode starting in search state 1 are as follows: hit-hit hit-miss-hit-hit hit-miss-hit-miss-hit-hit hit-miss-hit-miss hit-miss-hit-hit. n hits, n misses Since the above events are mutually exclusive, the probability of lock is sim- ply the sum of the probabilities of these events, i.e., (1.292) PROBABILITY OF HIT IN SEARCH MODE, PD Figure 1.61. Probability of lock versus search mode detection probability (reprinted from [9]). Search / Lock Strategies or in view of the previously mentioned substitution for P1, (1.293) Figure 1.61 is a plot of PL versus PD1. 1.8.1.2 Evaluation of Mean Dwell Time The mean dwell time can also easily be computed by first identifying the events contributing to a dismissal of an incorrect cell starting in search state 1, and then assigning the appropriate dwell time and probability of occur- rence to each of these e