r combina- tion of hits and misses will maintain the SLS in the lock mode once it has entered that mode. Furthermore, the dwell time Td2 (>Tdi) is assumed to be the same for all three lock mode states. 1.81 Mean and Variance of the Acquisition Time A suitable analytical approach for evaluating the behavior of the SLS is to represent it as a finite Markov chain with absorbing boundaries. Such a Markov chain model for the SLS of Figure 1.59 is illustrated in Figure 1.60. Note that Figure 1.60 is analogous to the generating function flow graph for the single dwell system (Figure 1.5) except that, for convenience, we have omitted the branch parameter Z which was previously used to mark time as one proceeded through the graph. Each branch of Figure 1.60, however, is still labelled with the transition probability appropriate for going from one Pseudonoise Code Acquisition in Direct-Sequence Receivers REJECT CELL, SEARCH ADJUST PHASE (Tdl) SEARCH (Tdl) ENTER LOCK MODE, SET LOCK MODE PARAMETERS ENTER SEARCH MODE, SET (Td2) SEARCH MODE PARAME TERS (Td2) (Td2) Figure 1.59. A search/lock strategy. state to the other. Using straightforward techniques for analyzing Markov chains with absorbing boundaries, it can be shown [9] that the mean and vari- ance of the acquisition time of the combination of the single dwell acquisi- tion system of Figure 1.4 and the SLS of Figure 1.59 are given by (1.288) (1.289) Search / Lock Strategies P = P(HIT|SEARCH MODE) 90=1-PO P1 P(HIT LOCK MODE) 91=11-P1 Figure 1.60. Markov chain model of search/lock strategy. where PL is the probability of lock, i.e., the probability of entering the lock mode assuming the search has reached the correct cell, and Td is the mean dwell time for an incorrect cell. In terms of the Markov chain model of Figure 1.60, PL is simply the probability of going from state 1 to state 3 with P1 = PD1 and 91=1 - PD1 where PD1 is the detection probability for the search mode. Furthermore, Td is the mean time to reach states 0 or 6 (the two absorbing states) from state 1 with 