e used to compute a generating func- tion for acquisitioni time, the Z;'s have the following associations: Z1 repre- sents a time delay of Td1, Z2 a time delay of Td2 Td1,..., and ZN a time delay of TdN - Td,N-1. Thus i=1,2, N represents the additional dwell time one must wait before testing the i-th threshold after the (i - 1)-st threshold has been tested. The detection transition probability P Dili-i; = 1,2, N corresponds to the probability that, for the cell containing signal plus noise, the i-th dwell integrate-and-dump output Z exceeds its threshold conditioned on Z, Z, , Zi-1 all having exceeded their respective thresholds. In mathematical terms, letting Ni; i=1,2, , N denotes the i-th threshold; then > N2, , > ni-1}. (1.102) The Multiple Dwell Serial PN Acquisition System S = START NODE F 8 FINISH NODE 1-Pq- PD >FA Figure 1.17. Generating function flow graph for acquisition time of the N-dwell process. Pseudonoise Code Acquisition in Direct-Sequence Receivers party Poili-12 y;=(1-Poili-) & B1 Bi of DB B1 El Figure 1.18. Flow graphs for intra-cell behavior of N-dwell process. Similarly, for a cell containing noise only the false alarm transition proba- bility PFAili-1 is defined identically to (1.102). With the meaning of the branch labels having been defined in Figure 1.18, the significance of each of the sub-flow graphs (actually a collection of branches corresponding to a single branch in Figure 1.17) is explained as fol- lows. Figure 1.18(a) corresponds to reaching the event of a successful acqui- sition, i.e., reaching the finish node starting at a node corresponding to the correct cell. This event can occur only if all of the N integrate-and-dump out- puts exceed their thresholds. Hence, each node along OD represents one of the N dwells and the probability Pop associated with the traversing this entire branch is the system detection probability²1 PD=IIP = nn}. (1.103) Figure 1.18(b) corresponds to the event of causing a code phase update, i.e., advancing the search to the next cell starting at a node 