 relative code phase posi- tions of the received and locally generated codes, the local PN generator is assumed to start the search at any code phase position with equal probability. Stated in mathematical terms, the probability P1 of having the signal present (true hit) in the first cell searched is 1/q, and the probability of it not being there is 1 - 1/q. For example, if the number of code chips to be searched is denoted by N and the search proceeds in half-chip increments, then q = 2N and P1 = 1/2 Nu- More generally, if it has been determined that the signal is not present in the first k - 1 cells, then the a priori probability Pk of find- ing it present in the k-th cell is 1/(q + 1 - k), where q + 1 - k is obviously the number of remaining cells to be searched, each possessing an equal prob- ability of having the signal present. A generating function flow graph for the q-state Markov chain which char- acterizes the acquisition process of the single dwell system is illustrated in Figure 1.8. As is customary in such flow graphs, each branch is labelled with the product of the transition probability associated with going from the node at the originated end of the branch to the node at its terminating end, and an integer (including zero) power of a parameter denoted here by Z. The parameter Z is used to mark time as one proceeds through the graph and its power represents the number of time units (dwell times) spent in travers- 8If one of the cells corresponds to perfect sync., i.e., the peak of the triangular correlation curve, then there are only three cells which correspond to non-zero code correlation. The Single Dwell Serial PN Acquisition System (1-PFA)z (1-PD)8 (1-PFA)Z (1-PFA) z 11-PEARZ POT (1-PD)z (1-PFA)z (1-PFA)Z S = START NODE (1-PFA) F = FINISH NODE K = NUMBER OF PENALTY TIME UNITS DUE TO FALSE ALARM PD = DETECTION PROBABILITY PFA = FALSE ALARM PROBABILITY (1-PFA)Z 1-Pq-1 (1-PD)z (1-PFA) PFA21 (1-P-18 PA (1-PFA)2 (1-PD) (1-PFA)z Figure 1.8. Generating function flow graph for acquisition time. ing th