or a single dwell serial search system indi- cating the effect of multiple cells with non-zero correlation. lar correlation curve). Then, the H region of the flow graph expands as in Figure 1.24, where PD(Qi); i = 1,2, 3, 4 denotes the detection probability eval- uated via (1.71) or (1.80) at the relative code misalignment corresponding to Qi Thus, instead of the simple entries of H(z) and HM(2) as in Table 1.1, we now have (1.160) (1.161) As promised, we conclude this section with a discussion of how to apply the flow graph model to the limited acquisition time case. We recall from the introduction that this case is characterized by the requirement to achieve acquisition (with a given probability) within a finite time, say Ts. Thus, the appropriate performance measure to use here is the probability that the acquisition time TACQ is less than Ts, which can be calculated by evaluating the cumulative distribution function of TACO at Ts. Alternately, if Ts corre- sponds to J dwells, then we are interested in the probability PACQ(J) of acqui- Rapid Acquisition Using Matched Filter Techniques sition in J or fewer dwells as given by a relation analogous to (1.98), which can be evaluated by finding the generating function corresponding to this cumulative probability distribution. Such a generating function is defined by (1.162) which can be written in the form V(2)= (1.163) Comparing (1.163) with (1.94), we observe that (1.164) Since PACO(I) is the coefficient of ZI in the power series of (1.162), we can evaluate it with a contour integral analogous to that used to evaluate inverse Z transforms, i.e., (1.165) where U(z) is given by (1.154) and T is a counterclockwise closed contour in the region of convergence of V(z) that encircles the origin. 1.5 RAPID ACQUISITION USING MATCHED FILTER TECHNIQUES Until now, we have considered only DS acquisition techniques in which the measure of PN correlation was produced by an active correlation of the received signal with a locally generated PN reference. For example, in the single