-10 -12 -14 -16 -18 -20 -22 -24 E INO. dB Figure 1.32a. Mean acquisition time versus EJNo; N = 1,A = 4,B = 2, PACQ > .95 (reprinted from [14]). Pseudonoise Code Acquisition in Direct-Sequence Receivers 2/1'0'2/1 = 3 1538 0321WI100 01/000 WOWININ MINIMUM ACQUISITION TIME M = 64 OPTIMAL THRESHOLD M = 1024 MINIMUM ACQUISITION OPTIMAL THRESHOLD INO, dB Figure 1.32c. Mean acquisition time versus EJNo; N = 4, A = 4,B = 2, PACQ > .95 (reprinted from [14]). Pseudonoise Code Acquisition in Direct-Sequence Receivers START OF SEARCH CODE UNCERTAINTY REGION (q CELLS) Figure 1.33. A three-window optimized sweep strategy. per pass, in search of the correct code alignment. When the a priori pdf of the signal location is in some sense peaked rather than uniform, then it is more likely to find the correct code phase in the "region" surrounding the peak and one's sweep strategy should be adjusted accordingly. Since, for this situation, full sweeps across the entire uncertainty region would clearly not be the best strategy, one should instead postulate a suitable performance measure, e.g., acquisition time, and proceed to choose a search pocedure that optimizes this measure subject to the given system constraints. Indeed, it is intuitively obvious that the number of cells to be searched (and thus the acquisition time) will be reduced by a procedure which begins searching in the region where the likelihood of finding the signal is highest. 1.6.1 An Example-Single Dwell Serial Acquisition with an Optimized Expanding Window Search As a means of illustration, we shall reduce the scope of the general search problem discussed above by considering first the specific, but practical, case of a single dwell PN acquisition system with a symmetric "expanding window" search centered around the mean of a symmetric, unimodal, a priori signal location pdf (x) [20]-[24]. An example of such a search strategy for Nsw = 3 sweeps prior to acquisition is illustrated in Figure 1.33. Let L1 < LN,10 denote the lengths (in number of cells) of uncertainty re