gions to be searched during the Nsw sweeps. (We shall set Lo= for convenience.) Then if, as before, k (inte- PN Sync Search Procedures and Sweep Strategies ger) denotes the particular search of the uncertainty region during which the correct cell is first detected, then the generalization of (1.8) for the pdf of k is [20] p(k) - P(Ln-1)]: = 1,2,3, (1.203) where P(L) is the probability that the signal location x is within the set L, i.e., (1.204) with P(L0) = 0 and PD is still the probability of detection given that the sig- nal is there. Note that for a uniform a priori signal location pdf and L1 = = LN,w =q then P(L1) = P(L2) = P(LN, = 1 and only the n = 1 term has a non-zero contribution to the sum in (1.203), whereupon p(k) immediately reduces to the result in (1.8). Although (1.203) can be formally derived using Bayes' probability rule, it can also be obtained by a simple heuristic argument as follows. Let Lk be divided into k non-overlapping regions, namely, L1, L2 - L1, L3 - L2, Lk - Lk-1 Each of these regions represents the additional number of cells searched on a given sweep relative to the previous sweep. By the initiation of the k-th sweep, the region Ln - Ln-1 has been searched k 2 n times; n = 1, 2, , k - 1. Thus the joint probability of first detecting signal in Ln - Ln-1 and that indeed it was in that region is P(1 - - Ln21) or, in view of (1.204), P(1 - P)k-"[P(L") - P(Ln-1)]- Since the region Lk - LK21 has not as yet been searched, the joint probability of detecting the sig- nal in this region and that it is indeed there is simply P[P(Lk) - P(Lk21)]- Since the above set of joint probabilities corresponds to mutually exclusive events, (1.203) follows immediately. To define an optimum symmetric search strategy, we must first define a criterion of optimization along with any additional constraints imposed by the physical system. As suggested earlier, we shall choose as an optimum search strategy that which minimizes the total acquisition time for Nsw sweeps where the constraint is to accomplish this 