nified approach discussed in Section 1.4. PN Sync Search Procedures and Sweep Strategies (1.213) Satisfaction of (1.213) with the equality sign gives a lower bound on Nsw, namely, (1.214) Similarly, since L1 < L2 < . . . < LN,100 then P(L1) < P(L2) < ... S P(L,). Hence, (1.215) (1.216) Before presenting a specific example of the application of the previous results and the benefits gained therein by using an optimum search strategy, we must first discuss a measure of improvement which can be used in com- paring the optimized scheme to the uniform (full sweeps across the entire uncertainty region) sweep scheme. We recall that for a uniform a priori cell location pdf, the probability of first acquiring during the k-th full sweep is given by p(k) of (1.8). Thus, for a given desired probability of acquisition PN33 , the number NF of full sweeps (each having q cells) would be obtained from the solution to (1.217) (1 - PD)N V < 1 - (1 (1.218) The solution to (1.218) is easily shown to be (1.219) where again x denotes the largest integer less than or equal to X. Since within a given sweep interval, say the k-th, the cumulative probability of acquisition would be a linear interpolation between the upper and lower bounds of (1.218), the total search length LTU (in cells) for the uniform sweep Table 1.2 Improvement in acquisition time performance of optimized non-uniform sweep relative to uniform sweep. % Reduction Uniform Sweep Optimized Sweep Acquisition Time LTU/O* ( 1-1) x 100 1 - < 100 (Nsw = 3) PD=.25 14.67 PN310 = .5 (Nsw = 4) (Nsw = 4) Pp = .5 15.25 (Nsw = 5) 15.22 For the uniform sweep case, we assume the search region corresponds to + 30, i.e., q = 60. PN Sync Search Procedures and Sweep Strategies strategy is given by (1.220) or upon simplification (1.221) The improvement factor of the optimized sweep strategy over the uniform sweep strategy is then (1.222) where LT is determined from the solution of (1.211) using the same PD and As an example, consider a truncated Gaussian a priori pdf for (x). Then, the solutio