n time improvement factor ver- sus P. We observe that the maximum improvement occurs for PD = 1 (absolute probability of detecting the correct cell once it is reached) in which case (1.235) reduces to (1.236) T ACQ broken i.e., a 37.5 percent saving in acquisition time. In the more general case where the a priori probability distribution of the code phase uncertainty is arbitrary (but symmetric), for PD = 1 and V large, it is simple to show that29 (1.237) T ACQ broken 29 When v is large, the assumption of v odd is inconsequential. Acalcont ACO / BROKEN 1.37. Mean acquisition time improvement factor versus detection probability for single dwell acquisition system Figure angular a priori code phase uncertainty distribution. Pseudonoise Code Acquisition in Direct-Sequence Receivers which is lower and upper bounded by Incolorm (1.238) corresponding to the a priori distributions (1.239a) (1.239b) Thus, regardless of the a priori probability distribution of the code phase uncertainty, the broken/center Z search potentially offers an improvement of at least 20 percent and at most 100 percent over the continuous/center Z search. Of course, for PD < 1, these improvements will decrease accordingly. Finally, we consider the class of expanding window search strategies, two representative cases of which (A and B) are shown in Figure 1.38. The two cases differ in the way the search is continued once the entire uncer- tainty region has been covered without success. In particular, case A repeats the search starting from the R1 window,30 while case B continues by repeat- ing the RN,19 window. We note that the strategies analyzed in [21]-[23] constitute slight variations of case B. The equivalent circular state diagrams for the two cases are shown in Figure 1.39. We observe that, after complet- ing the first sweep, case B is indistinguishable from the continuous/ center Z. search. Furthermore, the diagrams are composed of hexagons with an inscribed Ri; those represent portions of the state diagram which corre- spond to the partial