n to (1.211) for the optimized sweep lengths can be expressed in the form [20] (1.223) where o is the standard deviation of (x). Using (1.212) to eliminate l requires solution of the transcendental equation (1.224) which although impossible analytically can be accomplished numerically on a digital computer for each allowable value of Nsw. Several numerical exam- ples were worked out in [20] with the results shown in Table 1.2. 1.6.2 Application of the Circular State Diagram Approach In Section 1.6.1 we considered the optimization and performance of a par- ticular expanding window serial search strategy as applied to a single dwell acquisition system. This strategy was but one of a class of search strategies that attain improved acquisition performance when a priori probabilistic information about the true code sync position is available. In this section, we generalize these results by allowing for an arbitrary ser- ial search strategy and an arbitrary detector configuration. The approach taken is based upon the circular state diagram method introduced in Section Pseudonoise Code Acquisition in Direct-Sequence Receivers 1.4 as a tool for modelling and analyzing the complete acquisition behavior of straight (uniform) serial search schemes. The advantage of this approach in the application being considered here is that it circumvents complicated combinatorial arguments used in [21]-[23] to characterize the performance of such systems by employing a transform domain description of the sto- chastic acquisition process. Such a description allows a simple and more sys- tematic evaluation of the generating function of the process using well-known flow graph reduction techniques. While the method to be described applies to arbitrary serial search strate- gies, the focus here will be on the two classes of non-uniform strategies depicted in Figure 1.2, namely, the z-search and the expanding window search. These two classes can be further subdivided into broken or continu- ous searches (depending on whether the receiver empl