oys rewinding in order to skip certain cells), and edge or center searches (depending on where the search and each subsequent sweep are initiated). Recall from Section 1.4.1 that for a straight serial search, the process can be modelled by a circular state diagram (see Figure 1.23) with v + 2 states, where V - 1 of these correspond to out-of-sync cells (hypothesis H0), one to the collecting state (hypothesis H1), one to the absorbing correct state (ACQ), and one to the possibly absorbing false alarm state. Along the branches between these various states are found generalized gains H(z) that represent the generating functions of the individual discrete-time detection processes associated with the corresponding paths. Applying standard flow graph reduction techniques to the circular state diagrams then allows eval- uation of the moment generating function U(z) of the underlying acquisi- tion process. To apply this approach to the non-uniform search case, one merely trans- lates the motion of the specific search strategy under consideration into a circular motion along an equivalent circular state diagram analogous to Figure 1.23. To demonstrate how this is accomplished, let us consider first the continuous/center Z serial search illustrated in Figure 1.34. Here the search is initiated at the center of the code phase uncertainty region and proceeds following the arrows in the manner shown; i.e., it reverses direc- tion every time the boundaries are reached. Assuming that the location of the true sync state (H1) is at the shaded cell, the search process will meet it once during each sweep at the dotted positions. We indicate the starting cell by V - k where, for the H cell to be in the indicated side, k must sat- isfy 1 - 1)/2 (for convenience, we assume V to be odd). Similar diagrams can be drawn for k = 0 or (v + 1)/2 < k < v - 1; however, that will not be necessary due to the symmetry of the problem. Furthermore, we note that since the search is always initiated at the center, II should be interpreted as the proba