H (recall that Nu/q corresponds to the fractional search update in chips), and the total number of cells for H and H combined is q, then V is determined from either p-1+2-4 (1.152a) (1.152b) These V states are indexed in a circular arrangement (see Figure 1.23) with the i-th state, i = 1, 2, q - 1 corresponding to the i-th offset code phase position to the right of the "true" sync position (H1). The remaining two states are the false alarm (FA) state and the correct acquisition (ACQ) state. 25This excludes schemes based on sequential detection methods, which will be discussed by themselves later on in the chapter. Pseudonoise Code Acquisition in Direct-Sequence Receivers HD(2) FALSE ALARM STATE 2-A H Figure 1.23. A flow graph representation of a generalized serial search acquisition system-the circular state diagram. These are also indicated in Figure 1.23 where it is observed that the acqui- sition state can be directly reached only from the v-th (H1) state, whereas the false alarm state can be directly reached from any of the V - 1 states corresponding to the offset cells (H). A flow graph model such as that illustrated in Figure 1.23 is an exact rep- resentation of the state transition diagram of serial search acquisition sys- tems with no absolute limit on acquisition time. Although we are primarily interested in this class of systems (since their underlying process is indeed Markovian), we shall briefly mentioned at the conclusion of this section how the above model can be used in the presence of a finite limit on acquisition time. The first way in which the flow graph model of Figure 1.23 is a general- ization of those previously considered is that the a priori probability distri- A Unified Approach to Serial Search Acquisition with Fixed Dwell Times bution {;j=1,2,...,V) = assigned to the V states at which the search process can be entered is arbitrary. In the absence of any a priori information con- cerning the initial relative position of the codes, the system designer would assign a uniform distribution