 of the acquisition time in the presence of code Doppler, namely [1], KPFA) TACQ / no code Doppler (1.48a) O'ACQ A'CC / no code Doppler (1.48a) Since Afc can be either positive or negative, depending upon its sign, the code Doppler can either speed up or slow down the search. With regard to the 12The prime on q is used here to denote the number of cells searched in the absence of Doppler. The Single Dwell Serial PN Acquisition System magnitude of the code Doppler, we shall assume that Afdad + KPFA) << Nu/q', SO that the denominator of (1.48a) and (1.48b) never approaches zero and the search always proceeds in the direction dictated by the code phase update provided by the local PN generator. Finally, note that, when Af = 0, then q' = q and (1.48a) and (1.48b) reduce to (1.4) and (1.7), respectively as they should. The way in which code Doppler is accounted for in extending the results of (1.4) and (1.7) to those given in (1.48a) and (1.48b) can also be applied to further extend them to include the effect of code Doppler rate. In par- ticular, one computes the mean search update analogous to (1.47) and again replaces q by Nu/u in the expression for mean acquisition time and acquisi- tion time variance. When code Doppler alone was present, we observed that the mean (sta- tistical) search update was time invariant, i.e., the expression in (1.47) char- acterizes every cell being searched. When, in addition, code Doppler rate is present, the mean search update is now time dependent in the sense that it is now a function of the cell being searched. In general, the mean search update in any given search cell is equal to the nominal search update Nu/q' (typically, 1/2 for half-chip search incre- ments) of the local PN code generator plus the mean change in phase of the received code over the search time of that cell.¹³ Thus, letting Un denote the mean search update in the n-th cell being searched, and f the code Doppler rate in chips/sec2, then from the Markov model previously estab- lished for the single dwell time syst