Finally, if in addition K << q, then (1.45) simplifies to (1.46) which is in exact agreement with (1.7). Although somewhat lengthy, the heuristic derivation of (1.34) and (1.46) is important in that false alarms and missed detections are readily identified in terms of their individual contributions to the mean acquisition time and variance. 1.2.3 Single Dwell Acquisition Time Performance in the Presence of Code Doppler and Doppler Rate When code Doppler is present, the acquisition time performance of the sys- tem of Figure 1.6 is affected in two ways. First, the code Doppler causes the relative code phase between received and locally generated PN codes to be time varying during the dwell time of the integrate-and-dump. This has the Pseudonoise Code Acquisition in Direct-Sequence Receivers effect of increasing or decreasing the probability of detection P, depend- ing on whether the code Doppler is causing the relative code phase to increase or decrease. The second and potentially more dominant effect is that code Doppler affects the average search rate. In fact, if the code phase shift caused by the Doppler over a single dwell time is equal to the step size (phase update) of the search, then the average search rate is reduced to zero. To take both of these effects into account when computing mean acqui- sition time is indeed a difficult, if not impossible, analytical task. However, it is possible to account for just the effect of Doppler on average search rate in a way which represents an obvious extension of the previous results. Letting Afc denote the code Doppler in chips/sec, then the mean search (code phase) update in chips is given by [1]: (1.47) where12 Nu/q' represents the search update in the absence of Doppler or, equivalently, the step size of the search in fractions of a chip, AfcTd is the code phase shift due to Doppler during the dwell time, and is the code phase shift during verification caused by a false alarm. Thus, replacing q by Nu/u in (1.4) and (1.7) gives expressions for the mean and variance