gives the desired result, namely, (1.14) Similarly, E{(T'u - Th = P)k-1 (1.15) Differentiating (1.13) with respect to PD and simplifying by using (1.13) prior to differentiation gives (1.16) Finally, expanding the square in (1.15) and substituting (1.12), (1.13), and (1.16) gives the desired result, namely, (1.17) Having now characterized the period of unsuccessful search, we turn our attention to the k-th search interval during which the acquisition process will terminate at the location of the correct cell. Letting m denote this correct cell location, the time required to successfully reach this point from the time the k-th search is initiated is clearly Ts = MTd. (1.18) Since, for lack of any a priori information regarding correct cell location within the uncertainty region, m will be uniformly distributed in this region, i.e., p(m)=-;m=1,2.3..... (1.19) with mean (1.20) and variance (1.21) The Single Dwell Serial PN Acquisition System then the mean and variance of Ts are respectively given by (1.22) Finally, the total acquisition time T ACQ.10 is the sum of T'u and Ts with and variance¹1 (1.24) which for q>>1 becomes (1.25) All that remains is to include the effect of a non-zero false alarm proba- bility on the results in (1.23) and (1.25). Since out of the total of N' + m cells searched, k of them are actually correct (one per each of the k searches of the entire uncertainty region), then there is a possibility of a false alarm only on any of the NFAN'um-kq(k-1)+m - - k (1.26) remaining cells. Equivalently, NFA is the maximum number of false alarms that can occur. If n denotes the actual number of false alarms that occur, each with probability PFA of occurrence, then conditioned on NFA, n has the bino- mial pdf n==0,1,2,3,...,NFA (1.27) with conditional mean E{n NFA} = NFAPFA (1.28) and conditional variance (1.29) Superscript(1)-The zero subscript is used to denote the fact that we have assumed PFA = 0. 11t is reasonable to assume that Tu and Ts are essentially independent. Pseudonoise Code Acquisition in Di