corresponding to the correct cell. This event will occur if any of the N integrate-and-dump outputs fails to exceed its threshold as one progresses through the N-dwell 21 By definition, The Multiple Dwell Serial PN Acquisition System system. Thus, the probability associated with AD is22 = Pr{Z,<n1orZ2<2or Or ZN K NN}. (1.104) Figure 1.18(c) corresponds to a false alarm, i.e., all N integrate-and-dumps exceed their thresholds starting at a node corresponding to an incorrect cell. Note that the last sub-branch of OFA has associated with it ZKN+1, which rep- resents the additional KN penalty time units in accordance with (1.101). The probability POFA associated with this event is clearly the system false alarm probability = Pr{Z; nN} (1.105) where again PFA1|0 All Finally, Figure 1.18(d) is analogous to Figure 1.18(b) and represents the event of updating the search starting from a node corresponding to an incor- rect cell. Again a code search update will occur if any of the N integrate- and-dump outputs fails to exceed its threshold which occurs with probability = Pr{Z1 < N1 Z2 < N2 or or ZN < NN}. (1.106) 1.3.2 Multiple Dwell Acquisition Time Performance With the same standard flow graph reduction techniques [31]-[33] as were used to obtain the generating function for the single dwell system, the flow graph of Figure 1.17 together with Figure 1.18 can be reduced to a single branch whose label is then the N-dimensional generating function for the N-dwell system, namely [7] (1.107) For the i = 1 term, we define Pseudonoise Code Acquisition in Direct-Sequence Receivers where now H(z) = (1.108) With in defined as the integer-valued random variable that represents the number of time delay units of duration Tdn - Td,n-1 that have elapsed when the final node F is reached (acquisition occurs), the acquisition time TACQ is given by23 TAce== (1.109) With U(z) as the moment-generating function for the joint probability den- sity function in), i.e., (1.110) then, analogous to (1.3), the mean acquisition time TACQ is obtained f