HM(z) = gain for missed verification of detection HFA(Z) = gain for false alarm occurrence HNFA(2) = gain for no false alarm occurrence Hp(z) = gain for penalty after false alarm occurrence Proper combination of these gains then allows computation of the gain asso- ciated with the "generalized" branch between any pair of nodes, e.g., Ho(z) = H NFA(Z) + H FA(Z)H (z) (1.153) represents the gain in going from node i to node i+1 for i = 1,2,...,V - 1. As before, the flow graph representation of the system is used to compute the moment generating function U(z) of the underlying acquisition process. Using standard flow graph reduction techniques, it can be shown [14] that (1.154) For the two special cases of uniform and worst case a priori state probabil- ity distributions, (1.154) reduces to (1.155a) (2) , (worst case). (1.155b) The complete statistical description of the acquisition process is obtained by substituting for the various H(z)'s in (1.154) the expressions appropriate to the particular configuration at hand and then, as before, expanding the result in a power series in Z (see (1.94)). In general, obtaining the complete Pseudonoise Code Acquisition in Direct-Sequence Receivers set of coefficients of this series is a difficult task and approximations must be made in the manner discussed in [7]. Alternately, if one is pleased with the first few moments of the acquisition time, then the relations of (1.3) and (1.6) as applied to U(z) of (1.154) or its special cases in (1.155) are appro- priate. In particular, for the mean acquisition time TACQ, we obtain from (1.3) and (1.155) the results 1 HM(1)H,-1(1) (uniform) HD(1) H'D(1) + + - if H0(1) = 1 (1.156a) H(1) PACQ H0(1) (worst case) [H'D(1) + H'M(1) + (v - 1)H'(1) HD(1) if H0(1) = 1 (1.156b) where the primed quantities denote differentiation with respect to Z, i.e., H'(1) = d/dzH(z):=1: and (1.157) i.e., the probability of acquiring after any number of dwells (see (1.98)). Furthermore, note that in the case H1(1) = 1, (1.154) and (1.157) combine to yield (1.158