at branch. Furthermore, note that the sum of the branch probabilities (letting Z. = 1) emanating from each node equals unity. Using standard signal flow graph reduction techniques [31]-[33], one can show the the generation function for the flow graph in Figure 1.8 is given by (1.1) Pseudonoise Code Acquisition in Direct-Sequence Receivers where B=1-PD - H(z) = PEAZK+1 (1 - PFA)Z. (1.2) The mean acquisition time TACQ is obtained by differentiating U(zTd)9 with respect to Z and evaluating the result at z=1. After some routine algebra, one arrives at the desired result, namely, 2 + (2 PD)(q 1)(1 KPFA) (1.3) which >> 1 (the case of practical interest) simplifies to (1.4) The variance of the acquisition time is determined from the first two deriv- atives of U(z) by (1.5) or, since U(1) = 1, by the equivalent relation (1.6) Taking the natural logarithm of (1.1) together with its first two derivatives, substituting them into (1.6), and simplifying the resulting algebraic expres- sions, one obtains (for q >> 1 and K<<q) the desired result, namely, (1.7) We hasten to point out that although Figure 1.6 was drawn for a single dwell system with a non-coherent band-pass detector, the above results apply equally to a single dwell system with a coherent detector, the only difference between the two cases being the interrelation of the parameters Td, PFA, and PD for the detector. This interelationship, which is essential for computing acquisition time performance, will be discussesd later on for the non-coher- ent band-pass detector. The above analytical results for the mean and variance of the acquisition time can also be obtained by a simple heuristic approach [34] which, although lacking the mathematical elegance of the Markov chain signal flow graph 9Note that since the generating function has the property that U(1) = 1, we can, if convenient, equivalently differentiate the natural logarithm of U(zTd) and evaluate it at Z = 1. The Single Dwell Serial PN Acquisition System technique, provides additional insight into the acqui