17) an equal or smaller acquisition time mean and variance. Thus, in conclusion, evalua- tion of (1.113) and (1.117) using (1.124) for the choice of unconditional detection probabilities, i.e., p=1+Pp (1.125) gives an upper bound on T ACQ and ACQ for the double dwell system. To proceed further, we note that, analogous to (1.120), (1.126) Since (1.127) The right-hand side of (1.127) represents [see (1.105)] the system false alarm probability for the two-dwell system. Thus, if PEA denotes the system false alarm probability of the single dwell system and we set P F A2 = P F A (1.128) then we are guaranteed that the two-dwell system will have an equal or lower false alarm probability. Thus, including (1.128) as a condition on the design will once again produce upper bounds on TACQ and OCA evaluated from (1.113) and (1.117), respectively. Since, as previously shown, both (1.113) and (1.117) depend on F(N) of (1.118), we shall focus our attention on the evaluation of F(2) using (1.125) and (1.128), or, for equal false alarm penalty times for the single and dou- ble dwell systems, the simpler function (1.129) evaluated for N = 2. Letting N = 2 in (1.129) gives G(2)TdPTd (1.130) which, from (1.115), when less than T of the single dwell system, will yield an improved acquisition performance. From the general relationship among false alarm probability, detection probability, pre-detection signal-to-nosie ratio, and IF bandwidth-dwell time product for a non-coherent detector (see (1.81)) we can write, for the sin- gle dwell system, (1.131) where A2/NBB is replaced by y', the effective pre-detection signal-to-noise ratio, and f() represents the solution of (1.81) for BTd. Similarly, for the Pseudonoise Code Acquisition in Direct-Sequence Receivers double dwell system, Then, since by definition Td1 < Td2, we conclude that PEA1 > PFA2, or in view of (1.128), PEA = PFA2 PEA < 1. (1.133) Now, if PEAI = PEA2, then Td1 = Td2 and from (1.130) G(2) =Td2 = Td. (1.134) Alternately, if PFA1 = 1 and P FA2 = PFA <1, then, from (1.130) G(