small Afc and Afc, the loss L of (1.88) is well approximated by (1.89) Using (1.88) or (1.89) in (1.85), one is able is compute, to a first-order approximation, the effective signal-to-noise ratio in the pre-detection filter Pseudonoise Code Acquisition in Direct-Sequence Receivers bandwidth when the received signal dynamics are characterized by code Doppler and its derivative. Because of the dependence of L on dwell time Td, the procedure for ulti- mately calculating mean acquisition time is more complex but may be sum- marized as follows: 1. For a given detection probability (P'D) , solve for PD from (1.82). 2. For a specified bandwidth B and filter type, compute M2 from (1.83) and N'o from (1.84). (Actually, carrier and code Doppler affect these com- putations, but we shall assume these are second-order effects.) 3. Using M2 and N' computed in (2) and L from (1.88) or L from (1.89), determine y' from (1.85) (assume A2/No is given). 4. Letting NB = BTd, then for a given PFA, solve for B from (1.79), which together with PD determined from (1) and y' from (3), allows us to solve (transcendentally) from Td from (1.80). 5. Using T as determined in (4), and the given values of P'D and PFA, cal- culating T ACQ from (4) and ACA from (1.7). PD=.01 BANDWIDTH X DWELL TIME, NB Figure 1.9. False alarm and detection probability performance of non-coherent (square-law) detector; y' = -20 dB. The Single Dwell Serial PN Acquisition System PD OI BANDWIDTH X DWELL TIME, NB Figure 1.10. False alarm and detection probability performance of non-coherent (square-law) detector; y' = - 10 dB. To aid in carrying out step (4), Figures 1.9 and 1.10 illustrate PEA versus NB with PD as a parameter for y' = -20 dB and -10 dB respectively. These curves are computed using (1.81). Clearly, for fixed PD and y', the square- law detector performance improves (PFA decreases) as NB increases. However, increasing NB for fixed bandwidth B increases the dwell time Td, which acts to incresae mean acquisition time. 1.2.9 Probability of Acquisition for t