tion probability as in (1.71) and (1.80) would be based on an effective reduction in the nominal signal-to-noise ratio A2/No of 10 log10(.75)2 = 2.5 dB. Since, however, in real- ity two worst case correlation positions exist, then the effective probability of detection P'D for use in computing mean acquisition time is computed (1.82) where the first term in (1.82) represents the probability of detecting signal present on the first corrrelation point and thesecond term is the joint prob- Pseudonoise Code Acquisition in Direct-Sequence Receivers ability of not detecting signal on the first correlation point and detecting sig- nal present on the second correlation point. Clearly, for low signal-to-noise ratios (small PD), the effective detection probability is approximately twice that computed on the basis of a single signal present cell [(1.71) or (1.80)]. In summary, then, the computation procedures would be as follows: For a given PFA, determine from (1.79). For a specified P'D, find PD from (1.82), degrade the given nominal value of Y by 2.5 dB and solve for NB in (1.80). Determine the dwell time from Td = N/B, where B is the given band-pass filter bandwidth determined by considerations on allowable modulation dis- tortion (to be discussed next). Using P'D, , PEA, and Td in (1.4) and (1.7), solve for TACQ and 1.2.6 Modulation Distortion Effects Typically, the PN modulated carrier is also biphase modulated by data. Depending on the ratio of pre-detection filter bandwidth B to data rate R, this data modulation will suffer distortion and an equivalent power reduc- tion as it passes through this filter. The equivalent power reduction factor M2 is computed from ¹8 (1.83) where Sm(f) is the power spectral density of the data modulation and H(j2f) is the equivalent low-pass transfer function of the pre-detection band-pass filter. Thus, the nominal signal power A2 must be multipled by M2 to account for this effect when computing the effective signal-to-noise ratio to be used in the previous detection and false alarm pro