noise only. If y(t) is sampled at intervals T = 1/B, then these samples are approxi- mately independent, and furthermore, the integrate-and-dump output can be approximated by a summation over these sampled values, namely,17 (1.64) where (1.65) Superscript(1)For the moment, we shall not enter into a discussion concerning the various system losses and gains which enter into the calculation of the effective signal amplitude to be used in predict- ing true system signal-to-noise ratio behavior. Such a discussion will be given later on in the development. Superscript(1)7or simplicity of notation, we assume that i = 0 in Figure 1.6 and set Z = Z. Furthermore, is convenient to assume that NB is integer, although the results which follow are, for large N, valid for NB non-integer. The Single Dwell Serial PN Acquisition System Using the approximation in (1.64) and the first order pdf's of (1.61) and (1.63), the pdf of Z, namely, p(Z), for signal present is given by Z > 0 otherwise (1.66) and for signal absent is given by (1.67) otherwise. Normalizing Z by 2o 2/N = No/Ta or, equivalently, letting Z Ill ZN/2o², we can rewrite (1.66) and (1.67), respectively, in the simpler form, p(Z*) (1.68) Z* > 0 otherwise Z* > 0 (1.69) otherwise. The probability of false alarm, PFA, is the probability that Z exceeds the threshold n when signal is absent or, equivalently, in terms of the normal- ized random variable Z and the normalized threshold n* All nN/2o-, (1.70) The detection probability PD is the probability that Z exceeds the threshold Pseudonoise Code Acquisition in Direct-Sequence Receivers n when signal is present. Thus, using (1.68) rather than (1.69), we get Pp=1-2z = (1.71) which, if desired, can be expressed in terms of a generalized Marcum's Q- function. For large NB (the case of most practical interest), things become quite a bit simpler. Defining YK = y(kT)/202, then from (1.61) and (1.63), the pdf's yk in the presence and absence of signal are, respectively, = otherwise (1.72) (1.73) otherwise. Also, from (1.64) and the