bability computations. 1.2.7 Reduction in Noise Spectral Density Caused by PN Despreading Multiplication of the equivalent noise process at the PN acquisition system input by the locally generated PN sequence spreads the spectrum of this noise process and simultaneously reduces its effective spectral height into the data filter. Letting N' denote this effective noise spectral density, then since the bandwidth of the data (pre-detection) filter is much narrower than that of the PN process, we have that (1.84) In (1.84), we have assumed for simplicity of the calculation that the PN line 18We shall again encounter this equivalent power reduction factor in our discussion of PN track- ing loops in the next chapter. The Single Dwell Serial PN Acquisition System spectrum is approximated by its envelope. Thus, again in computing the effec- tive signal-to-noise ratio of the system, No should be replaced by N'. Finally, summing up the effects discussed in Sections 1.2.5-1.2.7, the effec- tive signal-to-noise ratio y' in the pre-detection filter bandwidth is given by (1.85) where M2 is defined in (1.83), N'o in (1.84), and L, the loss due to a chip mis- alignment T from the correlation curve peak, is given by 4-(1-7) (1.86) Again, for half-chip search updates, the worse case loss corresponds to T/T = 1/4. 1.2.8 Code Doppler and Its Derivative When code Doppler and its derivative characterize the received signal dynamics, the timing error between received and local PN codes is not con- stant over the dwell time of the detection process. This "smearing" effect has a direct bearing on the calculation of the loss due to fractional chip timing misalignment and thus the expression for this loss given in (1.86) requires modification. Considering the case where the received signal is characterized by code Doppler and Doppler rate, the normalized signal input to the acquisition dwell time integrator in Figure 1.6 is (under the signal present hypothesis): (1.87) The corresponding normalized dwell time integrator output is (1.88) For 