y of the half-chip search step, the signal-present condition occurs at sev- eral points along the PN correlation curve. Furthermore, the received PN code is, in general, not synchronous with the local replica SO that none of the above signal-present conditions corresponds to fully on; thus, the true sig- nal-to-noise ratio is a random variable that depends on the degree of mis- alignment between the two codes. Although some approximate analytical modifications were suggested in Section 1.2.5 to try and account for these effects, a simulation can directly model these effects by modelling the code start time as a uniformly distributed random variable between zero and one half of a chip. Simulation results [30] indicate an SNR penalty of about 1 dB due to this random code alignment rather than the pessimistic 2.5 dB sug- gested in Section 1.2.5 corresponding to a worst case (quarter of a chip) mis- alignment. (3) It allows for the consideration of other simplified detector imple- mentations whose performance is either difficult or impossible to evaluate analytically. For example, with a digital implementation, an absolute value detector function might be preferable. Comparison of this implementation with a square-law envelope detector, envelope detector, or the "ideal" detector of Figure 1.45 is then straightforward with a simulation approach. (4) Finally, the simulation approach is useful in establishing the regions of validity of the various analytical and numerical approximations. We begin our discussion of simulation results with a comparison of the noise-only behavior of the sequential test for four different detector types. In particular, we examine the variation of false alarm probability and aver- age number of samples to dismiss as a function of bias for: 1. the "ideal" detector (Figure 1.45) 2. the square-law envelope detector (Figure 1.46) Pseudonoise Code Acquisition in Direct-Sequence Receivers 3. the envelope detector (Figure 1.46 with an envelope instead of a square- law envelope detector) 4. the abso