nitial phase offset at the start of the search after an unsuccessful sweep of the entire uncertainty region. Clearly, if the uncer- tainty region corresponds to the full code period as for short codes or spe- cific acquisition preambles, then realignment is automatic and fr would be zero. As numerical examples of the application of the foregoing results, Figures 1.32a, 1.32b, and 1.32c illustrate the normalized minimum mean acquisition time TACO/Tu and optimized27 normalized detection threshold n* versus chip signal-to-noise ratio EJNo in dB with N, the number of cells per chip, and M, the number of chips per matched filter integration as parameters. Other parameters assumed were PACQ > .95, a code rate Rc = 1/T = 512 kchips/sec, an uncertainty time = 64 msec corresponding to Nu = = 32767 = 2 15 - 1 uncertainty chips, a reset time T, = R msec (f, = .078), and best and worst case values of E. For all cases considered, it was found that A = 4 and B = 2 (2 out of 4 majority logic decision) was the optimal choice for the coin- cidence detector, although the performance was relatively insensitive to the actual A and B values as long as A was roughly two times B. Furthermore, we observe that even for an optimized system, there exists a rather sharp "thresholding" effect in the sense that below a certain value of EJNo the per- formance degrades rapidly. 1.6 PN SYNC SEARCH PROCEDURES AND SWEEP STRATEGIES FOR A NON-UNIFORMLY DISTRIBUTED SIGNAL LOCATION Until now, we have assumed that the a priori pdf of the signal location across the uncertainty region was uniform, i.e., the correct cell was equally likely to occur in any of the q cells searched in one complete pass. As such, the acquisition system was designed to make complete passes by sweeping (continuously or in discrete steps) across the entire uncertainty region, once 27For any EJNo and fixed M and N, an optimum threshold exists in the sense of minimum TACQ. MINIMUM ACQUISITION TIME M=1024 OPTIMIZED THRESHOLD MINIMUM ACQUISITION TIME OPTIMIZED THRESHOLD -2 -4 -6 -8 