.4 dB supe- rior to the wideband detector. In fact, as will be shown in Section 1.2.2.2, even the 3.4 dB advantage virtually disappears when the practical problem of fre- quency synchronization is considered. Obviously, since the PB-FBC will cost significantly more than the wideband energy detector (see Section 1.2.3), its slight performance advantage is judged insufficient to justify its general use. 1.2.1.3 Signal Structure and Modulation Considerations In the preceding subsections, the performance of the various detector types was viewed solely from the perspective of pure FH modulation. The effects of using PN and TH modulation in conjunction with FH will now be exam- ined. We begin by briefly examining the effects on the impractical optimum multichannel detector. When PN modulation is used in conjunction with frequency hopping as in (1.3), the bandwidth of each hop is increased to the PN chip rate R = 1/T Thus the time-bandwidth product of each hop becomes (1.19) The optimum multichannel detector in this case has a structure identical to Figure 1.4 with the operation Io() replaced by KN() where (1.20) The performance of this detector is similarly given by (1.7) with I1() replaced by KN ( ), i.e., (1.21) For convenience, the function ) (in dB) is plotted against y in dB in Figure 1.8, with N as a paremter. For larger values of N, a good approxima- tion to 1KN1(y) is [4] (1.22) which is quite accurate for KN (y) < 1(66BB) which corresponds to N 200 for the range of y plotted in Figure 1.8. Thus, using (1.22) in (1.221) gives the simplified relation (1.23) Low Probability of Intercept Communications N=WhTh=1 y, dB Figure 1.8. Optimum receiver channel weighting factor for several bandwidth-time products (reprinted from [4]). For the more important practical detector types, namely, the wideband energy detector and the partial-band filter bank combiner, it has previously been seen that the underlying equation of performance is of the form (1.24) where nd is a function of the desired PD and PFA together with the st