el PB-FBC for absolute detection; thus, if detection is possible, hop following is also possible provided a 106 channel spectrum analyzer can be realized! But it has already been pointed out that a 106 channel receiver of any sort is intractable. It would seem then that, even though FH following is theoretically possible, it cannot reasonably be implemented by a spectrum analyzer. There is, however, a technique which offers the potential of a realizable solution without the need for calculat- ing the spectrum at each FH frequency. The method, first proposed by Kleinrock [8], involves time-domain autocorrelation operations on a Th seg- ment of received signal-plus-noise, and the principles may be summarized as follows. Superscript(1)For perfect time and frequency synchronization, such a receiver performs slightly better than the optimum multichannel FH pulse-matched detector introduced in (2) of Section 1.2.1.2. THRESHOLD SAMPLING RATE = 2fm COMPUTE TRANSLATED FOURIER Xc(f)) COMPUTE FREQUENCY SINE & COSINE COMPARATOR DETECTION MAGNITUDE (0,fm) Xs(fj) DECISION TRANSFORMS OF SQUARED Ns SAMPLES Xj= = SAMPLE VALUES OF x(t) s(t) = FREQUENCY HOP PULSE (WHEN PRESENT IN LOWPASS BAND) FOURIER COSINE TRANSFORM = FOURIER SINE TRANSFORMX(f)) sin Figure 1.16. Spectrum analyzer operation. Low Probability of Intercept Communications Consider, for the moment, that a finite variance time function x(t) has a power spectrum Sx(f), and that the largest spectral value occurs at a fre- quency f = fmax Define the normalized autocorrelation function of x(t) by the relationship (1.73) Next calculate the autocorrelation function of the autocorrelation function, viz., (1.74) and continue this process again and again. The n-th iteration therefore becomes (1.75) Now it can be shown as n that the following limiting result is obtained: lim Rn(T) cos[2nfmaxT], (1.76) n->00 that is, after an infinite number of iterations, a pure cosine function is obtained whose frequency corresponds to the location of the spectral max- imum of x(t). As seen, the