f3+f/F 14+FIF f++f/F 15-16-11-1-81 17-18-17-81 MIXER DIFFERENCE fif-iil IF-1; iF-1; fif-ii IF-t; fif-tk 16-17-1-87 INDICATES COMPONENTS NOT EFFECTIVE FOR CORRELATION DETECTION Figure 3.6. Received FFH/MFSK signal and local hop signal misaligned by less than a single hop interval. FH Acquisition Techniques In the absence of noise, for the symbol interval during which fi was the frequency of the transmitted MFSK tone, the m-fold accumulated output samples of the M non-coherent demodulators are given by Rk(T) = mS k=1,2, M. (3.8) Thus if of is small compared with the spacing between adjacent MFSK tones, then the largest Rk(t) will occur for the value of k for which fi = fsk. Since this occurrence will be true independent of which symbol we examine, the input to the post-detection accumulator will be given by R(t) of (3.6) mul- tiplied by m. For ordinary (without diversity) SFH/MFSK, the appropriate serial search acquisition system analogous to Figure 3.5 is illustrated in Figure 3.7 with a corresponding time-frequency diagram in Figure 3.8. Since in each hop inter- val, the mixer difference signal contains sinusoidal bursts at different fre- quencies corresponding to the MFSK tones transmitted in that hop, then in contrast with Figure 3.5, no non-coherent combining ocfurs at the outputs of the M non-coherent demodulators. Rather, the largest of these M outputs is selected each symbol interval. Post-detection accumulation (over say NSFH symbols) of these selections and comparison with a preset threshold again determines whether or not to continue the search. Another characteristic of the acquisition system in Figure 3.7 is that the set of M non-coherent demodulator outputs does not necessarily remain unchanged as one passes from symbol to symbol within a given hop. For example, if the timing error T is less than a symbol interval Ts (as is the case illustrated in Figure 3.8), then for all symbols except the last in a given hop interval, the sets of M outputs will be identical, although not neces- sarily ordered the s