s to transmit a single known frequency chosen halfway between two standard MFSK frequencies. By using the spectral estimates evaluated at these two standard MFSK frequencies, a frequency error esti- mator can now be formed which, in the absence of noise, will be a linear func- tion of frequency error. To see how the above approach can be applied to an FH/MFSK com- munication system, consider the simplified frequency synchronization system illustrated in Figure 3.24. Letting fo + m/2T; m = 1, 2, , M/2 denote the standard MFSK frequencies used for data transmission, then during fine frequency synchronization, we generate the single data sym- bol frequency equal to fo, which is halfway between the two center (inner- most) standard frequencies. This data frequency is frequency-hopped over the SS bandwidth. As in the case of the time synchronization system, the received signal plus jamming noise is first cross-correlated with the local hop generator, which has a frequency error relative to the transmit- ted signal equal to l Hz. Also, we assume here that only coarse time syn- chronization has been obtained, and thus the local hop generator is also FREQUENCY DISCRETE BAND-PASS MODULATOR FOURIER FILTER CONVERTER GENERATOR TRANSFORM ajibj CENTER LOCAL FREQUENCY FREQUENCY SPECTRAL SELECTOR ESTIMATES GENERATOR ( ) 2 FREQUENCY SYNCHRONIZATION ACCUMULATOR ESTIMATE Figure 3.24. Simplified frequency synchronization of a frequency-hopped system with on-board processing. Frequency Synchronization of Non-Coherent FH / MFSK Systems in time error relative to the transmitted signal by an amount equal to T seconds, where, as before, T is less than a hop duration. The cross-corre- lation is band-pass filtered and the output of this filter is passed through an A/D converter. The resultant signal samples are discrete Fourier trans- formed to produce spectral estimates corresponding to the MFSK fre- quencies for each frequency hop. The squares of these estimates are then accumulated over many hop intervals and the square roots of these a