on, only a fraction of the total signal energy available in a sin- gle hop interval will pass through this filter since the remaining fraction of the hop interval will contain noise only. The output of the band-pass filter is passed through an A/D converter and the resultant signal samples are dis- crete Fourier transformed to produce spectral estimates corresponding to the advanced and delayed transmitted frequency hop. The squares of these estimates are then accumulated over many hop intervals and the square roots of these accumulated values are then used in much the same fashion as described for the conventional MFSK receiver to form a time synchro- nization estimate [11], [12]. Finally, this estimate, which is formed in the receiver, is directly used to update the current timing position of the local hop generator. Alternately, in the case of a passive processor such as a satel- lite, the accumulated estimates could be transmitted back to the originating terminal, where the timing estimate would be formed and used to correct the transmitted hop timing (see Figure 3.15). Once again the specific details and mathematical analysis of the above time synchronization estimation technique are essentially immune to the activity or passivity of the proces- sor. Hence, in the sections that follow we shall pursue the simplified system of Figure 3.14 with the understanding that the results apply to either imple- mentation. 3.2.1 The Case of Full-Band Noise Jamming 3.2.1.1 Signal Model and Spectral Computations The transmitted signal s(6)(t) in the j-th hop interval is of the form (3.35) where S is the average power, fs is the frequency corresponding to the trans- mitted data symbol, and fi is the j-th hop frequency. Assuming first that the additive Gaussian distributed jamming noise J(t) is spread across the entire hop frequency band, then in the same hop interval, the received signal is given by (3.36) where is the unknown received signal phase in this interval, assumed to be uniformly distributed on (0,2), and J(t) is a