ty degradations in terms of the synchronization error and then use these results to arrive at an expression for the E- conditional error probability of the system. To illustrate the procedure we shall first discuss the case of FH/MFSK with no diversity, i.e., one data symbol per hop. Following this we shall extend these results to the case of FH/MFSK with m chips per symbol diversity and Time and Frequency Synchronization of Frequency-Hopped Receivers non-coherent combining at the receiver. The performances of these SS tech- niques have previously been discussed in Chapter 2, Volume II, for a per- fectly synchronized system and thus our purpose here is to show how they are modified to account for a time synchronization error. 3.2.3.1 Conditional Error Probability Performance-No Diversity Based on the spectral computations performed in Section 3.2.1.1, it is clear that the spectral estimate rj corresponding to the actual transmitted fre- quency in the j-th hop interval is characterized by (3.42) and has the E- conditional attenuation caused by the lack of perfect time synchronzation is represented by the factor D(s) = (1 - 18). (3.69) Assuming now that the MFSK tones are orthogonally spaced by k/T (1/Th is the minimum tone separation for orthogonality), then the spectral esti- mate rjn for an incorrect correlator spaced in frequency by nk/T from the correct one is obtained by evaluating the discrete Fourier transform opera- tions of (3.41) at the frequency f = fIF + nk/T rather than f = fIF. If ajn and bin, respectively, denote the results of these operations, then it can be shown that the loss of orthogonality degradation Din(E) is given by (3.70) where & is defined in (3.45). For large Ns, (3.70) simplifies to (3.71) Note that for E = 0 and n # 0, Din = 0, i.e., in the perfectly synchronized system, the incorrect correlator outputs consist of noise alone. Now, since (3.72) then, analogous to (3.47), the e-conditional pdf of rjn is given by 0 Srin 500 0; otherwise. (3.73) To compute the e-conditional error probab