us to (3.63), the square root of the accumulated spectral estimates is now (3.112) For large pN the central-limit theorem can be applied to (3.112). Once again, Z = R2 are Gaussian random variables with the first two statistical moments given by (3.113) and, hence, [p(B|B) is given by (3.110) with Nh replaced by pN Y6 of (3.105) with Yh replaced by PY and X1, X2, 02 and o2 as defined in (3.111) but evaluated using + and 02 of (3.113). 3.3.3 The Effects of Frequency Synchronization Error on FH/MFSK Error Probability Performance The presence of a frequency synchronization error in an FH/MFSK receiver causes a degradation in system error probability performance due to factors Time and Frequency Synchronization of Frequency-Hopped Receivers not unlike those produced by a timing synchronization error. In fact, both signal attenuation and loss of orthogonality degradations once again exist; however, the functional dependence of these degradation components on the frequency error is quite different from the corresponding relationships for a timing error. Nevertheless, once these differences are identified, the remaining task of relating the above degradations to their impact on system error probability performance is straightforward in view of our previous detailed discussion for the effects of time synchronization errors. Thus, our discussion here will be brief and, wherever possible, draw heavily upon the results given in Section 3.2.3. Starting first with the simple case of FH/MFSK with no diversity and orthogonal tones spaced by k/Th, then if, for example, the transmitted MFSK symbol in the j-th hop interval is given by (3.114) then following the development in (3.97)-(3.103), and taking the sine and cosine Fourier transforms at f = fIF + 1/2T the spectral estimate rj corre- sponding to the transmitted MFSK symbol has the conditional pdf 0; otherwise (3.115) where (3.116) Similarly, the spectral estimate rjn for an incorrect correlator spaced in fre- quency by nk/Th from the correct one has the pdf of (3.115) with D