 of p such that pNh and (1 - p)Nh are not integer, we take the nearest integers, respec- tively, to these quantities. Time and Frequency Synchronization of Frequency-Hopped Receivers with pdf's p(R+|E) = 0; elsewhere. (3.64) Then, analogous to (3.55), we have that (pNn)2(1 + 282)] p(E) = (3.65) 0; elsewhere where (3.66) Note that when p = 1, i.e., jamming over the total hop frequency band, then y+ = y- = y, and (3.65) reduces to (3.55) as it should. 3.2.2.1 Results for Large pN As was true for (3.55), the general result of (3.65) can be simplified now when pNh is large. Once again, Z Ill R2, with R+ now defined in (3.63), Time Synchronization of Non-Coherent FH / MFSK Systems becomes a Gaussian random variable with (3.67) Note that ( E ) are independent of p but 02(8) are not. Thus, the condi- tional pdf's of R+ and R_ are still given by (3.59) with + ( e ), 04(8)m2(8), and o2(e), now defined by (3.67), and similarly p(E)E) is given by (3.60) with Yh and N replaced by PY and pN respectively, X1 and X2 given by (3.61), (3.68) with 02 still defined in (3.62) using now and 02 of (3.68). 3.2.3 The Effects of Time Synchronization Error on FH / MFSK Error Probability Performance The presence of a time synchronization error in an FH/MFSK receiver causes a degradation in system error probability performance that is attrib- utable to the following two factors. First, the signal component of the receiver correlator corresponding to the true transmitted frequency is atten- uated. Second, a spillover of transmitted signal energy occurs in each of the adjacent M - 1 correlator outputs where, ordinarily (perfect time sync), only noise appears. This second contribution to the performance degradation, namely, the presence of signal components in the incorrect frequency cor- relator outputs, is referred to as a loss of orthogonality [13]. Clearly, then, the first step in assessing the impact of a time synchronization error E on the performance of the FH/MFSK receiver is to evaluate the signal attenu- ation and loss of orthogonali