esired result, namely, p(E|E) = 0; elsewhere (3.55) from which the conditional variance of the estimator (00 is given by (3.56) where (3.57) Time Synchronization of Non-Coherent FH / MFSK Systems 3.2.1.2 Results for Large Nh The general result of (3.55) can also be simplified by Nh, the number of hop intervals over which the spectral estimates are accumulated, is large. More specifically, for large N we can apply the central limit theorem to (3.52) from which are Gaussian random variables with (3.58) Thus, the conditional pdf's of R+ and R_ are p(R+|E) (3.59) Using methods similar to those employed in arriving at (3.55), we obtain, HELE 0.15 Yh=5dB -0.35 -0.25 -0.15 -0.05 -0.01 -0.20 -0.25 -0.30 -0.35 Figure 3.16. Conditional mean MEE versus E with Yh as a parameter; N = 10. Time and Frequency Synchronization of Frequency-Hopped Receivers after much simplification, N°(1-87)07 0; elsewhere (3.60) where Nn(1+8) 1 + 2 x (1 - 8) (3.61) Na(1-8) (3.62) The conditional mean and variance of (C) are still determined from (3.57) and (3.56) with p(E) as given in (3.60). Figure 3.16 is a plot of this conditional Time Synchronization of Non-Coherent FH / MFSK Systems y = O dB E = 0.0 10 dB Figure 3.17. Conditional standard deviation OEE versus N and Yh and E as para- meters. mean versus E with N = 10 and Yh as a parameter. Figure 3.17 is the cor- responding plot of the conditional standard deviation of (c) versus Nh with E and Yh as parameters. 3.2.2 The Case of Partial-Band Noise Jamming When the additive jamming noise is not spread over the total hop frequency band, then the previous results can be modified to account for this fact as follows. Let Nh still be the total number of hop intervals per time synchro- nization estimate, of which pNh are now contaminated by jamming noise of power spectral density Nj/p and (1 - p)N are noise free. 4 As in our previ- ous discussions of partial-band noise jamming, p denotes the fraction of the total hop frequency band that is jammed. Then analogous to (3.52), we have (3.63) 4For values