ill be appropriate with Yh replaced by S/2NB where B is again the single-sided low-pass filter noise bandwidth. Under these conditions, (3.32) becomes analogous to (1.81) of Chapter 1. In fact, the same substitution is appropriate to all of the previous Time and Frequency Synchronization of Frequency-Hopped Receivers results for acquisition with MFSK modulation if the integrate-and-dumps in Figures 3.5 and 3.7 are replaced by low-pass filters with noise band- width B. To modify the previous results to allow for a non-ideal in-sync condi- tion, we proceed as follows. Assuming that the MFSK tones are orthogo- nally spaced, e.g., for FFH we could have fsj - Fs.j-1 = k/T since 1/T is the minimum tone separation for orthogonality, then in the absence of fre- quency error (Sf = 0), the m-fold accumulated output samples of the M non-coherent demodulators would in the absence of noise be given by (see (3.8)) R(T)=0;11,2,...,M;l (3.33) where fi is the transmitted tone. Thus, multiplying Yh by the loss factor L All (1 - E)2 in (3.30) is sufficient to account for this degrading effect. A simi- lar result was obtained in connection with our previous discussion of PN code acquisition (see (1.86) of Chapter 1). When, in addition, frequency error is present, then, even for the above orthogonal tone spacing, the m-fold accumulated output samples of the M non-coherent demodulations will in the absence of noise all contain non-zero signal components. Further, this set of output signal components will depend on which MFSK tone was indeed transmitted; i.e., (3.34) As a result, all of the normalized output samples have pdf's of the form in (3.27) with myh replaced by 1, 2, M. Although for- mally the procedure is straightforward, the computation of acquisition per- formance for this case is tedious and is not presented here. However, a similar problem will be considered in detail later on in the chapter relative to the computation of error probability performance in the presence of resid- ual time and frequency tracking errors. It sho