mance of FH/BFSK (K = 1) sig- nals with diversity m chips/bit in worst case partial-band noise against exact Pb (dashed curves). Coding Countermeasures 3.52 dB 0.76 dB Eb/N, dB Figure 2.25. Same as Figure 2.24, except FH/MFSK signals with K = 3 or M=8, and m chips/8-ary symbol. UNIVERSITY 5.52 dB 0.79 dB Eb/N, dB Figure 2.26. Same as Figures 2.24 and 2.25, except K = 5 or M = 32 with m diver- sity chips/32-ary symbol. Non-Coherent Frequency-Hopped Systems Table 2.5 Asymptotic accuracy of performance upperbound in (2.64) for low Pb overbounds the signal-to-noise level required to achieve a particular : (2.66) The actual required signal-to-noise ratio is given by (2.65): (2.67) The bound accuracy may be specified by the ratio AEb/Nj (2.68) M=MOPT 10-62 Eb/Nj,dB Figure 2.27. Variation in performance upperbounds for FH/BFSK signals in worst case partial-band noise with diversity m chips/bit; optimum diversity (mopt) perfor- mance is lower envelope, shown as dotted curve. Coding Countermeasures which is given in Table 2.5 for selected values of K and m. We see that the bound is quite accurate for larger values of m; for example, it is only 3/4 dB above the exact result for m = 10, with minor variation over K. However, for small m the bound is pessimistic by several dB, and the accu- racy degrades with increasing K. Returning to the upperbounds now, (2.63) and (2.64) are used to illus- trate the variation in performance with diversity m for a given K in Figures 2.27-2.29. Notice that the curves cross each other, SO that for fixed K and Eb/N, the performance actually degrades if m is too large due to non-coherent combining of the detected chip energies in the metric of (2.57). For example, consider the performance curves for K = 3 in Figure 2.28: if Eb/N, = 12 dB, Pb is lower at m = 10 than at m = 5 or 20. The existence of an optimum amount of diversity for a given K and Eb/N, is further illustrated in Figure 2.30. (Although the diversity m is treated like a continuous variable, it should be remembered that it only has 