d noise (pwc = 3/4, AK and Eb/N, 4/K). Non-Coherent Frequency-Hopped Systems WC PARTIAL-BAND NOISE NO DIVERSITY (EXACT Pb) WC PARTIAE BAND NOISE OPTIMUM DIVERSITY (Pb UPPERBOUND) BROADBAND NOISE NO DIVERSITY (EXACT Pb) Eb/Nj,dB Figure 2.32. Improvement in performance of FH/BFSK signals in worst case (WC) partial-band noise due to optimum diversity; recovery from no diversity case (dashed curve) is significant at low Pb's (e.g., better than 29 dB at Pb = 10-5), and performance is within 3 dB of broadband noise (dotted curve). WC PARTIAL-BAND NOISE NO DIVERSITY (EXACT Pb) WC PARTIAL- BAND NOISE OPTIMUM DIVERSITY (Pb UPPERBOUND) BROADBAND NOISE NO DIVERSITY (EXACT Pb) Eb/Nj,dB Figure 2.33. Same as Figure 2.32, except FH/MFSK signals with K=3 (M = 8); optimum diversity recovers about 31 dB relative to no diversity case at Pb = 10-5 (benchmark). Coding Countermeasures WC PARTIAL-BAND NOISE NO DIVERSITY (EXACT Pb) WC PARTIAL- BAND NOISE OPTIMUM DIVERSITY (P UPPERBOUND) BROADBAND NOISE NO DIVERSITY (EXACT p) Eb/Nj,dB Figure 2.34. Same as Figures 2.32 and 2.33, except K = 5 (M = 32); optimum diver- sity recovers over 32 dB relative to no diversity case at Pb = 10-5. with K, as it did with no diversity in worst case partial-band and broadband noise (see Figure 2.9). Most important, we see in (2.70) that optimum diver- sity restores the desired exponential performance behavior characteristic of brute force broadband noise jamming. As shown in Figures 2.32-2.34, opti- mum diversity recovers most of the advantage that a worst case partial-band noise jammer enjoys against uncoded FH/MFSK signals. For example, Table 2.6 contrasts the performance with no diversity and optimum diversity at the benchmark Pb = 10-5, based on the exact expressions of 2.25 and the upper- bound of (2.70): Table 2.6 Effectiveness of diversity against worst case partial-band noise: is improvement with optimum diversity at Pb = 10-5. Pb = 10-5 m=mopt EIN dB Eb/N, dB AEIN, dB (Exact) (Upperbound) (Lowerbound) 45.66 5.43 X 10-5 16.36 29.30 43.67 5.12 X 10