jamming for K = 1, whereas the reverse is true for K > 2. Coding Countermeasures Table 2.18 Relative performance of coded FH/MFSK signals with optimum diversity in worst case multitone and partial-band noise jamming based on exponential coefficient kR'ly in (2.167). (Be)- 1.000 1.250 Now let us briefly consider the performance of FH/MFSK systems employing RS outer codes cocatenated with optimum diversity. Using the notation introduced in Section 2.3.2.2, each RS code symbol over GF(2°) is sent by using the M-ary channel L times. Although the soft decision/side information metric is used with linear combining of the m diversity chip ener- gies, hard decisions are made on each M-ary symbol, and these are combined in groups of L to recreate the received RS characters. Using Berlekamp's table of RS symbol error rates Po required to achieve a given Pb for a par- ticular (n, k) RS code [21], (2.153) converts it to an M-ary channel symbol error rate PK, which implies an effective channel Ph defined by (2.154). For worst case noise and tone jamming, the channel P is related to EbIN1 by (2.159) and (2.162)-(2.164), where G(D) = M D (2.168) for uncoded M-ary signalling, and R' = K K (2.169) is the overall code rate exclusive of diversity. These equations reduce to WC noise (2.170) WC multitone. Table 2.19 compares the performance of various combinations of RS codes, M-ary channels, and worst case jamming for the system P of 10-5. The results are not as good as those in Table 2.16 for convolutional outer codes: for exam- ple, the best system in Table 2.16 required EBIN1 = 9.43 dB for any kind of Table 2.19 Required SNR to achieve P = 10-5 for FH/MFSK systems with (n,k) Reed-Solomon outer codes and optimum diversity Mopt, in worst case partial-band noise and n = 1 band multitone jamming; PK is M-ary (M = 2K) channel symbol error rate. Noise Multitone Eb/N,, dB Eb/N, dB 31, 15 1.20 X 10-2 14.89 13.95 63, 31 1.65 X 10-2 14.43 13.56 127, 63 1.97 X 10-2 14.16 13.33 255, 191 8.38 X 10-3 13.39 12.39 511, 447 3.76 X 10-3 13.49 12.3