.3(a) or (b). If this band structure is destroyed, for example, by hopping each MFSK tone independently as suggested in [22] (a relatively expensive implementation requiring not one but M separate frequency synthesizers), the worst case multitone jammer must use the independent tone placement Table 2.21 Performance of several concatenated FH/MFSK systems employing RS outer codes, binary convolutional inner codes, and optimum diversity on the M-ary symbols. The inner codes are the (7,1) Odenwalder code for K = log2M = 1, and the (7,1) and (7,3) Trumpis codes for K = 2 and K = 3, respectively. Hard decisions are made on inner code M-ary symbols based on soft decision diversity chip metric with perfect jamming state side information and linear chip energy combining. E/N, dB and Mopt (lower parameter) for Pb = 10-5 Noise Multitone RS Code Convolutional Code Pb K = 2 255,191 8.379 X 10-3 10.16 511,447 3.756 X 10-3 1023, 959 1.733 X 10-3 Coding Countermeasures strategy. And we have already seen that independent multitone jamming is less effective than n = 1 band multitone jamming. If we assume only worst case partial-band noise jamming, the best system considered is the (1023, 959) RS outer code with the dual-5, rate 1/2 convolutional inner code and optimum diversity (~ 2), which achieves Pb = 10-5 with Eb/N, = 5.85 dB; furthermore, the performance improves as K and the RS block length increase. 2.3.3.1 Optimum Code Rates Many different combinations of coding and optimum diversity have been considered in this section. Using a system Pb = 10-5 as a benchmark, in most cases with worst case noise or tone jamming, the optimum diversity was greater than unity, implying that the coding without diversity did not pro- vide enough (or the appropriate kind of) redundancy to effectively counter the assumed threat. Some notable exceptions where diversity was not needed (i.e., Mopt = 1) were the (7,3) Odenwalder convolutional code (see Table 2.16), and several of the concatenated Reed-Solomon/binary convolutional codes (Table 2.21)