t Frequency-Hopped Systems (7,1/2) BINARY CONVOLUTIONAL CODE 10-31 WC PARTIAL on BAND NOISE WCn=1 BAND MULTITONE E /N, dB Figure 2.99. Performance improvement available from diversity inner code for FH/BFSK system employing Odenwalder (7,1) binary convolutional code in worst case noise and multitone jamming. In this case, diversity provides only a small per- formance gain. Note that broadband noise jamming (AWGN) is more effective than multitone jamming here. Some codes are powerful enough over jamming channels that diversity does not produce significant performance gains: the Odenwalder binary convo- lutional codes fall into this category, and, in particular, the (7,1) code Mopt = 1 for both noise and tone jamming implying no benefits from diver- sity. At the other extreme, the dual-K (Figure 2.102), and M-ary orthogonal (not illustrated) convolutional codes show major improvements with the addition of optimum diversity, indicating that these codes by themselves are not well-matched to the jamming channel and require additional redundancy to provide acceptable AJ performance. We also see in Figures 2.99 and 2.100 that for the binary convolutional codes with FH/BFSK modulation, broad- band noise jamming is more effective than worst case tone jamming. This is not a general result for other K = 1 systems: for example, (2.20b) tells us that an uncoded FH/BFSK system in broadband noise requires EBIN, = 13.35 dB to produce Pb = 10-5, whereas Table 2.12 shows that the same sys- tem with optimum diversity in worst case tone jamming needs EIN = 14.95 dB to achieve this performance. As in previous sections, it is useful to compare the performance of all of these systems in worst case noise and tone jamming by tabulating the required Eb/N, to achieve Pb = 10-5: Table 2.16 does this for all of the FH/MFSK systems considered with convolutional codes and optimum diversity inner codes. An overall benchmark is the system that requires the Coding Countermeasures WC n= I BAND MULTITONE (7, 1/3) BINARY CONVOLUTIONAL CODE WC PARTIA