2.85 and 2.86. Each curve is characterized by a different value of Eb/N,, selected to achieve a Ph upperbound of 10-5 at the corresponding Mopt In each graph, the curves are approximately lateral translations of each other, implying that all four systems are essentially equally sensitive to proportional deviations from Mopt (since the m axis is logarithmic). However, on an absolute basis, the curves with smaller values of Mopt are less robust with respect to m: for example, the performance of the (7, 1/) convolutionally coded system in Figure 2.85 is significantly degraded at m = Mopt +1 1. (Recall that although it is analytically convenient to treat m as if it were continuously valued, only Coding Countermeasures (1/2) 4-ARY CONVOLUTION- AL CODE UNCODED 4-ARY ORTHOGONAL CONVOLUTIONAL DUAL-2, RATE CONVOLUTIONAL WC PARTIAL-BAND NOISE DIVERSITY m PER M-ARY SYMBOL Figure 2.85. Comparison of sensitivities of various FH/MFSK systems to variations in diversity for K = 2 and worst case partial-band noise. More powerful codes (requir- ing smaller Eb/N, to achieve P = 10-5 at m = Mopt) need less diversity to combat jamming. integer values are physically meaningful.) In the absence of diversity, we saw in Figures 2.67 and 2.72 and Table 2.12 that for FH/4-ary FSK signalling in worst case jamming, the most powerful of the convolutional codes consid- ered was the (7,1) Trumpis code, followed by the dual-2 and 4-ary orthog- onal codes. When these codes are combined with optimum diversity, this anti-jam effectiveness hierarchy is preserved as indicated by the required val- ues of Eb/N1 in Figures 2.85 and 2.86. Furthermore, the more powerful codes need less additional diversity redundancy to cope with worst case jamming, although they all need some improvement since Mopt > 1 in all cases. The orthogonal convolutional code is particularly weak, providing a meager 0.2 dB advantage over uncoded signalling, both with optimum diversity. In the multitone jamming case of Figure 2.86, each curve has a local minimum, which we still use