optimum diversity in worst case n = 1 band multitone jamming. At Pb = 10-5, the dual-1 codes are about 3 dB better than uncoded signalling, and about 3 dB worse than the Odenwalder convolutional codes. WC n= I BAND MULTITONE OPTIMUM DIVERSITY DUAL-2, RATE 1/2 CONVOLUTIONAL DUAL -2, RATE 1/3 CONVOLUTIONAL CODE 4 ARY ORTHOGONAL CONVOLUTIONAL UNCODED (7, 1/2) 4-ARY CONVOLUTIONAL E 1Nj, dB Figure 2.93. Same as Figure 2.92, but for K = 2. With diversity, we see that the uncoded and orthogonally coded systems have comparable performance, the dual- 2 codes are about 3 dB better at Pb = 10-5, and the Trumpis (7,1) code provides another 2 dB improvement. Coding Countermeasures WCn=1 BAND MULTITONE OPTIMUM DIVERSITY DUAL - 3, RATE 1/2 CONVOLUTIONAL CODE DUAL-3, RATE 1/ 13 CONVOLUTIONAL CODE 8-ARY ORTHOGONAL CONVOLUTIONAL UNCODED (7, 1/3) 8-ARY CONVOLUTIONAL CODE Eb/Nj,dB Figure 2.94. Same as Figure 2.92, but for K = 3. As in other cases considered, the dual-K convolutional codes provide a significant improvement over uncoded sig- nalling with optimum diversity, while the Trumpis code is better still. WCn=1 BAND MULTITONE OPTIMUM DIVERSITY DUAL - RATE 1/2 CONVOLUTIONAL CODE 16-ARY - ORTHOGONAL CONVOLUTIONAL CODE UNCODED DUAL - 4, RATE 1/3 CONVOLUTIONAL E6/N,,BB Figure 2.95. Same as Figure 2.92, but for K = 4. The dual-K code with optimum diversity is about 3 dB better than the uncoded system for small Pb's. Non-Coherent Frequency-Hopped Systems WC n=1 BAND MULTITONE OPTIMUM DIVERSITY DUAL-5, RATE 1/2 CONVOLUTIONAL CODE DUAL- 5, RATE 1/3 CONVOLUTIONAL CODE UNCODED 32-ARY ORTHOGONAL CONVOLUTIONAL /N,,BB Figure 2.96. Same as Figure 2.92, but for K = 5. The 3 dB performance advantage of the dual-K code over the uncoded system with optimum diversity continues for small Pb's at K = 5. The variation in performance of a given coded system concatenated with optimum diversity as a function of the channel dimensionality K and the type of jamming is exemplified by Figures 2.97 and 2.98. For both the M- ary orthogonal and dual-K convolu