formance of the rate 1/2 and 1/3 dual-K convolutional codes with optimum diversity for low bit error rates; and, although Mopt is smaller for the lower rate (R') code, the overall code rate R is essentially independent of R' for any K. We can illuminate this observation and provide further analytical insights by deriving asymptotic expressions for the performance of these concate- nated systems in the region of large EIN From (2.159), (2.162), and (2.163), we know that the performance of coded FH/MFSK systems with optimum diversity is given by (2.165) Table 2.16 Required Eb/N, in dB (left columns) to achieve Pb = 10-5 for coded FH/MFSK systems with optimum diversity Mopt (right columns) in worst case partial-band noise (upper rows) and n = 1 band multitone jamming (lower rows). Type of K = log2M Outer Code Uncoded 16.36 13.62 12.12 11.11 10.36 14.95 14.21 14.58 15.49 16.76 (7,1) Binary 10.73 Convolutional (7,1) Binary 10.38 Convolutional (7,1) 4-ary Convolutional (7, 1) 8-ary Convolutional 10.70 M-ary Orthogonal 13.36 11.61 10.40 Convolutional 13.96 14.10 14.81 15.90 Dual-K, Rate 2 13.46 10.70 Convolutional 12.03 11.27 11.63 12.53 13.79 Dual-K, Rate 13.41 10.66 Convolutional 11.99 11.24 11.60 12.51 13.78 Non-Coherent Frequency-Hopped Systems where n=12 in worst case partial-band noise, n = 1 in worst case n = 1 band multitone jamming, and y varies with the type of jamming according to (2.164). If EIN, is large enough, the argument of G(.) in (2.165) is sufficiently small to approximate the expressions of (2.146)-(2.151) by their dominant terms, which all have the form G(D)=CD D<1 (2.166) where C and k are listed in Table 2.17 for the systems under consideration. Therefore, the anti-jam performance of these systems for sufficiently large E/N is of the order of (2.167) This is a very succinct and useful gauge of the relative performance of all these systems in worst case jamming for small bit error rates. Since the expo- nential term dominates the behavior of (2.167) in this region, a larger coef- ficient kR'ly usu