which are satisfied for partial-band noise jamming (see Appendix 2A). Using (2.20a) and optimizing over l and p for worst case jamming, (2.62) for arbitrary K, Eb/N, and m. Computing the joint extrema over p and 1, there are two distinct solutions: (i) m KE,331 (2.63) where (ii) 1 (2.64) Note that as m increases for a given KEIN, the jammer's need to hit all m diversity transmissions forces it to broaden the jammed frequency band; Table 2.4 Parameters derived by Trumpis [7] for exact performance of FH/MFSK signals with diversity m in worst case partial-band noise (see (2.65)). K = 4 y, dB y, dB y, dB y, dB y, dB .4168 .5959 .8575 1.0796 1.3659 .5210 .8265 1.2565 1.8198 2.5937 .6797 1.1401 1.8320 2.8251 4.1493 1.2392 2.2245 3.8464 6.4370 10.3502 2.3584 4.4101 8.0165 14.0997 24.0142 4.6110 8.8385 16.5774 30.2829 61.6169 Non-Coherent Frequency-Hopped Systems when m. KE/3N, the worst case partial-band noise jammer is simply the broadband noise jammer with p = 1. The accuracy of these upperbounds can be investigated by comparing them with exact expressions derived by Trumpis [7], involving the opti- mization of a sum of generalized Laguerre polynomials over p, which must be performed by a computer for each combination of K and m (the com- putation is lengthy for larger values of K and m since the number of terms in the summation is (M - 1)[1MM - 1) + 1] ~ m22K-1) . For small Eb/N, Pwc = 1 and Pb must be computed numerically for each value of Eb/Nj; how- ever, in the region of interest where Pb is low, Trumpis showed that Pr=B(MN) Pwc ENN (2.65) provided Eb/N, y where B and Y are given in Table 2.4. The accuracy of the upperbounds for several values of K and m is illustrated in Figures 2.24-2.26. For large enough Eb/N,, it is seen that the separation between the bounds and the exact performance approaches an asymptotic limit. We can compute this asymptotic difference analytically using (2.64) and (2.65) for large Eb/N. For a given K and m, (2.64) 2.07 dB 0.71 dB Eb/Nu,dB Figure 2.24. Comparison of upperbounds on perfor