and E is the average chip energy. For a code rate of R bits per chip, E = REb. . With diversity m and M = 2K this is the special case of R = Klm and G(D) = 2K-2D given in (2.274). The union Chernoff bound given by (2.274) and (2.275) applies for the ML metric that assume jammer state information J, namely, the jammer noise power distribution. The jammer noise power distribution that maximizes the coded bit error bound (2.274) is the one that maximizes D(J) given in (2.275). Applying the Worst Noise Jammer Distribution-Slov Fading Uniform Channel Kuhn-Tucker Theorem to maximizing D(J) under equality constraint (2.242) results in the necessary and sufficient conditions 4E2W2 (2.276) with equality for values of q where 0. Here the function D(J) is concave in J SO the maximizing J = J* is unique. Again we see that the worst jammer noise distribution is the broadband noise jammer with (2.277) For this worst distribution 0(10) (2.278) (E/N ) ) ² which is the result shown earlier in (2.234). Again for a slowly varying Rayleigh fading uniform channel, the worst jammer noise power distribution is uniform across the band which is the broadband jammer. This is exactly true for uncoded FH/MFSK signals and was shown here for the union Chernoff bound for coded FH/MFSK signals with ideal ML decoders having jammer state information. For coded systems using other metrics, similar union Chernoff bounds can be obtained in which the broadband jammer is not necessarily the worst noise jammer. Consider the coded FH/MFSK signal using the energy metric m(e,x) = ex (2.279) which assumes no knowledge of J, the jammer state. This is known to be the optimum metric when there is broadband noise. Since the broadband noise jammer was the worst case in the uncoded case, we might expect good per- formance with this metric. The coding parameter obtained using the Chernoff bound has the form (2.280) for l' # 1. Here E{exe||1,q} (2.281) Non-Coherent Frequency-Hopped Systems (2.282) 1 + X(E + Nq) Thus, (2.283) where (2.284) Consider the two-level pa