ing values of Eb/N J Changes in the signal-to-noise ratio caused by the signal hopping to a jammed part of the frequency band no longer results in large changes in the uncoded bit error probability and the broadband jammer turns out to be the worst case. Coding in the form of diversity still shows dramatic improvements, but this time to overcome the effects of Rayleigh fading. In general, for arbitrary fade statistics, if the derivative with respect to r of the bit error probability given in (2.238) is positive for a given symbol- energy-to-noise ratio and all p&[0, 1], then p = 1 maximizes the bit error probability. Taking the derivative of (2.238) with respect to p gives (2.240) p(E/N ) which must be satisfied for all p&[0,1] where Pb(x) is the derivative of Pb(x). This condition defines how slowly the bit error probability must decrease with E/N J in order to have broadband noise jamming as the worst case. It is satisfied by all uncoded FH/MFSK signals in a Rayleigh fading channel. For small values of E/N , , condition (2.240) is usually satisfied for non- fading channels as well. With the use of coding, the worst fraction p of the partial-band noise jam- mer depends on the coding metric used. With Rayleigh fading, and the ML metric, which assumes jammer state information, the broadband jammer (p = 1) is again the worst case. This is not true, however, for the energy met- ric with no jammer state information. We show this next with a more gen- eral noise jammer power distribution. 5We assume it is infinite. Worst Noise Jammer Distribution-Slow Fading Uniform Channel 2.5 WORST NOISE JAMMER DISTRIBUTION-SLOW FADING UNIFORM CHANNEL Most of this chapter assumed the worst case noise jammer was a partial band jammer that jammed some fraction, p, of the spread-spectrum frequency band with constant noise power spectral density. In this section consider the Rayleigh fading channel with arbitrary power spectral density for the noise jammer and then find the worst noise power spectral density. This presen- tation sets th