met- ric m(y, 1), the general coded bit error bound is given by P, =G(D) = B(R) = (2.232) where for FH/MFSK the cutoff rate R is given by (2.180) where (2.233) with l' # 1. For the energy metric (2.232), D is given by DEPARTMENT (2.234) (2 + (E/N ) ) ² Also, for the special case of an m diversity code, the function G() is G(D) = 2K-2D (2.235) with code rate R = Klm bits per chip and E = REb = (K/m) Eb. This is the result given by (2.229). Rather than the energy metric, if a hard decision is made for each MFSK chip then (2.236) where (2.237) which is the chip error probability given by (2.208). Figures 2.114 and 2.115 show the performance for optimum diversity and diversity m = K where M = 2K for the hard decision metric. 2.4.3 Partial-Band Jamming Next consider the case of a Rayleigh fading channel together with a partial- band noise jammer with average power J that jams a fraction r of the total spread-spectrum band. Assume that when an FH/MFSK signal hops into the Hard Decision Bound Hard Decision Bound Figure 2.114. Pb-FH/MFSK optimal diversity. Figure 2.115. P,-FH/MFSK, diversity. Non-Coherent Frequency-Hopped Systems part of the band where there is no noise jamming, the bit error probability is negligibly small since the signal-energy-to-background noise is large. When a noise jamming signal is present in the transmitted signal band, the symbol-energy-to-noise ratio is pEIN. Thus, with no coding or diversity, the bit error probability is given by = pPb(pE/NJ) + (1-p)Pb(00) = pPb(pE/NJ) (2.238) where Pb(x) is the uncoded bit error probability when the symbol-energy- to-noise ratio is X. For the binary case, M = 2, (2.239) The choice of the worst partial-band parameter p that maximizes this bit error probability is p = 1. Thus, the broadband jammer is the worst noise jammer in a Rayleigh fading channel. This is primarily due to the fact that Rayleigh fading has already created the same impact as the worst case par- tial-band jammer with a resulting uncoded bit error probability that changes slowly with increas