me value of the cutoff rate parameter R, then the bit error bound is also the Translation of Coded Error Bounds Es/Nj (dB) Figure 4.8. Soft decision with no jammer state knowledge-DS/BPSK. same, which in this case is 10-6. For our new coded channel, we determine from Figure 4.8 that for R0 given by (4.55) and p = .05, the new required EIN1 is E&/N, = 12.2 dB (4.56) Eb/N 1 = 15.2 dB. (4.57) Thus, in this pulse jamming example, we require 15.2 dB of Eb/N, defined by (4.3) to achieve 10-6 coded bit error probability with the given convolu- tional code. By continuing this translation for several bit error probabilities, we obtain the complete coded bit error bound for the case of interest by translating the standard coded bit error bound curve. The translation of standard coded bit error bounds to obtain corre- sponding bit error bounds for different coding channels applies to all binary General Analysis of Anti-Jam Communication Systems input coding channels. It also generalizes to M-ary input coding channels of the kind that arise in most spread-spectrum systems. This will be shown next with frequency-hopped non-coherent MFSK signals with partial-band jam- ming. For anti-jam communication systems, where jamming and receiver structures can take many possible forms, the general approach of first obtaining numerically computable values of the cutoff rate parameter and then translating standard error rate curves serves as a useful general approach to the analysis of anti-jam communication systems. 4.7 CONVENTIONAL NON-COHERENT MFSK Conventional MFSK modulation consists of transmitting one of M symbols where the symbol is represented by one of M non-coherently orthogonal fre- quency tones of duration Ts seconds and energy Es. We assume the M tones are separated in frequency by Af = 1/i (4.58) For MFSK modulation with the additive white Gaussian noise channel, the optimum non-coherent detector has the form shown in Figure 4.9. The detector output consists of (4.59) where ei is the normalized energy of the received signal