 = Z2 = ... = Zm=1. (3.65) Basic Concepts and System Models That is, an error can only occur when all m coded symbols encounter a jamming pulse. This occurs with probability Pr{Z1 = 1,Z2 = 1, , Zm = = 1} = pm. (3.66) 3.5.3.1 Soft Decision Decoder Z = Z2 = ... = Zm=1, the soft decision decoder makes the decision a 1, 1, Eri>0 (3.67) Known Channel State Soft Decision p=1.0 Eb/N, (dB) Figure 3.17. Repeat code m = 3 with known jammer state/soft decision. Coded Direct-Sequence Spread Binary Phase-Shift-Keying Hence, the probability of a bit error is Ph = pm m Pr Ni > V mEb } = 2Eb (3.68) Figures 3.17 to 3.19 show that for this case the impact of pulse jamming is effectively neutralized. For m =9 and larger, for example, p = 1 gives the worst bit error probability for most values of interest. For p = 1, the repeat code gives the same performance as the uncoded DS/BPSK with constant power jamming. With more powerful codes, we can get coding gain in addi- tion to neutralizing the degradation (40 dB at 10-6 bit error probability) as a result of worst case pulse jamming. p=1.0 Known Channel State Soft Decision P =.1 Eb/NJ (dB) Figure 3.18. Repeat code m = 5 with known jammer state/soft decision. Basic Concepts and System Models p=1.0 10-6 o 3 6 Eb/NJ 9 (dB) Figure 3.19. Repeat code m = 9 with known jammer state/soft decision. 3.5.3.2 Zm=1, the hard decision decoder makes coded hard deci- sym- Hard Decision Decoder When on Z each = Z2 coded = symbol = in accordance with (3.61), where a sions bol error is = Pr{ni > Eb/m} (3.69) Applying the overall bit decision rule of (3.62) results in the bit error (3.70) prob- ability Uncoded Frequency-Hopped Binary Frequency-Shift-Keying Known Channel State Hard Decision Eb/Nj (dB) Figure 3.20. Repeat code m = 3 with known jammer state/hard decision. 3.20-3.22 show this bit error are probability smaller than for various the unknown values chan- of the m. As Figures expected, the bit error decision probabilities detectors. With jammer state decision knowledge case. soft nel state decision