erleavers the channel disturbance can be assumed to be indepen- dent for each transmitted coded bit. Assuming the soft decision metric of (1.120) where r is given by (1.207) and 1x e - - 1,1} the pairwise error bound for two sequences x and X is given by (1.131) where D(A) = X. (1.210) From (1.181) and (1.198) [(d,A}VE,+ Am) (1.211) where {n1} are i.i.d. zero-mean Gaussian random variables with variance N/2. D(1) = II EA (1.212) where the amplitudes {A1} are again assumed Rayleigh distributed with vari- ance as in (1.185). Then, define parameter (1.213) where E is given by (1.187) with Eb replaced by Es. Suppose ET is the total average energy and each multipath energy term is the same. That is, (1.214) Other Coding Metrics for Pulse Jamming Then S = 1 minimizes the bound and (1.215) For the hard decision channel with the usual unweighted metric we have simply D = V4s(1 - 8) (1.216) where now E = Pb given by (1.201) and (1.202). 1.8 OTHER CODING METRICS FOR PULSE JAMMING In the previous section, the ideal Rake receiver was approximated by a receiver that estimated the slowly varying multipath fading envelopes. Earlier, we had examined a similar ideal case in Section 1.4 where we con- sidered various decoding metrics for DS/BPSK signals agianst pulse jam- ming. The ideal metric for this case is the soft decision metric iwth jammer state information given by m(y,x;Z) = (Z)yy (1.217) where Z is the jammer state random variable with probabilities Pr{Z = 1} = p Pr{Z = 0}=1-p (1.218) and c(Z) is a weighting function such that c(0) is chosen as large as possi- ble and c(1) = 1. Under these conditions, it was previously shown in Chapter 4, Part 1, that the channel parameter for this case is given by D = nin pexp{-2XEs + = = pe-pE,/N, (1.219) which when translated to its equivalent computational cutoff rate R via (1.92) is illustrated as curve (1) in Figure 1.8. When using the same soft decision metric, i.e., (1.217) without jammer state information, we observed in Chapter 4, Part 1, that the appropriate met- ric weighting