e metric of (1.217) is still appropriate except that now Z is replaced by an estimate Z of the jammer state. The manner in which the estimate Z is obtained and its statistics are the sub- ject of the following discussion. As in the Rake receiver illustrated in Figure 1.18, an estimate Z of the jammer state might be based on the previous BPSK transmission.6 Another approach would be to base the estimate on the amplitude of the received signal in the current interval as follows: (1.227) Basically, this receiver assumes that when the channel output y is close to one of the two signal terms, VE and - VE then the channel contains only background noise. Substituting (1.226) in (1.217) then gives the metric examined by El-Wailly and Costello [35]: (1.228) It should be noted that the metric of (1.228) can also be regarded as one that assumes no jammer state information since indeed the jammer state information comes directly from measurements on the observable (i.e., the channel output) rather than from an external source. Thus, combining (1.227) 6This estimate can be done before deinterleaving at the receiver to make the channel memoryless. Coherent Direct-Sequence Systems and (1.228), we get the alternate form (1.229) if|y|>BVEs For the metric of (1.229), El-Wailly and Costello [35] have shown that the channel parameter D is given by + No] + No]} + I[(1 -B)VE,,(1+ B)VE,,N, N'o] + I[(1 + VEs,+oo, N', N']], (1.230) where I[L, H, N, Ne-/F(L)-F(H) = (1.231) F(t)QtV2/N -V(2E/)(N/)] (1.232) Figure 1.22 illustrates the performance of a receiver using the metric of (1.229) in terms of D versus p with B as a parameter for EJN1 = 5 dB and a background-to-jammer-noise-spectral-density ratio No/N1 = 1.0. Also shown for comparison are the corresponding results for the ideal soft deci- sion metric with unknown and perfectly known jamming state information. We observe that the performance corresponding to (1.230) is much improved over that of the unknown jammer state case but not as good as when the jammer state is perfectly known. A