 the jammer is on, the channel is like an additive white Gaussian noise channel with power spectral density (one sided) (4.46) where Wss SS is the spread-spectrum signal bandwidth. During the transmission of a coded symbol define the jammer state random variable Z where Pr(Z = 1) = = p Pr(Z = 0) = 1 - p. (4.47) This is the jammer state side information that may be available at the receiver where Z = 1 indicates a jammer is transmitting during a coded sym- bol time while Z = 0 indicates there is no jammer signal. With Z available at the receiver, the metric we consider is m(y,x; z) = (c(z): = (4.48) which is a weighted correlation metric. Next compute the parameter D(1) = =pexp{-21c(1)E$+12c2(1)ENjp} (1-p)exp{-2xc(0)Es} (4.49) If the receiver has jammer state side information (knowledge of z) then the metric can have c(0) as large as possible to make the second term in (4.49) negligibly small. Also without loss of generality normalize c(1) = 1 to obtain D(A) = pexp{-2xE + (4.50) Translation of Coded Error Bounds = min[pexp{-2XE, = + (4.51) Suppose the receiver has no side information. Then the metric is indepen- dent of Z, or equivalently has weighting c(1) = c(0) which we can normal- ize to unity. Then, from (4.49) D(1) = p exp{-21E + (1 - p)exp{-21E}} (4.52) and D is obtained by minimizing D(1) over 10. Both (4.50) and (4.52) correspond to soft decision detectors. The only dif- ference between these two is the availability to the decoder of side infor- mation concerning the jammer state. The difference is shown in Figures 4.7 and 4.8 where R = 1 - log2(1 + D) is sketched versus EJN1 for various val- ues of p. Clearly having jammer state knowledge helps improve the overall bit error probability. The special case where p = 1 coincides with the con- ventional soft decision curve shown in Figure 4.4. Similar results can be obtained for hard decision detectors. A complete discussion of DS/BPSK sys- tems is covered in Chapter 1 of Part 2. 4.6 TRANSLATION OF CODED ERROR BOUNDS The numerical evaluation of R versus EJN1 