 input and k 0 is a parameter which is either fixed or is allowed to vary with EJN1 and the pulse jammer's strategy, i.e., p. In the absence of jammer state information, El-Wailly [34] has shown that using the normalized maximum-likelihood metric m(y', x) = y'x/N, the channel parameter D is given by (1.222) where Q(x) is again the Gaussian probability integral and 1==1-k)V2pE,IN,- - B + k)V2pEg/NJ -1V2E/(pNj) - (1.223) Other Coding Metrics for Pulse Jamming Intuitively, one would expect that a clamped (fixed or variable) soft deci- sion receiver characterized by (1.221) would outperform a hard decision decoding metric and at the same time not be totally vulnerable to the opti- mum pulse jammer as is the unclamped soft decision metric (i.e., k = 80). The degree to which this observation is true is demonstrated by the follow- ing illustrations and discussion. Figure 1.19 is an illustration of D as computed from (1.222) versus EJN1 for a fixed clamping level of k = 1 and the worst case jammer who chooses his p to maximize D for each value of EJN1. Also illustrated for purposes of comparison is the corresponding result for the hard decision decoding met- ric (with no jammer state information) which from Chapter 4, Volume I, is given by D=V4(1 -); =pQ(V2pEg/Nj). (1.224) As a reminder, the curve for the unclamped soft decision decoder (with no jamming state information) for worst case pulse jamming would simply be a horizontal line corresponding to D = 1 for all EJN1. When the clamping level is allowed to vary, then assuming that the receiver contains an intelligent controller that can choose the value of k SO as to minimize D for each value of p, Figure 1.20 illustrates the corresponding performance in terms of a three-dimensional plot of D versus EJN1 and p. Alternately, suppose it is assumed that the receiver has no intelligence, i.e., 1.000 0.800 0.600 HARD DECISION 0.400 0.200 CLAMPED 0.000 -2.000 -0.000 2.000 4.000 6.000 8.000 Es/N,(dB) Figure 1.19. Channel parameter versus signal-to-noise ratio for worst case ja