 then becomes c(0) = c(1) = 1. For this case, we obtain (see Chapter 4, Volume I) (1.220) which has the equivalent computational cutoff rate R0 = 0 for all ENo as illustrated by curve (3) in Figure 1.8. The implication of this result is that the soft decision metric without jammer state information has no protection against a jammer who concentrates his available power in a very narrow Coherent Direct-Sequence Systems pulse. Stated another way, a receiver that uses a soft decision metric with no jammer state information has, in the presence of an optimized pulse jam- mer, an unbounded probability of error. One way of getting around this intol- erable degradation in the absence of jammer state information is to use hard decision decoding. This was shown, however, to result in a relatively poor performance, as can be witnessed by examining curve (4) in Figure 1.8. In this section, we first examine other metrics that allow soft decision decoding to be used with an optimized pulse jammer and no jammer state information. Following this, we reexamine the behavior of soft decision decoding with jammer state information and the necessary modifications to the metric when, indeed, the estimate of the jammer state Z is not perfect, e.g., in the presence of background noise. Perhaps the simplest modification of the soft decision receiver to allow operation in the presence of a pulse jammer is to clamp the input to the decoder at either a fixed or variable level, the latter case requiring an intel- ligent controller in the decoder. Clamping the decoder input level provides a means for limiting the potentially large excursions in this level caused by narrow pulse jammers and as such prevents the decoder's decision metric from being dominated by these extreme signal level swings when the jam- mer is present. Mathematically speaking, the operation of clamping is equiv- alent to first passing the decoder input y through a zero mean non-linearity with transfer function (1.221) E;; y< -kVE where y' now represents the actual decoder