 this may seem like Unknown Jommer State Hard Decision Eb/N, (dB) Figure 3.14. Repeat code m = 3 with unknown jammer state/hard decision. Basic Concepts and System Models p = 1.0 Unknown Jammer State Hard Decision Eb/NJ (dB) Figure 3.15. Repeat code m = 5 with unknown jammer state/hard decision. of the fact that for the additive Gaussian decoders. noise channel, In our exam- soft a contradiction always do better than hard decision decision decoder because ples, the pulse a jammer lot more jammer noise power For the hard decision case, decision decoders can do more harm to a soft in the final decision statistics it can by place (3.56) through a single detector output. do to any given detector output given the amount of harm the pulse hard jammer decision. can In general, decision rules optimum that are is limited because of the additive noise channel are not necessarily single decision optimum for the with classical intentional jamming. Indeed, there decision is no rule is one that over a channel all jamming signals. A good much. The soft deci- rule that is optimum sense for that no jammer can degrade low it very duty cycle pulses while sion rule can be is less sensitive to pulse jamming. single coded is robust in the degraded badly with high peak, With coding, it is important the hard decision to consider rule decision rules that limit the impact a Coded Direct-Sequence Spread Binary Phase-Shift-Keying Unknown Jammer State Hard Decision Eb/Nj (dB) Figure 3.16. Repeat code m = 9 with unknown jammer state/hard decision. channel symbol output can have on the final decision. This usually means that some nonlinear function such has hard decisions or clipping must be used. 3.5.3 Known Channel State Suppose that because of channel measurements, the decoder knows which of the m channel outputs r1, r2, , rm have a jammer term in them. This is equivalent to knowing the values of Z, Z2, , Zm at the decoder. Naturally, when any Z = 0, then ri = Eb/m and d is known correctly. Hence, the only way an error can be made is when Z