n a digital processing algorithm or decoding process. This means the coding metric must be some quantized function of the M-sam- pled energy detector outputs. Generally, smaller number of bits used to rep- resent metric values means faster decoding speeds with less memory requirements. Consider the channel output in the form y=f(e) (2.331) where f() is some function of the sampled M energy detector outputs. The simplest form of this function is the hard decision output defined by (2.332) emzek all k # m. For this case the channel conditional probability p(yx, q) is given by (2.315) where Pq(Jq) is the symbol error probability given by (2.291). For the hard decision channel the ML metric m(y,x/q) is given by (2.317). This assumes jammer state information J is known. The suboptimum hard decision metric without jammer state information is given by (2.325), which can be represented by a single binary digit. The above soft decision and hard decision channels are special cases of the demodulator-to-decoder interface function f(). This is illustrated in Figure 2.117, where the dotted line shows the equivalent coding channel with input X, output y, and conditional probability p(yx,q). For a given interface function y = f(e), the conditional probabilities can be computed. Once a coding channel is defined by the input symbols, output symbols, and conditional probabilities, a coding metric m(y, XIq) is chosen. For the given channel and chosen coding metric, the coding parameter is (2.333) for x # X Here the expectation E{ is over the random variable y given X, x, and q. In terms of a given J and p the cutoff rate is then Ro(p,J) = log2M - log2[1 + (M 1)D(p,J)] (2.334) in bits per FH/MFSK chip. When an ML metric of the form8 m(y,xJq)=alogp(yx,q)+b (2.335) Memory requirements in both the decoder and the deinterleaver. 8This is a maximum likelihood metric for the given function FREQUENCY FREQUENCY M ENERGY MODULATION HOPPER DEHOPPER f (.) DETECTORS GENERATOR GENERATOR MEMORYLESS CHANNEL Ply x, 9) Figure 2.117. Equivalent codin