ies of the cod- ing channel created by the demodulator-to-decoder interface function that provides an ordered list of the M energy detector output samples. Here the ML metric is clearly m(y,x)J==logp, = (2.379) This ML decision rule results in the coding parameter (2.380) Other Coding Metrics where (2.381) with {Pk} given by (2.377). Next consider a suboptimum metric that assigns a value or number to each place on the list in the output. In particular let the metric be given by m(y,x) = Nyx (2.382) This assignment is defined by the vector N = (N1,N2,...,NM) (2.383) where N is the assigned number placed on the energy detector output with the 1-th largest value. For the general metric defined by (2.382) the coding parameter is given = min = = = (2.384) where Pr{yx=k,yx=jx}=Pr{yx=jyk=k,x}Pr{yk=kx} = = = = = = (2.385) Non-Coherent Frequency-Hopped Systems (2.386) Creighton [30] considered this list metric for the uniform channel with no background noise where there is Rayleigh fading and partial-band noise jam- ming. For the partial-band noise jammer that jams p fraction of the band, define the binary random variable Z where Pr(Z = 1) = p and Pr(Z = 0) = 1 - p. Since the probabilities {Pk} depend on the jammer noise level, we emphasize this by writing Pk = Pk(Z) showing this dependence. Recall that each probability depended on the hopped sub-band that had a jammer noise level characterized by Bq1q q' Here there are only two levels of noise jamming characterized by the random variable Z. The general metric now has the m(y,x Z) = N,(Z) (2.387) where for the ML metric with jammer state information (JSI) where Z is known at the receiver (2.388) When the receiver does not have JSI, then we have average probability Pk=pPk(1)+(1- p)Pk(0) = k = 1, 2, ... , M (2.389) and the ML metric without JSI given by Ny,(Z) = log Py, (2.390) In general an arbitrary assignment of numbers to the list values in y is pos- sible. Here too we can consider the case with JSI where Z is known and dif- ferent assignments are used for Z = 1 and Z =