est energy 2, indicates 1, e2 was the second largest, etc. Other Coding Metrics r = 6 Eo/N, (dB) Figure 2.123. D for M = 16. list output can be obtained without using any AGC work to maintain [28],[29] Note that thresholds such as in the energy quantizer. Previous shown that this optimum considered list-of-L detection with optimum metrics has is not that is inferior to energy quantization for AWGN channels. channels. This, however, necessarily true in jamming and multiple access channel that outputs the ordered list of the M energy detector lists. For out- this For the there are M! distinct possible outputs or ordered for the chan- put M input, samples, M! output coding channel we now derive expressions nel conditional probabilities {p(yx)}. 7:64, Other Coding Metrics Suppose x = 1 and e1 is the 1-th largest energy detector output sample SO that = 1. Assume further the M energy detector output samples satisfy (2.372) SO that the channel output becomes (2.373) It is difficult to find an expression for p(yx) directly. By symmetry, since {em: m # 1} are i.i.d. random variables and there are (l - 1)! ways to order e2,l3, e1 and (M - 1)! - ways to order we have the relationship I<k<M (2.374) where y is given by (2.373). This merely states that different ordering of the largest l - 1 energy samples and the smallest M - l energy samples all have the same conditional probability when E1 is the I-th largest and x = 1. Next consider the probability M - 1 (2.375) Thus the conditional probability of the input x with output y where yx=1 Non-Coherent Frequency-Hopped Systems is given by Since there are (M - 1)! outputs y with yx = l, (2.377) This is the probability that the transmitted symbol has a corresponding energy detector output that is the 1-th largest among the M energy detector outputs. Comparing (2.376) and (2.377) (2.378) when y is any output with component yx which is the place on the list that resulted for the energy detector output corresponding to input X. We now have an expression for the conditional probabilit