 worst case noise jammer. that is the 1-th largest among all M energy detector samples. Indeed, with the usual symmetry assumptions, the same expressions apply for the coding parameter D. In some circumstances it may be desirable to shorten the list to the L largest energy detector outputs where L < M. In this case the lowest M L energy detector outputs are treated indistinguishably as a single off-list group. Here the probability of the correct symbol energy detector sample (3)(4) E/N, (dB) Figure 2.130. List and energy metrics R for FH/32FSK against worst case noise jam- Non-Coherent Frequency-Hopped Systems being 1-th on the list is 1=1,2,...,L P{(L) (2.391) With the ML metric the coding parameter is then (2.392) This is the list-of-L detection scheme presented in [28], [29], and [32]. For the uniform channel with no receiver noise, Crepeau [32] has evalu- ated the performance of the ML metric with a list-of-L where there is worst case multitone jamming and broadband noise jamming with slowly varying Rayleigh fading. Figure 2.131 shows the M = 16 case with Rayleigh fading for R in bits per symbol. There is little difference in the performance due to increasing the list size. For worst case multitone jamming, Figures 2.132 to 2.135 show a more dramatic difference in just going from L = 1 to L = 2. In general, the list metric is a useful metric when there are multiple tones in the channel due to a jammer and/or other users. 2.7.4 Metrics for Binary Codes For FH/MFSK signals there are three well-known types of codes one can use that have M-ary code symbols. Reed-Solomon codes [21] are natural block codes to use where the decoders generally require a hard decision M-ary channel. M-ary alphabet convolutional codes include those found by Trumpis [18] and dual-K codes9 [20] where M = 2K. These codes can be decoded using the Viterbi algorithm with all metrics discussed in this chapter. Today, however, most codes used in practice are binary codes, especially binary convolutional codes. These have been used primarily wi