one jammed MFSK data signal. Non-Coherent Frequency-Hopped Systems Table 2.2 Normalized energy detector outputs. If tone jammed If not jammed Transmitted M-ary symbol Any of the (M - 1) other symbols The table reveals the range of a for which symbol errors can occur. If none of the M dehopped symbols is jammed, there can be no error. If the data symbol is not jammed and any of the other symbols is hit with a jam- ming tone, an error will always be made if a < 1, and never for a > 1 (ties that occur when a = 1 can be resolved with an M-sided coin flip, or sim- ply assigned to the error side of the ledger). Note that in the uncoded case, with hard decisions made on each symbol, there is no advantage to hit- ting more than one of the untransmitted symbols. If only the data symbol is hit, its energy detector output is greater than zero except for a singu- lar value of depending on a; since that singular point occurs with prob- ability zero, an error cannot occur. Finally, if the transmitted symbol and any of the other symbols are simultaneously jammed, an error can occur with probability Professor (2.35) which is non-zero for 0<a<4. This is a surprising result. Most multitone jamming analyses simply assume axiomatically that the jammer should set a = 1_, SO that each jamming tone has power slightly in excess of S. Houston pointed out that the jammer could do better by optimizing a, but he neglected the impact of the random jammer phase and restricted a to the range (0,1) [5, pp. 53-54]. Only Trumpis [7, p. 16] recognized that an error could still occur even when the power in each jamming tone was up to 6 dB below the received signal power. It remains to be seen whether in fact a worst case jammer would ever select a > 1 for any of the multitone strategies, and this will be resolved in the next two sections. 2.2.2.2 Band Multitone Jamming The simplest scheme to analyze is n = 1 band multitone jamming. The ran- dom jamming phase has no effect on the system performance, and it demon- strates the basic approach to determ