fer from (2.70) [11]. Let us consider the implications of (2.69). The underlying assumption is that the three extrema are computed for arbitrary but fixed values of K (or M) and E/N. The first minimization over 1 simply guarantees the tightest Chernoff upperbound, and the opti- mum l is in general a function of m and p: 1V1+ 6B-(1)] (2.72) where which is a variation of (2.63). Next, the Pb bound with 1 given by (2.72) is maximized over p for any m, and the optimum p depends on m, as does 1 above. In particular, if Eb/N, 3m/K SO that Pwc < 1, the solution is (2.64) with the optimum l in (2.72) reducing to 1/2 for smaller Eb/N,, Pwc = 1 and Coding Countermeasures (2.72) reduces to (2.63). The implication is that no matter which value of m is selected by the communicator, the jammer is privy to that parameter, either through surveillance or espionage, and can subsequently choose Pwc accordingly. Since the communicator must reveal his strategy first while the jammer gets the last move in this game of electronic countermeasure (ECM) and counter-countermeasure (ECCM), the jammer realizes an advantage in principle. Under these playing rules, the best strategy for the communicator is to choose m according to (2.70), provided Eb/N, 4/K SO that Mopt 1; then Pwc in (2.64) reduces to 3/4. Suppose instead that the jammer must declare his choice of p first, and the communicator can subsequently select m knowing p. Under this rever- sal of the game rules to the detriment of the jammer, the optimized perfor- mance is given by (2.71), with l still defined by (2.72). The solution is then Mopt = 1, corresponding to the performance of an uncoded FH/MFSK system in broadband Gaussian noise [11]. The performance improvement is illustrated in Figures 2.32-2.34. This introduces some game theoretic considerations regarding the selec- tion of m and p. The arguments are easier to follow in the context of a spe- cific example, SO suppose we want to achieve of P of 10-5 with K = 4. Based on (2.70), the communicator would design for EbIN1 = 11