mmed with probability 1 - p independent of other transmitted sym- bols. As before, define the jammer state random variable Z where P{Z = 1} = = p P{Z = 0} =1 - p. (4.86) This is the jammer state information that may be available at the receiver where Z = 1 indicates that the transmitted symbol hopped into the jammed band while Z = 0 indicates that it hopped outside the jammed band. With Z available at the receiver, the metric we consider is (4.87) which is a weighted version of the energy detector output corresponding to input X. For the above metric the parameter (4.18) has the form D(1) = = 1}|x*x + (1 - (4.88) From (4.67), (4.68), and (4.69) we have (4.89) for 0<22c(1)<1and (4.90) Thus, (4.91) When side information is available, the metric can be chosen with c(0) large enough SO that the second term in (4.91) is negligible and c(1) = 1/2 chosen for normalization. Then, the parameer D becomes (4.92) FH/MFSK and Partial-Band Jamming Es IN, (dB) Figure 4.15a. Parameter D for soft decision with jammer state knowledge- FH/MFSK. With no side information, c(1) = c(0) which can be normalized to 1/2 to get = 011 min p 12 e + (1 - p)e-^p(E,/N,) (4.93) Figures 4.15a and 4.15b show D given by (4.92) and (4.93), respectively, for various values of p. Next, in Figures 4.16 through 4.18, the correspond- ing cutoff rates given by (4.27) for M = 2, 4, and 8 are shown. The special case of p = 1.0 is the broadband noise jamming case discussed in the previ- ous section. 4 There D is given by (4.70) hich is the same as (4.92) and (4.93) 4The broadband noise jammer case is the same as having an additive white Gaussian noise chan- nel with No = N. General Analysis of Anti-Jam Communication Systems Es S IN, (dB) Figure 4.15b. Parameter D for soft decision with no jammer state knowledge- FH/MFSK. for p = 1.0. Thus, in Figures 4.15 through 4.18, we can compare the broad- band noise jammer (p = 1.0) with various partial-band noise jammers. For any code, the bit error bounds for all these cases can be directly compared using these figure