s. As an example, suppose we assume the receiver has no jammer state knowledge and the jammer is a partial-band noise jammer which jams a frac- p = .05 (4.94) of the total spread-spectrum band. Assume the conventional non-coherent MFSK metric of (4.62). With M = 8 and using the error bound on the Trumpis code given by (4.78), what is the EIN, given by (4.3) required to achieve 10-5 bit error p = 1.0 -3 -2 -1 O I 2 3 4 Es INJ (dB) Figure 4.16a. Cutoff rate of FH/BFSK for soft decision with jammer state knowledge. p=1.0 Es IN (dB) Figure 4.17a. Cutoff rate of FH/4FSK for soft decision with jammer state knowledge. P 1.0 E S IN, (dB) Figure Cutoff rate of FH/4FSK for soft decision with no jammer state knowledge. 4.17b. p=1.0 Diversity for FH/MFSK probability? From the curve labelled D in Figure 4.12, the required E/No for the additive white Gaussian noise channel is Eb/No = 7.5 dB. (4.95) Here, since, R = 1, Es = Eb SO this is also the value of E/N , the coded sym- bol energy-to-noise ratio. Figure 4.14 shows that the cutoff rate is R = 1.8 bits/symbol. (4.96) This is also shown in the p = 1.0 curve in Figure 4.18b since broadband noise jamming and the additive white Gaussian noise channels are the same. To achieve the same value of R and, thus, the same 10-5 bit error probability for p = 0.05 we require E/N, = Eb/NJ = 16.8 dB. (4.97) This is determined from Figure 4.18b. By repeating this procedure for sev- eral values of the bit error probability, the bit error probability curve for the Trumpis code with an additive white Gaussian noise channel can be trans- lated into the corresponding bit error probability curve for a partial-band noise jammer with p=.05. 4.9 DIVERSITY FOR FH/MFSK In the FH/MFSK example with partial-band noise jamming for each trans- mitted M-ary symbol, the channel output signal-to-noise ratio is low with probability p and high with probability 1 - p. This is similar to a fading chan- nel except that here there are only two discrete fade levels.5 Since diversity techniques are useful in fading c