lity of error. Worst Case Jamming We should add that it does not matter whether the jammed band W1 is a sin- gle contiguous region as suggested by Figure 2.6: the analysis below is trans- parent to partitions of W1 SO long as each of them satisfies the assumptions above. Because of the pseudorandom hopping, it is reasonable to model the FH/MFSK system in partial-band noise as a two-state channel, independent from hop to hop. With probability p, an M-ary transmission is jammed and the conditional Pb is determined by the SNR ratio of (2.22); but, since we are neglecting thermal noise, with probability (1 - p), the transmission is noiseless and an error-free decision is made. Then the average error rate is simply (2.23) where the term on the right denotes the expression of (2.20b) with EBIN, replaced by pEIN. What (2.23) tells us is that if p is reduced, the probability that an M-ary transmission is jammed is decreased, but jammed signals suffer a higher con- ditional error rate: the net effect may degrade the average FH/MFSK per- formance, depending on the values of M and EIN The utility of jamming only part of the RF band is illustrated in Figure 2.7 for M = 2. Suppose S, J, , W ss SS' and Rb combine to make Eb/N, = 10.9 dB. In broadband noise (p = 1), the resulting Pb = 10-3. If the jammer concentrates the same noise power over half the SS band (p = 1/2), only half the transmissions are jammed, but these have a conditional 2.2 X 10-2 7.9 dB 10-31 Eb/N,,BB Figure 2.7. Illustration of partial-band jamming advantage against FH/MFSK sys- items. Referring to (2.20b) and (2.23), if M = 2 and EIN = 10.9 dB, when p = 1 then Pb = 10-3; however, if p = 1/2, = then conditional SNR ratio in jammed band is 7.9 dB, SO that conditional Pb = 2.2 X 10-2, resulting in average P = 1.1 X 10-2. Non-Coherent Frequency-Hopped Systems Pb = 2.2 X 10-2, which results in an average Pb = 1.1 X 10- according to (2.23). So in this example, reducing p to 1/2 degrades the performance more than an order of magnitude because of the steepness of t