sily obtained by differentiation and found to be (3.79) This yields the maximum value of P given by (3.80) Figure 3.25 shows this worst case value of the bit error probability. Here at 10-6 bit error probability there is a 40 dB difference between broadband Uncoded Frequency-Hopped Binary Frequency-Shift-Keying .0005 Eb/N, (dB) Figure 3.24. FH/BFSK-Partial-band noise jammer. noise jamming and the worst case partial-band noise jamming for the same jammer power. The partial-band noise jammer effect on the uncoded FH/BFSK system is analogous to the pulse noise jammer effect on the uncoded DS/BPSK sys- tem of Section 3.4. In both systems, these jammers cause considerable degra- dation by concentrating more jammer power on a fraction of the transmitted uncoded symbols. This potentially large degradation is explained by the fact that the uncoded bit error probability varies dramatically with small changes in the effective bit energy-to-jammer noise ratio, EIN Thus, the jammer can cause high error probabilities for a fraction of the transmitted bits resulting in a high average bit error probability. For the uncoded FH/BFSK system, pulse noise jamming and partial-band noise jamming have the same effect on performance. These are essentially equivalent ways of concentrating more jammer power on some fraction of Basic Concepts and System Models ED/NJ (dB) Figure 3.25. FH/BFSK-Agains jammers. the uncoded transmitted symbols. Using pulse noise jamming or a combi- nation of pulse noise and partial-band noise jamming would give the same results as we found for partial-band noise alone. 3.6.3 Multitone Jammer Recall that each signal tone of Tb second duration has one-sided first null bandwidth 1/Tb. For the total spread-spectrum signal bandwidth Wss, there N = WssTb possible orthogonal tone positions. Each FH/BFSK signal would then use an adjacent pair of these tone positions to transmit one data bit. The pair of Uncoded Frequency-Hopped Binary Frequency-Shift-Keying tone positions selected at any data bit time is determined by 