ulator. The band-pass noise n(t) has the usual narrowband representation n(t) = V2[Ne(t) cos (wht + 0) - Ns(t) sin (wht + 0)] (1.3) where Nc(t) and Ns(t) are statistically independent low-pass white Gaussian noise processes with single-sided noise spectral density No w/Hz. The partial- band multitone jamming J(t) is assumed to have a total power J which is evenly divided among Q jammer tones. Thus, each tone has power (1.4) Furthermore, since the jammer is assumed to have knowledge of the exact location of the spreading bandwidth Wss and the number N of hops in this bandwidth, then, as was done in our previous discussions, we shall assume that he will randomly locate each of his Q tones coincident with Q of the N hop frequencies. Thus, (1.5) represents the fraction of the total band which is continuously jammed with tones, each having power J. Once again, the jammer's strategy is to distrib- ute his total power J (i.e., choose p and J0) in such a way as to cause the com- municator to have maximum probability of error. Spreading Code Coherent Frequency Demodulator Dehopper Figure 1.2. Block diagram of a coherent FH/QPSK demodulator. Coherent Modulation Techniques In view of the foregoing, the total received signal in a signalling interval which contains a jamming tone at the hop frequency is given by (1.6) where (1.7) n(t) is given by (1.3) and (1.8) with OJ uniformly distributed on (0,2) and independent of the information symbol phase . Over an integral number of hop bands, the fraction p of the total number of signalling intervals will have a received signal charac- terized by (1.6). In the remaining fraction (1 - p) of the signalling intervals, the received signal is simply characterized by (1.9) After ideal coherent demodulation by the frequency hopper, the in-phase and quadrature components of the received signal become3 + 0)] = Vs cos (i) - VJo OJ Ns(t) = sin (ii) + VJo + Nc(t). (1.10) These signals are then passed through integrate-and-dump filters of dura- tion equal to the information symbol interval T to