ution of the jammer power is guaranteed. In this case the jammer appears as white noise of power spectral density bounded by N //2. Multiplying the channel output signal by the PN waveform results in the narrowband signal s(t) in broadband noise n(t). Here s(t) has bandwidth 1/Tb while n(t) has bandwidth greater than Wss = 1/T = N/T which is N times wider than the signal bandwidth. Since Sn(f) is essentially flat over the nar- rowband signal bandwidth, the detection problem reduces to demodulation of a BPSK signal in white noise of double-sided power spectral density less than or equal to Nj/2. Thus, making the Gaussian approximation, the uncoded bit error probability is bounded by (1.72) Here equality is achieved for narrowband jamming signals. This gives the same result as with a CW jammer and QPSK modulation where the same data is entered in both the inphase and quadrature components (BPSK data modulation with QPSK PN spreading). It also is the baseline performance where the jammer simply transmits broadband Gaussian noise. Based on these results for CW and random jammers, we would expect the direct-sequence BPSK anti-jam systems to be robust and insensitive to all jammers that produce waveforms which are independent of the transmis- sion. They appear to always give as good a performance as the basline jam- mer case and that is all one can expect from a good anti-jam communication system. This, however, is true only for constant power jammers. 1.4 PULSE JAMMING Now consider the impact of pulse jamming and its generalization where the jammer can arbitrarily distribute its energy in time under a long time average power constraint. The worst time distribution of energy by the jam- mer is the two-level jammer corresponding to pulse jamming. This distri- bution results in considerable degradation to the uncoded DS/BPSK system. 1.4.1 Arbitrary Time Distribution Consider an arbitrary continuous time distribution of the jammer power which is approximated as having L discrete levels J1, 1, J2, , JL with corresponding f