raction of time occurrences given by p1, p2, PL. Thus, assume that at any given time the jammer power is J with probability P for l = 1,2, , L where Pulse Jamming (1.73) is the average power constraint. Also during the transmission time of a data bit, Tb, the jammer power is assumed to be constant with value equal to one of the L levels. Thus compared to Tb, the jammer power is slowly varying. Even with faster jammer power time variations this assumption is reason- able, since the receiver correlates or integrates the received channel output signal over every Tb seconds. It is convenient to define (1.74) where the average power constraint (1.73) becomes (1.75) For a DS/BPSK system when the jammer is transmitting with power J the uncoded bit error bound is analogous to (1.36) (1.76) For CW jamming assume the same data is sent in both the inphase and quad- rature components of a direct-sequence spread QPSK system. Next, using the inequality (1.37) we obtain (1.77) and the average uncoded bit error rate bound (1.78) Using the inequality (1.79) (1.78) is further bounded by (1.80) Coherent Direct-Sequence Systems (1.81) when constraint (1.75) is imposed. The upper bound (1.81) can be achieved with two jammer power levels (L = 2) given by (1.82) where P1=1-p 2 = p (1.83) (1.84) provided (1.85) When (1.85) is not satisfied we have the special case of constant jammer power, i.e., p = 1. 1.42 Worst Case Jammer The jammer time distribution of power that maximizes the bound on the uncoded bit error probability is the pulse jammer with peak power I peak = J(E6/N3) (1.86) for a fraction p of the time where p is given by (1.84). This is not necessar- ily the jammer that maximizes the true bit error probability. Assuming a nar- rowband pulse jammer (or CW pulse jammer at the carrier frequency) which is on a fraction p of the time, the exact uncoded bit error probability is Pb(p) = pQ(V2p(E,/N,)). (1.87) The choice of p that maximizes (1.87) is 0.709 (1.88) Eg/N, < 0.709 resulting in the bit error probability Eb/N J > 0.709 (1.8