averaged power J. 1.3.1 CW Jammer The most harmful jammer waveform is one that maximizes J given by (1.22) for each value of k. Since the jammer does not know the PN sequence {ck} this means the jammer should place as much energy as possible in the cosine coordinate which is achieved with a CW signal. Generally, the jammer may not know the transmitted signal carrier phase SO consider the deterministic jammer waveform model (1.46) which is characterized by the phase parameter 0. Thus Jk=VJT.cos A, all k (1.47) which is maximized when O = 0. For this CW jammer the conditional variance of n given in (1.35) is Var{n|J} = JT, cos't. (1.48) For the Gaussian approximation (Central Limit Theorem applied for large N = T/ the conditional bit error probability is Pb(A) = Pb(I) (1.49) Using JT N1 this becomes (1.50) for the CW jammer. The choice of O = 0 maximizes Pb(A) yielding the bound (1.51) Uncoded Bit Error Probability for Specific Jammer Waveforms This upper bound is the same as that for binary orthogonal signals in an addi- tive white Gaussian noise channel for single-sided spectral density N. For a jammer with constant power J this is the worst performance of the direct- sequence spread BPSK system. Against a CW jammer an effective technique is to use BPSK data mod- ulation with QPSK PN spreading. This is a DS/BPSK signal of the form (1.52) where cct and cs(t) are PN waveforms. This is the special case of d = ds = d in the QPSK modulation given in (1.13) where the QPSK symbol energy is also the bit energy (one bit per QPSK signal). For this case (1.14) and (1.17) have the form (1.53) (1.54) where nc and NS are zero mean independent with conditional variances (1.55) (1.56) Next use (1.57) as the statistic for the decision rule given in (1.19). Since (1.58) the bit error probability for the Gaussian approximation is (1.59) This is independent of O and is a 3 dB improvement over the worst case (A = 0) BPSK PN spreading system. Thus, to minimize the maximum possible degradation due to a CW jammer, one should use QPSK mo