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A conjugate-gradient (CG) constant-modulus adaptive processor is proposed. For the generalized sidelobe canceler (GSC) signal processing configuration, this algorithm, CG-GSC, exhibits improved convergence over previous methods. Theoretical expressions are presented for convergence and weight update of a linearly constrained constant modulus generalized sidelobe canceler. Theoretical expressions are then derived for the conjugate direction vectors. These vectors are used to update the filter weights for a conjugate gradient adaptation rule. A simulation study of the conjugate adaptation rule reveals the increase in convergence rate for the generalized sidelobe canceler. Performance comparisons of the CG-GSC and a first-order gradient GSC for a BPSK signal with multipath and white noise interference indicate that the CG-GSC adaptation rule not only increases convergence by a factor of five compared to the first-order gradient GSC, but in some instances improves the bit error rate of the demodulated BPSK signal