An investigation into the direction finding problem in the case of a consta
nt-modulus signal is presented. A simple expression for the maximum likelih
ood estimator (MLE) is derived in the single source case. The MLE correspon
ds to an L-1-type beamformer as opposed to the L-2-beamformer that results
in a deterministic but not necessarily constant-modulus signal. Numerical e
xamples show that the proposed estimator has a performance very close to th
e Cramer-Rao Bound for a wide range of scenarios.