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We propose a novel algorithm to perform jointly the azimuthal direction-of-arrival (DOA) estimation and the multiuser detection (MUD) of signals impinging on an array of antennas. We treat the DOA estimation as an inverse problem of identifying a specific set of parameters that explains the received signal for a suitable physical model. We reformulate the estimation problem as a highly underdetermined linear system and solve the resulting least squares problem using the well-known conjugate gradients (CG) iterations on the normal equations (NE). Unlike methods such as MUSIC, our method does not require any a priori information concerning the number of sources and also it is independent of the. type of modulation employed. Simulation results confirm the robustness of our algorithm in the regimes of perfect correlation and low signal-to-noise ratios (SNRs). We also propose a MUD algorithm using the least squares solution obtained during the DOA estimation.