A subspace estimation-based constrained optimization method for the suppression of multiple-access interference (MAI) is proposed. The proposed method entails a new algorithm that approximates the noise subspace in a more robust manner compared with several existing methods. Simulations demonstrate that the performance of the proposed method is almost the same as that of some known subspace methods but the method leads to a significant reduction in the amount of computation. Relative to some known constrained optimization methods, our method offers a significantly improved performance while requiring a comparable amount of computation.