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We propose a quasi-maximum-likelihood (quasi-ML) detection scheme with soft output and low decoding complexity for multiple antenna wireless channels modulated with phase-shift keying (PSK). These detectors, which we refer to as quasi-ML PSK decoders, deploy a nonlinear programming relaxation and are able to achieve the performance of exact ML detection in a wide variety of coded or uncoded and PSK modulated multiple-antenna channels. Yet, the decoding complexity or the soft quasi-ML PSK decoders is much less than of ML detectors using exhaustive search. We also demonstrate that the quasi-ML PSK decoders possess favorable complexity properties compared to the existing sphere decoders.