Abstract: Maximum likelihood (ML) detection problems for several multiuser systems result in nonlinear optimization problems with unacceptably high complexity. One way of achieving near-optimum performance without the complexity associated with the ML detector is using nonlinear programming relaxations to approximate the solution of the ML detection problem at hand. Using this approach, new detectors are formulated and it is observed that some popular suboptimum receivers correspond to relaxations of the ML detectors. We concentrate on two types of systems to demonstrate this concept and evaluate the performance of the resulting detectors.