Constrained maximum-likelihood detection in CDMA

The detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a (0, 1)-constrained maximum-likelihood (ML) problem, a problem which is known to be NP-hard. In contrast, the unconstrained ML problem can be solved quite easily and is known as the decorrelating detector. In this paper, we consider the constrained ML problem where the solution vector is restricted to lie within a closed convex set (CCS). Such a design criterion leads to detector structures which are ML under the constraint assumption. A close relationship between a sphere-constrained ML detector and the well-known minimum mean square error detector is found and verified. An iterative algorithm for solving a CCS constraint problem is derived based on results in linear variational inequality theory. Special cases of this algorithm, subject to a box-constraint, are found to correspond to known, nonlinear successive and parallel interference cancellation structures, using a clipped soft decision for making tentative decisions, while a weighted linear parallel interference canceler with signal-dependent weights arises from the sphere constraint. Convergence issues are investigated and an efficient implementation is suggested. The bit-error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ML are verified.