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 hit 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.