Constrained maximum-likelihood detection in CDMA

The detection strategy usually denoted optimal multiuser detection is equiv alent to the solution of a (0, 1)-constrained maximum-likelihood (ML) probl em, 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 de tector. In this paper, we consider the constrained ML problem where the sol ution; vector is restricted to lie within a closed convex set (CCS), Such a design criterion leads to detector structures which are ML under the const raint assumption. A close relationship between a sphere-constrained ML dete ctor and the well-known minimum mean square error detector is found and ver ified, An iterative algorithm for solving a CCS constraint problem is deriv ed 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 structur es, using a clipped soft decision for making tentative decisions, while a w eighted 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 i s studied via computer simulations and the expected performance improvement s over unconstrained ML are verified.