Box-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-complete. In contrast, the unconstrained ML problem can be solved quite easily and is known as the decorrelating detector. In this paper, we consider the box-constrained ML problem and suggest a general iterative solution algorithm. Special cases of this algorithm correspond to known, nonlinear successive and parallel interference cancellation structures, using a clipped soft decision function for making tentative decisions. These structures are therefore maximum-likelihood under the assumption that the detected data vector is constrained to lie within a hypercube. Convergence issues are investigated and an efficient implementation is suggested. The BER performance is studied via computer simulations and the expected performance improvements over unconstrained ML is verified.