Sphere-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 sphere-constrained ML problem and suggest an iterative solution algorithm. This detector is maximum-likelihood under the assumption that the detected data vector is constrained to lie within a sphere. Based on the defining Karush-Kuhn-Tucker point, it is shown that the suggested detector is closely related to the MMSE detector. Convergence issues are investigated and an efficient implementation is suggested. The BER performance is studied via computer simulations and the expected relations to the MMSE detector are verified