Hidden convexity based near maximum-likelihood CDMA detection

We propose a computationally efficient approximation of the maximum-likelihood (ML) multiuser detector based on a nonconvex relaxation of the ML optimization problem. Using the hidden convexity methodology we obtain an explicit solution to the relaxed problem, which has the same form as the linear minimum mean-squared error (MMSE) receiver, where the constant diagonal loading in the MMSE receiver is replaced by a data-dependent constant that can be found efficiently by a simple bisection algorithm. Combining this relaxation with a local search algorithm results in a detector whose performance is close to that of the ML receiver, with a computational complexity on the same order as that of the linear multiuser receivers.