  We present a framework for the design of low-complexity and high-performance
receivers for multidimensional overloaded NOMA systems. The framework is built
upon a novel compressive sensing (CS) regularized maximum likelihood
formulation of the discrete-input detection problem, in which the L0-norm is
introduced to enforce adherence of the solution to the prescribed discrete
symbol constellation. Unlike much of preceding literature, the method is not
relaxed into the L1-norm, but rather approximated with a continuous and
asymptotically exact expression without resorting to parallel interference
cancellation. The objective function of the resulting formulation is thus a sum
of concave-over-convex ratios, which is then tightly convexized via the
quadratic transform, such that its solution can be obtained via the iteration
of a simple closed-form expression that closely resembles that of the classic
zero-forcing (ZF) receiver. By further transforming the aforementioned problem
into a quadratically constrained quadratic program with one convex constraint
(QCQP-1), the optimal regularization parameter to be used at each step of the
iterative algorithm is then shown to be the largest generalized eigenvalue of a
pair of matrices which are given in closed-form. The method so obtained,
referred to as the IDLS, is then extended to address several factors of
practical relevance, such as noisy conditions, imperfect CSI, and hardware
impairments, thus yielding the Robust IDLS algorithm. Simulation results show
that the proposed art significantly outperforms both classic receivers, such as
the LMMSE, and recent CS-based alternatives, such as the SOAV and the SCSR
detectors.
