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.