We a framework for the design of low-complexity and high-performance receivers for multidimensional overloaded non-orthogonal multiple access (NOMA) systems. The framework is built upon a novel compressed sensing (CS) regularized maximum likelihood (ML) formulation of the discrete-input detection problem, in which the $\ell _{0}$ -norm is introduced to enforce adherence of the solution to the prescribed discrete symbol constellation. Unlike much of preceding literature,.g., (Assaf et al. , 2020, Yeom et al. , 2019, Nagahara, 2015, Naderpour and Bizaki, 2020, Hayakawa and Hayashi, 2017, Hayakawa and Hayashi, 2018, and Zeng et al. , 2020), the method is not relaxed into the $\ell _{1}$ -norm, but rather approximated with a continuous and asymptotically exact expression without resorting to parallel interference cancellation (PIC). The objective function of the resulting formulation is thus a sum of concave-over-convex ratios, which is then tightly convexified via the quadratic transform (QT), 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, making the method particularly suitable to large-scale set-ups. 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 Iterative Discrete Least Square (IDLS), is then extended to address several factors of practical relevance, such as noisy conditions, imperfect channel state information (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 linear minimum mean square error (LMMSE), and recent CS-based state-of-the-art (SotA) alternatives, such as the sum-of-absolute-values (SOAV) and the sum of complex sparse regularizers (SCSR) detectors. It is also shown via simulations that the technique can be integrated with existing iterative detection-and-decoding (IDD) methods, resulting in accelerated convergence.

中文翻译：

---

大规模过载NOMA系统中的鲁棒符号检测

我们为多维超载非正交多路访问（NOMA）系统设计低复杂度和高性能接收器的框架。该框架基于离散输入检测问题的新型压缩感知（CS）正规化最大似然（ML）公式，其中 $ \ ell _ {0} $ 引入-norm以强制解决方案遵守指定的离散符号星座。与之前的许多文献不同，例如（（Assaf等。 2020年 等。 ，2019，长原（Nagahara），2015，Naderpour和Bizaki，2020，早川和林（2017），早川和林（2018）和曾 等。 （2020年），方法不放松 $ \ ell _ {1} $ -范数，而是使用连续且渐近精确的表达式近似，而无需求助于并行干扰消除（PIC）。因此，所得配方的目标函数是凹凸比率的总和，然后通过二次变换（QT）使其紧紧凸出，从而可以通过迭代一个简单的闭合形式表达式来获得其解。与经典的零强制（ZF）接收器极为相似，因此该方法特别适合于大型装置。通过将上述问题进一步转换为具有一个凸约束（QCQP-1）的二次约束二次程序，然后，将在迭代算法的每个步骤中使用的最佳正则化参数显示为以封闭形式给出的一对矩阵的最大广义特征值。然后将如此获得的方法称为迭代离散最小二乘（IDLS），以解决实际相关的几个因素，例如嘈杂的条件，不完善的信道状态信息（CSI）和硬件损伤，从而产生稳健的IDLS算法。仿真结果表明，所提出的技术明显优于经典的接收器，例如线性最小均方误差（LMMSE），以及最近基于CS的最新技术（SotA）替代，例如绝对和。值（SOAV）和复杂稀疏正则化器（SCSR）检测器的总和。