In this paper, we present a low-complexity recursive approach for massive and scalable code-domain nonorthogonal multiple access (NOMA) with applications to emerging low-capacity scenarios. The problem definition in this paper is inspired by three major requirements of the next generations of wireless networks. Firstly, the proposed scheme is particularly beneficial in low-capacity regimes which is important in practical scenarios of utmost interest such as the Internet-of-Things (IoT) and massive machine-type communication (mMTC). Secondly, we employ code-domain NOMA to efficiently share the scarce common resources among the users. Finally, the proposed recursive approach enables code-domain NOMA with low-complexity detection algorithms that are scalable with the number of users to satisfy the requirements of massive connectivity. To this end, we propose a novel encoding and decoding scheme for code-domain NOMA based on factorizing the pattern matrix, for assigning the available resource elements to the users, as the Kronecker product of several smaller factor matrices. As a result, both the pattern matrix design at the transmitter side and the mixed symbols’ detection at the receiver side can be performed over matrices with dimensions that are much smaller than the overall pattern matrix. Consequently, this leads to significant reduction in both the complexity and the latency of the detection. We present the detection algorithm for the general case of factor matrices. The proposed algorithm involves several recursions each involving certain sets of equations corresponding to a certain factor matrix. We then characterize the system performance in terms of average sum rate, latency, and detection complexity. Our latency and complexity analysis confirm the superiority of our proposed scheme in enabling large pattern matrices. Moreover, our numerical results for the average sum rate show that the proposed scheme provides better performance compared to straightforward code-domain NOMA with comparable complexity, especially at low-capacity regimes.

中文翻译：

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低容量信道的大规模编码 NOMA：一种低复杂度的递归方法

在本文中，我们提出了一种用于大规模和可扩展码域非正交多址 (NOMA) 的低复杂度递归方法，并将其应用于新兴的低容量场景。本文中的问题定义受到下一代无线网络的三大要求的启发。首先，所提出的方案在低容量体制中特别有益，这在诸如物联网 (IoT) 和大规模机器类型通信 (mMTC) 等最感兴趣的实际场景中很重要。其次，我们采用码域 NOMA 来有效地在用户之间共享稀缺的公共资源。最后，所提出的递归方法使具有低复杂度检测算法的码域 NOMA 能够随着用户数量的增加而扩展，以满足大规模连接的要求。为此，我们提出了一种基于对模式矩阵进行分解的码域 NOMA 的新编码和解码方案，用于将可用资源元素分配给用户，作为几个较小因子矩阵的 Kronecker 乘积。结果，发射器侧的模式矩阵设计和接收器侧的混合符号检测都可以在维度远小于整个模式矩阵的矩阵上执行。因此，这会显着降低检测的复杂性和延迟。我们提出了因子矩阵一般情况的检测算法。所提出的算法涉及若干递归，每个递归涉及对应于特定因子矩阵的特定方程组。然后我们根据平均总速率、延迟、和检测复杂度。我们的延迟和复杂性分析证实了我们提出的方案在启用大型模式矩阵方面的优越性。此外，我们对平均总和率的数值结果表明，与具有相当复杂性的直接码域 NOMA 相比，所提出的方案提供了更好的性能，尤其是在低容量情况下。