Massive Coded-NOMA for Low-Capacity Channels: A Low-Complexity Recursive Approach

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.