MIMO-NOMA Uplink and Downlink with Simultaneous Generalized Triangular Decomposition and SIC

This paper revisits both the uplink and downlink two-user multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. We present a novel concept of matrix decomposition called simultaneous generalized triangular decomposition (SGTD). The main idea is to simultaneously decompose two matrices into predetermined triangular forms while providing flexibility in designing the ratios of the diagonal elements. For uplink MIMO-NOMA, the proposed SGTD enables interference-free transmission between users by transforming MIMO channels into two triangular forms and successively decoding and canceling data streams. Unlike existing simultaneous diagonalization or triangularization approaches with fixed diagonal values, the proposed method provides flexibility in adjusting the diagonal elements of the triangular matrices. This adaptability makes it particularly advantageous for meeting specific design requirements, such as maximizing the weighted sum rate and ensuring stable transmission across each spatial stream. As an example, an optimized design is provided to maximize the weighted sum rate within the proposed framework. A similar approach is also proposed to develop a new precoding design for downlink MIMO-NOMA. Extensive simulations demonstrate that, for both uplink and downlink scenarios, the proposed scheme outperforms state-of-the-art MIMO-NOMA and orthogonal multiple access (OMA) systems.