Capacity-Achieving Iterative LMMSE Detection for MIMO-NOMA Systems

This paper considers a Iterative Linear Minimum Mean Square Error (LMMSE) detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO) systems with Non-Orthogonal Multiple Access (NOMA), in which all the users interfere with each other both in the time domain and frequency domain. It is well known that the Iterative LMMSE detection greatly reduces the system computational complexity by departing the overall processing into many low-complexity distributed calculations that can be executed in parallel. However, it is generally considered to be suboptimal and achieves relatively poor performance due to its sub-optimal detector. In this paper, we firstly present the matching conditions and area theorems for the iterative detection of the MIMO-NOMA systems. Based on the matching conditions and area theorems, the achievable rate region of the Iterative LMMSE detection is analysed. Interestingly, we prove that by properly design the Iterative LMMSE detection, it can achieve (i) the optimal capacity of symmetric MIMO-NOMA system, (ii) the optimal sum capacity of asymmetric MIMO-NOMA system, (iii) all the maximal extreme points in the capacity region of asymmetric MIMO-NOMA system, (iv) the whole capacity region of two-user and three-user asymmetric MIMO-NOMA systems, in a distributed manner for all cases. Finally, a practical Iterative LMMSE detection design is also proposed for the general asymmetric MIMO-NOMA systems.