Subarray Partition Algorithms for RIS-Aided MIMO Communications

In order to reduce computational complexity and hardware cost for reconfigurable intelligent surface (RIS)-aided multiple-input-multiple-output (MIMO) systems, in this article, the subarray partition algorithm designs at RIS are investigated. Without instantaneous channel state information (CSI) of the RIS-related links, the subarray partition algorithms aim at minimizing the number of subarrays while keeping a minimum sum rate requirement. In nature, the subarray partition optimization problem is a combinatorial optimization and NP-hard because of many discrete optimization variables. Three kinds of subarray partition algorithms are proposed. The first one is named as a fixed pattern subarray partition algorithm, in which subarray is arranged in a predefined manner. This algorithm is easy to implement but its performance is far from optimal. To reap the benefits of RIS as much as possible, two dynamic pattern subarray partition algorithms are given as well. The first dynamic pattern algorithm is the greedy dynamic pattern subarray partition algorithm that is more complicated than the fixed pattern one but benefits much better performance. To reduce complexity, the relaxation-based dynamic pattern algorithm is given, which has almost the same performance as the greedy dynamic algorithm but has a much lower complexity. At the end of the whole work, numerical results are given to access the performance of the proposed algorithms.