@article{Jiang2026, 
author = {Jinbing Jiang and Feng Shu and Xuehui Wang and Ke Yang and Chong Shen and Qi Zhang and Dongming Wang and Jiangzhou Wang},
title = {DoF Analysis and Beamforming Design for Active IRS-Aided Multi-User MIMO Wireless Communication in Low-Rank Channels},
year = {2026},
journal = {Tsinghua Science and Technology},
keywords = {degree of freedom (DoF), intelligent reflecting surface (IRS), sum-rate, multi-user multi-input multi-output (MU-MIMO), beamforming},
url = {https://www.sciopen.com/article/10.26599/TST.2025.9010084},
doi = {10.26599/TST.2025.9010084},
abstract = {Due to its ability to significantly improve data rate, intelligent reflecting surface (IRS) is a potential crucial technique for the future generation wireless networks like six-generation (6G). In this paper, we focus on the analysis of degree of freedom (DoF) in IRS-aided multi-user multi-input multi-output (MIMO) network. Firstly, the DoF upper bound of IRS-aided single-user MIMO network, i.e., the achievable maximum DoF of such a system, is derived, and the corresponding results are extended to the case of IRS-aided multiuser MIMO by using the matrix rank inequalities. In particular, in serious rank-deficient, also called low-rank, like line-of-sight channel, the network DoF may double over no-IRS with the help of IRS. To verify the rate performance gain from augmented DoF, three closed-form beamforming methods, null-space projection plus maximize transmit power and maximize receive power (NSP-MTP-MRP), Schmidt orthogonalization plus (SO-MMSE) and two-layer leakage plus minimum mean square error (TLL-MMSE) are proposed to achieve the maximum DoF. Simulation results show that IRS does make a dramatic rate enhancement. For example, in a serious rank-deficient channel, also called low-rank, the sum-rate of the proposed TLL-MMSE aided by IRS is up to 2.54 times that of no IRS. This means that IRS may make a significant DoF improvement in such a channel.}
}