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.

For a sub-connected hybrid multiple-input multiple-output (MIMO) receiver with K subarrays and N antennas, there exists a challenging problem of how to rapidly remove phase ambiguity in only single time-slot. A direction of arrival (DOA) estimator of maximizing received power (Max-RP) is proposed to find the maximum value of K-subarray output powers, where each subarray is in charge of one sector, and the center angle of the sector corresponding to the maximum output is the estimated true DOA. To make an enhancement on precision, Max-RP plus quadratic interpolation (Max-RP-QI) method is designed. In the proposed Max-RP-QI, a quadratic interpolation scheme is adopted to interpolate the three DOA values corresponding to the largest three receive powers of Max-RP. To achieve the Cramer Rao lower bound, a Root-MUSIC plus Max-RP-QI scheme is developed. Simulation results show that the proposed three methods eliminate the phase ambiguity during one time-slot and also show low computational complexities. The proposed Root-MUSIC plus Max-RP-QI scheme can reach the Cramer Rao lower bound, and the proposed Max-RP and Max-RP-QI are still some performance losses 2–4 dB compared to the Cramer Rao lower bound.