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.

To further improve the performance of passive intelligent reflecting surface (IRS)-assisted communication systems and mitigate the serious path loss due to “double-fading” of IRS-assisted links, an active IRS-aided simultaneous wireless information and power transfer (SWIPT) system is investigated. This paper jointly optimizes the transmit beamforming at the base station (BS) and the phase shifts at the active IRS in order to maximize the power collected by the energy harvesting receiver under both perfect and imperfect channel state information (CSI) states, subject to the signal-to-interference-noise ratio constraint of the information decoding receiver, and the power constraints of the BS/IRS. Under perfect CSI, the alternating optimization algorithm is utilized for obtaining the transmit beamforming at the BS and the phase shifts at the active IRS. For each subproblem, we first transform non-convex objective function and constraints into convex ones by performing a first-order Taylor expansion. Then, each subproblem is solved by using the interior point method. Given that obtaining perfect CSI is impractical, two robust beamforming designs are proposed for imperfect CSI case. Under the bounded CSI error model, we first transform the non-convex optimization problem into two semidefinite programming subproblems, and then solve each subproblem based on S-procedure and sequential rank-one constraint relaxation (SROCR) techniques. Under the stochastic CSI error model, the alternating optimization method is applied in an iterative manner based on Bernstein-type inequality and SROCR technique. Simulation results show that both robust and non-robust schemes for active IRS-assisted SWIPT systems can achieve extremely superior performance over conventional passive IRS-assisted systems under the same overall power budget.