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This work investigates the effect of double intelligent reflecting surface(IRS) in improving the spectrum efficient of multi-user multiple-inputmultiple-output (MIMO) network operating in the millimeter wave (mmWave) band.Specifically, we aim to solve a weighted sum rate maximization problem byjointly optimizing the digital precoding at the transmitter and the analogphase shifters at the IRS, subject to the minimum achievable rate constraint.To facilitate the design of an efficient solution, we first reformulate theoriginal problem into a tractable one by exploiting themajorization-minimization (MM) method. Then, a block coordinate descent (BCD)method is proposed to obtain a suboptimal solution, where the precodingmatrices and the phase shifters are alternately optimized. Specifically, thedigital precoding matrix design problem is solved by the quadraticallyconstrained quadratic programming (QCQP), while the analog phase shiftoptimization is solved by the Riemannian manifold optimization (RMO). Theconvergence and computational complexity are analyzed. Finally, simulationresults are provided to verify the performance of the proposed design, as wellas the effectiveness of double-IRS in improving the spectral efficiency.

Double Intelligent Reflecting Surface-assisted Multi-User MIMO mmWave Systems with Hybrid Precoding