Covariance-Aware Fixed-Cardinality IRS Design With Quantized Phases for Multiuser MISO and MIMO Systems

Abstract

Joint transmit precoding and finite-alphabet intelligent reflecting surface (IRS) control are particularly challenging when only <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> installed cells are active and the component-channel uncertainty depends on the selected surface state. This paper develops a covariance-aware, exact-cardinality design for multiuser MISO and multi-stream MIMO downlinks. Propagating errors in the direct, base-station–IRS, and IRS–user links yields a state-dependent effective covariance that permits non-diagonal spatial correlation. Scalar and matrix weighted minimum-mean-square-error (WMMSE) identities provide the transceiver updates. For fixed transceiver variables, the surface-dependent cost is an exact Hermitian quadratic. A tight spectral majorizer converts each finite-alphabet, exact-cardinality subproblem into per-cell phase projection and exact top-<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> selection; coordinate and swap refinements are accepted only when they decrease the objective. A hardware-aware extension incorporates phase-independent active-state loss and calibrated residual reflection in the inactive state. At the nominal operating points and under the stated method-specific phase alphabets and search budgets, the proposed method attains the highest observed mean rate among the tested equal-cardinality selected-element designs in the reported MISO and MIMO comparisons. The method outperforms static and energy-ranked subsets while retaining most of the corresponding full-surface quantized-phase rate with fewer controlled cells. Robust optimization provides a clear gain over designs that ignore uncertainty, whereas the incremental mean-rate gain of directional covariance over statewise trace-matched loading is modest. The numerical study also evaluates phase resolution, conditional-rate accuracy, runtime, energy efficiency, and nonideal surface responses under a normalized link-level channel model.