Hybrid Beamforming via Fourth-Order Tucker Decomposition for Multiuser Millimeter-Wave Massive MIMO Systems

To enhance the spectral efficiency of hybrid beamforming in millimeter-wave massive MIMO systems, the problem is formulated as a high-dimensional non-convex optimization under constant modulus constraints. A novel algorithm based on fourth-order tensor Tucker decomposition is proposed. Specifically, the frequency-domain channel matrices are structured into a fourth-order tensor to explicitly capture the couplings across the spatial, frequency, and user domains. To tackle the non-convexity induced by constant modulus constraints, the analog precoder and combiner are derived by solving a truncated-rank Tucker decomposition problem through the Alternating Direction Method of Multipliers and Alternating Least Squares schemes. Subsequently, in the digital domain, the Regularized Block Diagonalization algorithm is integrated with the subcarrier and user factor matrices—obtained from the tensor decomposition—along with the water-filling strategy to design the digital precoder and combiner, thereby achieving a balance between multi-user interference suppression and noise enhancement. The proposed tensor-based algorithm is demonstrated through simulations to outperform existing state-of-the-art schemes. This work provides an efficient and mathematically sound solution for hybrid beamforming in dense multi-user scenarios envisioned for sixth-generation mobile communications.