A Framework for Energy Efficiency Optimization in HMA-Assisted MU-MIMO Systems

Holographic metasurface antenna (HMA) has been envisioned as a new antenna paradigm anticipated to realize massive multiple-input multiple-output (MIMO) capability with greatly reduced hardware cost and power consumption. In this paper, we develop a framework for the energy efficiency (EE) optimization in the HMA-assisted uplink (UL) multiuser MIMO (MU-MIMO) system. We consider two types of power constraints, namely, the sum power and box eigenvalue constraints (SPBECs) and the multiple weighted power constraints (MWPCs). In this framework, we firstly formulate a general EE maximization problem subject to SPBECs and propose a novel EE-oriented water-filling algorithm by jointly exploring the quasi-concave property of the EE function and introducing an actual power consumption factor. Based on this, we then develop a low-complexity two-stage algorithm to separately optimize the HMA weighting matrix and the transmit covariance matrix. Specifically, in the first stage, two different algorithms, i.e., the channel alignment based algorithm and the weighted minimum mean square error (WMMSE) based algorithm, are proposed to optimize the HMA weighting matrix. In the second stage, we apply the proposed novel EE-oriented water-filling algorithm to optimize the transmit covariance matrix by respectively introducing per-user and all-user power consumption factors. Moreover, this two-stage algorithm is applicable to the EE optimization under MWPCs by leveraging duality theory to integrate multiple power constraints into a single one. Finally, numerical simulations validate that the proposed algorithms can achieve comparable EE performance to traditional benchmark schemes with significantly reduced computational complexities.