Movable antenna (MA) has emerged as a promising technology for enhancing communication performance over conventional fixed position antenna (FPA) by exploiting spatial channel variations. In this paper, we propose a general energy efficiency (EE) optimization framework for the MA-aided multi-user multiple-input multiple-output (MU-MIMO) downlink communications. We jointly optimize the precoding matrices and the positions of transmit and receive MAs considering two different types of power constraint models, i.e., the sum power constraint (SPC) and multiple weighted power constraints (MWPCs), and various physical constraints on MA positions. In both the SPC case and the MWPCs case, we optimize the MA positions by jointly employing the weighted minimum mean square error (WMMSE) and successive convex approximation (SCA) methodologies. As for the precoding matrices optimization, by exploiting the uplink-downlink duality of MU-MIMO systems, we transform the downlink EE optimization into their virtual uplink EE optimization counterparts. Then, we derive the optimal structures of the precoding matrices, where the involved optimal power allocations take the multi-user water-filling solutions. To compute the parameters of the multi-user water-filling solutions, by taking advantage of the underlying algebraic monotonicity of the problem, we propose three novel design strategies, i.e., the direct Dinkelbach based design, the modified Dinkelbach based design, and the bound-ware penalty based design. In contrast to conventional fractional programming (FP) based EE optimization methods, the proposed algorithms offer significantly lower computational complexities and explicit physical insights. Moreover, the simulation results demonstrate the superior performance and high efficiency of our proposed EE optimization algorithms.

Energy efficiency (EE) optimization has attracted significant research attention for implementing green communications. With cost-effective and low-power advantages, intelligent reflecting surface (IRS) and hybrid analog-digital transceiver have recently emerged as two promising technologies of next-generation green wireless systems. In this paper, we propose a comprehensive framework for EE optimization in four types of IRS-aided hybrid analog-digital multiuser multiple-input multiple-output communication systems, including the uplink (UL) systems under the sum power and box eigenvalue constraints as well as the per-radio-frequency chain power constraints (PRPCs), and the downlink (DL) systems under the sum power constraint and the PRPCs. This framework proposes a unified design methodology to these four considered systems by separating the optimization of analog and digital matrix variables. Specifically, for the UL EE maximization problems, we firstly propose a channel alignment based algorithm to separately optimize the analog precoders at users, the analog combiner at the base station and the IRS reflecting matrix, whose computational complexity is significantly reduced as compared with the traditional alternating optimization algorithm. Then, by introducing the auxiliary variables and exploiting the Karush-Kuhn-Tucker conditions based algorithm, the optimal digital precoders at users are obtained in closed forms. Furthermore, the intractable DL EE optimization can be equivalently transformed into its virtual UL counterpart using the DL-UL duality, leading to the general applicability of the proposed framework. Extensive simulations reveal that the proposed algorithm attains the almost identical EE performance to the traditional benchmarks with a lower computational complexity.

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.

Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including diagonal structure constraints and constant modulus constraints, both of which are closely related to the state-of-the-art wireless applications. Specifically, for diagonal structure constraints mostly considered in the uplink multi-user single-input multiple-output (MU-SIMO) system and the amplitude-adjustable intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system, the capacity maximization problem, the mean-squared error (MSE) minimization problem and their variants are rigorously investigated. By leveraging complex matrix derivatives, the optimal solutions of these problems are directly obtained in closed forms. Nevertheless, for constant modulus constraints with the intrinsic nature of element-wise decomposability, which are often seen in the hybrid analog-digital MIMO system and the fully-passive IRS-aided MIMO system, we firstly explore inherent structures of the element-wise phase derivatives associated with different optimization problems. Then, we propose a novel alternating optimization (AO) algorithm with the aid of several arbitrary feasible solutions, which avoids the complicated matrix inversion and matrix factorization involved in conventional element-wise iterative algorithms. Numerical simulations reveal that the proposed algorithm can dramatically reduce the computational complexity without loss of system performance.

Aiming at providing wireless communication systems with environment-perceptive capacity, emerging integrated sensing and communication (ISAC) technologies face multiple difficulties, especially in balancing the performance trade-off between the communication and radar functions. In this paper, we introduce a reconfigurable intelligent surface (RIS) to assist both data transmission and target detection in a dual-functional ISAC system. To formulate a general optimization framework, diverse communication performance metrics have been taken into account including famous capacity maximization and mean-squared error (MSE) minimization. Whereas the target detection process is modeled as a general likelihood ratio test (GLRT) due to the practical limitations, and the monotonicity of the corresponding detection probability is proved. For the single-user and single-target (SUST) scenario, the minimum transmit power for sensing has been revealed. By exploiting the optimal conditions, we validate that the optimal BS satisfies the maximum power allocation criterion and derive the optimal BS precoder in a semi-closed form. Moreover, an alternating direction method of multipliers (ADMM) based RIS design is proposed to address the non-convex radar constraint. For the sake of enhancing computational efficiency, a low-complexity RIS design is also developed based on the manifold optimization theory. Furthermore, the ISAC transceiver design for the multiple-users and multiple-targets (MUMT) scenario is also investigated, where a zero-forcing (ZF) radar receiver is adopted to cancel the interference signals from different targets. Then optimal BS precoder is derived under the maximum power allocation scheme, and the RIS phase shifts can be optimized by extending the proposed ADMM-based RIS design algorithm. Finally, the ISAC transceiver design with imperfect in-band full-duplex transceivers is also discussed and two radar receive beamformer designs have been proposed to mitigate the performance loss. Numerical simulation results verify the convergence and superior communication/sensing performance of our proposed transceiver designs.

Both the reconfigurable intelligent surface (RIS) and the hybrid analog-digital antenna array have been envisioned as two cost-effective and promising technologies for achieving various types of functionality enhancement of future wireless systems. In this paper, we develop a framework for the multi-functional optimization in the RIS-aided hybrid analog-digital multiple-input multiple-output (MIMO) system, where a board of performance metrics related to diverse system functionalities are considered, such as capacity and mean square error (MSE) for information transmission (IT), Cramer-Rao bound (CRB) for radar sensing, harvested energy for energy harvesting (EH) and so on. Under this framework, we focus on two types of multi-functional optimization problems, namely, the multi-objective multi-functional optimization and the single-objective optimization subject to multi-functional constraints, and propose a unified low-complexity algorithm by separately optimizing analog and digital matrix variables. Specifically, for the multi-objective optimization, we firstly propose the numerical quadratic optimization based (QuaOpt-based) algorithm and the low-complexity channel alignment based algorithm to separately optimize analog matrices, including the RIS reflecting matrix, the analog precoder and the analog equalizer. Then, for the optimization of digital precoder, the numerical semidefinite programming (SDP)-based algorithm and the QuaOpt-based algorithm are proposed to iteratively solve the digital precoder optimization problem, while the matrix-monotonic optimization based algorithm derives the optimal closed-form solution in low computational complexity. Whereas for the single-objective optimization, the above proposed algorithms are still applicable by applying the Lagrangian duality theory to tackle the multi-functional constraints. Numerical simulation results reveal that the proposed low-complexity algorithm can achieve comparable performance to numerical algorithms.