Intelligent reflecting surfaces (IRSs) have been regarded as a promising enabler for future wireless communication systems due to their capability of customizing favorable propagation environments. In the literature, IRSs have been considered power-free or assumed to have constant power consumption. However, recent experimental results have shown that for positive-intrinsic-negative (PIN) diode-based IRSs, the power consumption dynamically changes with the phase shift configuration, which implies that the beamforming quality of the IRS depends on the available power. Therefore, this phase shift-dependent power consumption (PS-DPC) introduces a challenging power allocation problem between the base station (BS) and the IRS, requiring to balance the BS transmit power and the IRS beamforming quality during system design. To tackle this issue, in this paper, we investigate a rate maximization problem for IRS-assisted systems under a practical PS-DPC model. For the single-user case, we propose a generalized Benders decomposition-based beamforming method to maximize the achievable rate while satisfying a total system power consumption constraint. Moreover, we propose a low-complexity beamforming design, where the powers allocated to BS and IRS are optimized offline based on statistical channel state information. Furthermore, we extend the beamforming design to the multi-user case, where we solve an equivalent weighted mean square error minimization problem with two different joint power allocation and phase shift optimization methods. Simulation results indicate that compared to baseline schemes, our proposed methods can flexibly optimize the power allocation between BS and IRS, thus achieving better performance. The optimized power allocation strategy strongly depends on the system power budget. Specifically, when the available system power budget is high, the PS-DPC is not the dominant factor in the system power consumption, allowing the IRS to turn on as many PIN diodes as needed to achieve high beamforming quality. When the system power budget is limited, however, more power tends to be allocated to the BS to enhance the transmit power, which consequently reduces the beamforming quality at the IRS due to the limited PS-DPC budget.

In this paper, we investigate the optimization of a double-intelligent reflecting surface (DIRS)-aided system under a practical power consumption model of DIRS elements. Specifically, the power consumption of DIRS elements, driven by the on/off-state of positive-intrinsic-negative (PIN) diodes, varies significantly based on their phase shift configurations. This phase shift-dependent power consumption (PS-DPC) model introduces an intractable power allocation problem to balance the power consumption at the BS and DIRS. To address this challenge, we develop a low-complexity joint beamforming and power allocation method to minimize the total system power consumption. By effectively exploiting the channel statistical characteristics (CSC), our method can determine the optimal power allocation strategy offline, thereby avoiding frequent updates in response to specific instantaneous channel state information. Moreover, the beamforming at the base station (BS) and DIRS can also be obtained by low-complexity closed-form solutions. Simulations reveal that by considering the PS-DPC, the proposed CSC method can effectively balance the power consumption between the BS and DIRS, thus significantly reducing the total system power consumption.

In this paper, we investigate the uplink channel estimation problem in intelligent reflecting surface (IRS)-assisted broadband millimeter wave multi-input multi-output communication systems. Considering the channel sparsity in both the angle and delay domains, we decouple the channel estimation problem into several sub-problems, namely, sequential estimations of the angles at the user, the base station, and the IRS, alongside the propagation path delays. By exploiting the Vandermonde structure of both the array manifold and the phase difference among multiple subcarriers caused by delays, we propose a multi-stage atomic norm minimization-based (MS-ANM) channel estimation algorithm. In particular, we take full advantage of the sharing of angle information among all subcarriers in the broadband channel to enhance the estimation accuracy. To reduce the computational complexity, we further propose a multi-stage orthogonal matching pursuit-based (MS-OMP) algorithm. Simulation results show that the MS-ANM algorithm significantly outperforms the benchmark algorithms, and the MS-OMP algorithm strikes a good balance between performance and computational complexity. By fully exploring the channel’s sparsity in the angle and delay domains along with the Vandermonde structure, both proposed algorithms remarkably reduce the training overhead and thus greatly improve the spectral efficiency over the benchmark algorithms.

Bilayer intelligent omni-surface (BIOS) has recently attracted increasing attention due to its capability of independent beamforming on both reflection and refraction sides. However, its specific bilayer structure makes the channel estimation problem more challenging than the conventional intelligent reflecting surface (IRS) or intelligent omni-surface (IOS). In this paper, we investigate the channel estimation problem in the BIOS-assisted multi-user multiple-input multiple-output system. We find that in contrast to the IRS or IOS, where the forms of the cascaded channels of all user equipments (UEs) are the same, in the BIOS, those of the UEs on the reflection side are different from those on the refraction side, which is referred to as the heterogeneous channel property. By exploiting it along with the two-timescale and sparsity properties of channels and applying the manifold optimization method, we propose an efficient channel estimation scheme to reduce the training overhead in the BIOS-assisted system. Moreover, we investigate the joint optimization of base station digital beamforming and BIOS passive analog beamforming. Simulation results show that the proposed estimation scheme can significantly reduce the training overhead with competitive estimation quality, and thus keeps the performance advantage of BIOS over IRS and IOS with imperfect channel state information.

Due to the passive nature and the unique capability of customizing propagation environments, intelligent reflecting surface (IRS) has been considered as a promising green communication technology to deal with the dramatically increasing power consumption of future wireless communication systems. However, most existing studies on IRS-aided green communication only considered the constant power consumption of IRSs, while ignoring the dynamic power consumption with respect to the states of PIN diodes. As the phase shifts of scattering elements are controlled by the PIN diodes in IRSs, this dynamic power consumption is strongly related to the phase shifts of IRS elements, and thus needs to be considered during the beamforming design. Therefore, in this paper, we investigate the green beamforming design for IRS-aided multi-input single-output systems under this phase shift-related (PSR) power consumption model. By taking the power consumption of the PIN diodes into consideration, we propose a generalized Benders decomposition-based green beamforming (GBD-GBF) scheme to minimize the total power consumption of the proposed system. Our simulation results reveal that the proposed GBD-GBF scheme can achieve a good balance between the transmit power consumption at the base station and the PSR power consumption of the IRS, and thus significantly reduce the total power consumption of the IRS-aided communication system.

Intelligent reflecting surface (IRS) consisting of a large number of low-cost and passive reflecting elements, has been proposed as a promising technology for future wireless communications due to its ability of customizing favorable propagation environment. In spite of its advantages, channel state information acquisition is an important and challenging task due to the passive nature of IRS. In this paper, we investigate the channel estimation problem for broadband IRS-aided millimeter wave (mm-wave) multiple-input multiple-output (MIMO) systems. From the practical implementation point of view, we consider the broadband scenario, realize the phase-amplitude-frequency relationship of the reflected signals, and adopt a practical model of reflection coefficients. Then, by utilizing the sparsity of the mm-wave channels, an efficient manifold optimization (MO) based algorithm is proposed to obtain a local optimal solution. Moreover, we propose a design approach for the optimization of the IRS reflection matrix to further improve the estimation performance. Simulation results show that the proposed MO based algorithm significantly outperforms the benchmark algorithm and the performance gain is especially significant for high-level sparse mm-wave MIMO channels.

Intelligent reflecting surface (IRS) has been regarded as a promising technology because of its ability in intelligently adjusting the propagation environment of wireless communication systems. However, channel estimation becomes a tough question due to the passive elements of IRS. In this paper, we investigate the channel estimation problem in broadband millimeter wave multi-input multi-output (MIMO) communication systems. Considering the channel sparsity in both the angular domain and the delay domain, we first perform a sparse representation of the cascaded MIMO channel. Then, we decompose the sparse recovery operation into several subproblems to reduce the computational complexity, and propose two algorithms in the frequency domain and the time domain, respectively, based on the compressed sensing technique. Simulation results verify the effectiveness of the two proposed algorithms.

Due to their ability to create favorable line-of-sight (LoS) propagation environments, intelligent reflecting surfaces (IRSs) are regarded as promising enablers for future millimeter-wave (mm-wave) wireless communication. In this paper, we investigate channel estimation for IRS-assisted mm-wave multiple-input multiple-output (MIMO) wireless systems. By leveraging the sparsity of mm-wave channels in the angular domain, we formulate the channel estimation problem as an$\ell _{1}$-norm regularized optimization problem with fixed-rank constraints. To tackle the non-convexity of the formulated problem, an efficient algorithm is proposed by capitalizing on alternating minimization and manifold optimization (MO), which yields a locally optimal solution. To further reduce the computational complexity of the estimation algorithm, we propose a compressive sensing- (CS-) based channel estimation approach. In particular, a three-stage estimation protocol is put forward where the subproblem in each stage can be solved via low-complexity CS methods. Furthermore, based on the acquired channel state information (CSI) of the cascaded channel, we design a passive beamforming algorithm for maximization of the spectral efficiency. Simulation results reveal that the proposed MO-based estimation (MO-EST) and beamforming algorithms significantly outperform two benchmark schemes while the CS-based estimation (CS-EST) algorithm strikes a balance between performance and complexity.

Direction-of-arrival (DOA) estimation is one of the most demanding tasks for the millimeter wave (mmWave) communication of massive multiple-input multiple-output (MIMO) systems with the hybrid beamforming (HBF) architecture. In this letter, we focus on the optimization of the HBF matrix for receiving pilots to enhance the DOA estimation performance. Motivated by the fact that many existing DOA estimation algorithms can achieve the Cramér-Rao bound (CRB), we formulate the HBF optimization problem aiming at minimizing the CRB with the prior knowledge of the rough DOA range. Then, to tackle the problem with intractable non-convex constraints introduced by the analog beamformers, we propose an efficient manifold optimization (MO) based algorithm. Simulation results demonstrate the significant improvement of the proposed CRB-MO algorithm over the conventional HBF algorithms and provide insights for the HBF design in the beam training stage for practical applications.

Hybrid beamforming (HBF) is an attractive technology for practical massive multiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems. Compared with the fully-connected HBF architecture, the partially-connected one can further reduce the hardware cost and power consumption. However, the special block diagonal structure of its analog beamforming matrix brings additional design challenges. In this paper, we develop effective HBF algorithms for spectral efficiency maximization (SEM) in wideband mmWave massive MIMO systems with the partially-connected architecture. One main contribution is that we prove the equivalence of the SEM problem and a weighted mean square error minimization (WMMSE) problem, which leads to a convenient algorithmic approach to directly tackle the SEM problem. Specifically, we decompose the equivalent WMMSE problem into the hybrid precoding and hybrid combining subproblems, for which both the optimal digital precoder and combiner have closed-form solutions. For the more challenging analog precoder and combiner, we propose an element iteration based algorithm and a manifold optimization based algorithm. Finally, the hybrid precoder and combiner are alternatively updated. The overall HBF algorithms are proved to monotonously increase the spectral efficiency and converge. Furthermore, we also propose modified algorithms with reduced computational complexity and finite-resolution phase shifters. Simulation results demonstrate that the proposed HBF algorithms achieve significant performance gains over conventional algorithms.

Intelligent reflecting surfaces (IRSs) are regarded as promising enablers for future millimeter wave (mmWave) wireless communication, due to their ability to create favorable line-of-sight (LoS) propagation environments. In this paper, we investigate channel estimation in downlink IRS-assisted mmWave multiple-input multiple-output (MIMO) systems. By leveraging the sparsity of mmWave channels, we formulate the channel estimation problem as a fixed-rank constrained non-convex optimization problem. To tackle the non-convexity, an efficient algorithm is proposed by capitalizing on alternating minimization and manifold optimization (MO), which yields a locally optimal solution. Simulation results show that the proposed MObased estimation (MO-EST) algorithm significantly outperforms two benchmark schemes and demonstrate the robustness of the MO-EST algorithm with respect to imperfect knowledge of the sparsity level of the channels in practical implementations.

Hybrid analog and digital beamforming (HBF) has recently emerged as an attractive technique for millimeter-wave (mmWave) communication systems. It well balances the demand for sufficient beamforming gains to overcome the propagation loss and the desire to reduce the hardware cost and power consumption. In this paper, the mean square error (MSE) is chosen as the performance metric to characterize the transmission reliability. Using the minimum sum-MSE criterion, we investigate the HBF design for broadband mmWave transmissions. To overcome the difficulty of solving the multi-variable design problem, the alternating minimization method is adopted to optimize the hybrid transmit and receive beamformers alternatively. Specifically, a manifold optimization-based HBF algorithm is first proposed, which directly handles the constant modulus constraint of the analog component. Its convergence is then proved. To reduce the computational complexity, we then propose a low-complexity general eigenvalue decomposition-based HBF algorithm in the narrowband scenario and three algorithms via the eigenvalue decomposition and orthogonal matching pursuit methods in the broadband scenario. A particular innovation in our proposed alternating minimization algorithms is a carefully designed initialization method, which leads to a faster convergence. Furthermore, we extend the sum-MSE-based design to that with weighted sum-MSE, which is then connected to the spectral efficiency-based design. Simulation results show that the proposed HBF algorithms achieve a significant performance improvement over existing ones and perform close to full-digital beamforming.