Multi-User MISO with Stacked Intelligent Metasurfaces: A DRL-Based Sum-Rate Optimization Approach

Stacked intelligent metasurfaces (SIMs) represent a novel signal processing paradigm that enables over-the-air processing of electromagnetic waves at the speed of light. Their multi-layer architecture exhibits customizable computational capabilities compared to conventional single-layer reconfigurable intelligent surfaces and metasurface lenses. In this paper, we deploy SIM to improve the performance of multi-user multiple-input single-output (MISO) wireless systems through a low complexity manner with reduced numbers of transmit radio frequency chains. In particular, an optimization formulation for the joint design of the SIM phase shifts and the transmit power allocation is presented, which is efficiently tackled via a customized deep reinforcement learning (DRL) approach that systematically explores pre-designed states of the SIM-parametrized smart wireless environment. The presented performance evaluation results demonstrate the proposed method's capability to effectively learn from the wireless environment, while consistently outperforming conventional precoding schemes under low transmit power conditions. Furthermore, the implementation of hyperparameter tuning and whitening process significantly enhance the robustness of the proposed DRL framework.

Flexible Antenna Arrays for Wireless Communications: Modeling and Performance Evaluation

Flexible antenna arrays (FAAs), distinguished by their rotatable, bendable, and foldable properties, are extensively employed in flexible radio systems to achieve customized radiation patterns. This paper aims to illustrate that FAAs, capable of dynamically adjusting surface shapes, can enhance communication performances with both omni-directional and directional antenna patterns, in terms of multi-path channel power and channel angle Cram\'{e}r-Rao bounds. To this end, we develop a mathematical model that elucidates the impacts of the variations in antenna positions and orientations as the array transitions from a flat to a rotated, bent, and folded state, all contingent on the flexible degree-of-freedom. Moreover, since the array shape adjustment operates across the entire beamspace, especially with directional patterns, we discuss the sum-rate in the multi-sector base station that covers the $360^\circ$ communication area. Particularly, to thoroughly explore the multi-sector sum-rate, we propose separate flexible precoding (SFP), joint flexible precoding (JFP), and semi-joint flexible precoding (SJFP), respectively. In our numerical analysis comparing the optimized FAA to the fixed uniform planar array, we find that the bendable FAA achieves a remarkable $156\%$ sum-rate improvement compared to the fixed planar array in the case of JFP with the directional pattern. Furthermore, the rotatable FAA exhibits notably superior performance in SFP and SJFP cases with omni-directional patterns, with respective $35\%$ and $281\%$.

Stacked Intelligent Metasurfaces for Wireless Sensing and Communication: Applications and Challenges

The rapid advancement of wireless communication technologies has precipitated an unprecedented demand for high data rates, extremely low latency, and ubiquitous connectivity. In order to achieve these goals, stacked intelligent metasurfaces (SIM) has been developed as a novel solution to perform advanced signal processing tasks directly in the electromagnetic wave domain, thus achieving ultra-fast computing speed and reducing hardware complexity. This article provides an overview of the SIM technology by discussing its hardware architectures, advantages, and potential applications for wireless sensing and communication. Specifically, we explore the utilization of SIMs in enabling wave-domain beamforming, channel modeling and estimation in SIM-assisted communication systems. Furthermore, we elaborate on the potential of utilizing a SIM to build a hybrid optical-electronic neural network (HOENN) and demonstrate its efficacy by examining two case studies: disaster monitoring and direction-of-arrival estimation. Finally, we identify key implementation challenges, including practical hardware imperfections, efficient SIM configuration for realizing wave-domain signal processing, and performance analysis to motivate future research on this important and far-reaching topic.

Environment-Aware Codebook Design for RIS-Assisted MU-MISO Communications: Implementation and Performance Analysis

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can proactively reshape the characteristics of wireless channel environments. In RIS-assisted communication systems, the acquisition of channel state information (CSI) and the optimization of reflecting coefficients constitute major design challenges. To address these issues, codebook-based solutions have been developed recently, which, however, are mostly environment-agnostic. In this paper, a novel environment-aware codebook protocol is proposed, which can significantly reduce both pilot overhead and computational complexity, while maintaining expected communication performance. Specifically, first of all, a channel training framework is introduced to divide the training phase into several blocks. In each block, we directly estimate the composite end-to-end channel and focus only on the transmit beamforming. Second, we propose an environment-aware codebook generation scheme, which first generates a group of channels based on statistical CSI, and then obtains their corresponding RIS configuration by utilizing the alternating optimization (AO) method offline. In each online training block, the RIS is configured based on the corresponding codeword in the environment-aware codebook, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Third, we analyze the theoretical performance of the environment-aware codebook-based protocol taking into account the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme. In particular, the simulation results demonstrate that our protocol is more competitive than conventional environment-agnostic codebooks.

Environment-Aware Codebook for RIS-Assisted MU-MISO Communications: Implementation and Performance Analysis

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can reshape the characteristics of wireless channels. In this paper, we propose a novel environment-aware codebook protocol for RIS-assisted multi-user multiple-input single-output (MU-MISO) systems. Specifically, we first introduce a channel training protocol which consists of off-line and on-line stages. Secondly, we propose an environment-aware codebook generation scheme, which utilizes the statistical channel state information and alternating optimization method to generate codewords offline. Then, in the on-line stage, we use these pre-designed codewords to configure the RIS, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Thirdly, we analyze the theoretical performance of the proposed protocol considering the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme.

Channel Estimation for Stacked Intelligent Metasurface-Assisted Wireless Networks

Emerging technologies, such as holographic multiple-input multiple-output (HMIMO) and stacked intelligent metasurface (SIM), are driving the development of wireless communication systems. Specifically, the SIM is physically constructed by stacking multiple layers of metasurfaces and has an architecture similar to an artificial neural network (ANN), which can flexibly manipulate the electromagnetic waves that propagate through it at the speed of light. This architecture enables the SIM to achieve HMIMO precoding and combining in the wave domain, thus significantly reducing the hardware cost and energy consumption. In this letter, we investigate the channel estimation problem in SIM-assisted multi-user HMIMO communication systems. Since the number of antennas at the base station (BS) is much smaller than the number of meta-atoms per layer of the SIM, it is challenging to acquire the channel state information (CSI) in SIM-assisted multi-user systems. To address this issue, we collect multiple copies of the uplink pilot signals that propagate through the SIM. Furthermore, we leverage the array geometry to identify the subspace that spans arbitrary spatial correlation matrices. Based on partial CSI about the channel statistics, a pair of subspace-based channel estimators are proposed. Additionally, we compute the mean square error (MSE) of the proposed channel estimators and optimize the phase shifts of the SIM to minimize the MSE. Numerical results are illustrated to analyze the effectiveness of the proposed channel estimation schemes.

Stacked Intelligent Metasurface Enabled LEO Satellite Communications Relying on Statistical CSI

Low earth orbit (LEO) satellite communication systems have gained increasing attention as a crucial supplement to terrestrial wireless networks due to their extensive coverage area. This letter presents a novel system design for LEO satellite systems by leveraging stacked intelligent metasurface (SIM) technology. Specifically, the lightweight and energy-efficient SIM is mounted on a satellite to achieve multiuser beamforming directly in the electromagnetic wave domain, which substantially reduces the processing delay and computational load of the satellite compared to the traditional digital beamforming scheme. To overcome the challenges of obtaining instantaneous channel state information (CSI) at the transmitter and maximize the system's performance, a joint power allocation and SIM phase shift optimization problem for maximizing the ergodic sum rate is formulated based on statistical CSI, and an alternating optimization (AO) algorithm is customized to solve it efficiently. Additionally, a user grouping method based on channel correlation and an antenna selection algorithm are proposed to further improve the system performance. Simulation results demonstrate the effectiveness of the proposed SIM-based LEO satellite system design and statistical CSI-based AO algorithm.

DRL-Based Orchestration of Multi-User MISO Systems with Stacked Intelligent Metasurfaces

Stacked intelligent metasurfaces (SIM) represents an advanced signal processing paradigm that enables over-the-air processing of electromagnetic waves at the speed of light. Its multi-layer structure exhibits customizable increased computational capability compared to conventional single-layer reconfigurable intelligent surfaces and metasurface lenses. In this paper, we deploy SIM to improve the performance of multi-user multiple-input single-output (MISO) wireless systems with low complexity transmit radio frequency (RF) chains. In particular, an optimization formulation for the joint design of the SIM phase shifts and the transmit power allocation is presented, which is efficiently solved via a customized deep reinforcement learning (DRL) approach that continuously observes pre-designed states of the SIM-parametrized smart wireless environment. The presented performance evaluation results showcase the proposed method's capability to effectively learn from the wireless environment while outperforming conventional precoding schemes under low transmit power conditions. Finally, a whitening process is presented to further augment the robustness of the proposed scheme.

Two-Dimensional Direction-of-Arrival Estimation Using Stacked Intelligent Metasurfaces

Stacked intelligent metasurfaces (SIM) are capable of emulating reconfigurable physical neural networks by relying on electromagnetic (EM) waves as carriers. They can also perform various complex computational and signal processing tasks. A SIM is fabricated by densely integrating multiple metasurface layers, each consisting of a large number of small meta-atoms that can control the EM waves passing through it. In this paper, we harness a SIM for two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to the conventional designs, an advanced SIM in front of the receiver array automatically carries out the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. As a result, the receiver array directly observes the angular spectrum of the incoming signal. In this context, the DOA estimates can be readily obtained by using probes to detect the energy distribution on the receiver array. This avoids the need for power-thirsty radio frequency (RF) chains. To enable SIM to perform the 2D DFT, we formulate the optimization problem of minimizing the fitting error between the SIM's EM response and the 2D DFT matrix. Furthermore, a gradient descent algorithm is customized for iteratively updating the phase shift of each meta-atom in SIM. To further improve the DOA estimation accuracy, we configure the phase shift pattern in the zeroth layer of the SIM to generate a set of 2D DFT matrices associated with orthogonal spatial frequency bins. Additionally, we analytically evaluate the performance of the proposed SIM-based DOA estimator by deriving a tight upper bound for the mean square error (MSE). Our numerical simulations verify the capability of a well-trained SIM to perform DOA estimation and corroborate our theoretical analysis. It is demonstrated that a SIM having an optical computational speed achieves an MSE of $10^{-4}$ for DOA estimation.

Stacked Intelligent Metasurface-Aided MIMO Transceiver Design

Next-generation wireless networks are expected to utilize the limited radio frequency (RF) resources more efficiently with the aid of intelligent transceivers. To this end, we propose a promising transceiver architecture relying on stacked intelligent metasurfaces (SIM). An SIM is constructed by stacking an array of programmable metasurface layers, where each layer consists of a massive number of low-cost passive meta-atoms that individually manipulate the electromagnetic (EM) waves. By appropriately configuring the passive meta-atoms, an SIM is capable of accomplishing advanced computation and signal processing tasks, such as multiple-input multiple-output (MIMO) precoding/combining, multi-user interference mitigation, and radar sensing, as the EM wave propagates through the multiple layers of the metasurface, which effectively reduces both the RF-related energy consumption and processing delay. Inspired by this, we provide an overview of the SIM-aided MIMO transceiver design, which encompasses its hardware architecture and its potential benefits over state-of-the-art solutions. Furthermore, we discuss promising application scenarios and identify the open research challenges associated with the design of advanced SIM architectures for next-generation wireless networks. Finally, numerical results are provided for quantifying the benefits of wave-based signal processing in wireless systems.