Wideband Channel Capacity Maximization With Beyond Diagonal RIS Reflection Matrices

Following the promising beamforming gains offered by reconfigurable intelligent surfaces (RISs), a new hardware architecture, known as \emph{beyond diagonal RIS (BD-RIS)}, has recently been proposed. This architecture enables controllable signal flows between the RIS elements, thereby providing greater design flexibility. However, the physics-imposed symmetry and orthogonality conditions on the non-diagonal reflection matrix make the design challenging. In this letter, we analyze how a BD-RIS can improve a wideband channel, starting from fundamental principles and deriving the capacity. Our analysis considers the effects of various channel taps and their frequency-domain characteristics. We introduce a new algorithm designed to optimize the configuration of the BD-RIS to maximize wideband capacity. The proposed algorithm has better performance than the benchmarks. A BD-RIS is beneficial compared to a conventional RIS in the absence of static path or when the Rician $\kappa$-factor is smaller than $10$.

Localization in Massive MIMO Networks: From Near-Field to Far-Field

Source localization is the process of estimating the location of signal sources based on the signals received at different antennas of an antenna array. It has diverse applications, ranging from radar systems and underwater acoustics to wireless communication networks. Subspace-based approaches are among the most effective techniques for source localization due to their high accuracy, with Multiple SIgnal Classification (MUSIC) and Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT) being two prominent methods in this category. These techniques leverage the fact that the space spanned by the eigenvectors of the covariance matrix of the received signals can be divided into signal and noise subspaces, which are mutually orthogonal. Originally designed for far-field source localization, these methods have undergone several modifications to accommodate near-field scenarios as well. This chapter aims to present the foundations of MUSIC and ESPRIT algorithms and introduce some of their variations for both far-field and near-field localization by a single array of antennas. We further provide numerical examples to demonstrate the performance of the presented methods.

Pilot Length Optimization with RS-LS Channel Estimation for Extremely Large Aperture Arrays

Extremely large aperture arrays can enable unprecedented spatial multiplexing in beyond 5G systems due to their extremely narrow beamfocusing capabilities. However, acquiring the spatial correlation matrix to enable efficient channel estimation is a complex task due to the vast number of antenna dimensions. Recently, a new estimation method called the "reduced-subspace least squares (RS-LS) estimator" has been proposed for densely packed arrays. This method relies solely on the geometry of the array to limit the estimation resources. In this paper, we address a gap in the existing literature by deriving the average spectral efficiency for a certain distribution of user equipments (UEs) and a lower bound on it when using the RS-LS estimator. This bound is determined by the channel gain and the statistics of the normalized spatial correlation matrices of potential UEs but, importantly, does not require knowledge of a specific UE's spatial correlation matrix. We establish that there exists a pilot length that maximizes this expression. Additionally, we derive an approximate expression for the optimal pilot length under low signal-to-noise ratio (SNR) conditions. Simulation results validate the tightness of the derived lower bound and the effectiveness of using the optimized pilot length.

Mixed Static and Reconfigurable Metasurface Deployment in Indoor Dense Spaces: How Much Reconfigurability is Needed?

In this paper, we investigate how metasurfaces can be deployed to deliver high data rates in a millimeter-wave (mmWave) indoor dense space with many blocking objects. These surfaces can either be static metasurfaces (SMSs) that reflect with fixed phase-shifts or reconfigurable intelligent surfaces (RISs) that can reconfigure their phase-shifts to the currently served user. The latter comes with an increased power, cabling, and signaling cost. To see how reconfigurability affects the network performance, we propose an iterative algorithm based on the feasible point pursuit successive convex approximation method. We jointly optimize the types and phase-shifts of the surfaces and the time portion allocated to each user equipment to maximize the minimum data rate achieved by the network. Our numerical results demonstrate that the minimum data rate improves as more RISs are introduced but the gain diminishes after some point. Therefore, introducing more reconfigurability is not always necessary. Another result shows that to reach the same data rate achieved by using 22 SMSs, at least 18 RISs are needed. This suggests that when it is costly to deploy many RISs, as an inexpensive alternative solution, one can reach the same data rate just by densely deploying more SMSs.

Parametric Near-Field Channel Estimation for Extremely Large Aperture Arrays

Accurate channel estimation is critical to fully exploit the beamforming gains when communicating with extremely large aperture arrays. The propagation distances between the user and receiver, which potentially has thousands of antennas/elements, are such that they are located in the radiative near-field region of each other when considering the Fraunhofer distance of the entire array. Therefore, it is imperative to consider near-field effects to achieve proper channel estimation. This paper proposes a parametric multi-user near-field channel estimation algorithm based on MUltiple SIgnal Classification (MUSIC) method to obtain the essential parameters describing the users' locations. We derive the estimated channel by incorporating the estimated parameters into the near-field channel model. Additionally, we implement a least-squares-based estimation corrector, resulting in a precise near-field channel estimation. Simulation results demonstrate that our proposed scheme outperforms classical least-squares and minimum mean-square error channel estimation methods in terms of normalized beamforming gain and normalized mean-square error.

Nonlinear Distortion Radiated from Large Arrays and Active Reconfigurable Intelligent Surfaces

Extremely large aperture arrays (ELAAs) and reconfigurable intelligent surfaces (RISs) are candidate enablers to realize connectivity goals for the sixth-generation (6G) wireless networks. For instance, ELAAs can provide orders-of-magnitude higher area throughput compared to what massive multiple-input multiple-output (MIMO) can deliver through spatial multiplexing, while RISs can improve the propagation conditions over wireless channels but a passively reflecting RIS must be large to be effective. Active RIS with amplifiers can deal with this issue. In this paper, we study the distortion created by nonlinear amplifiers in both ELAAs and active RIS. We analytically obtain the angular directions and depth of the nonlinear distortion in both near- and far-field channels. The results are demonstrated numerically and we conclude that non-linearities can both create in-band and out-of-band distortion that is beamformed in entirely new directions and distances from the transmitter.

Towards 6G MIMO: Massive Spatial Multiplexing, Dense Arrays, and Interplay Between Electromagnetics and Processing

The increasing demand for wireless data transfer has been the driving force behind the widespread adoption of Massive MIMO (multiple-input multiple-output) technology in 5G. The next-generation MIMO technology is now being developed to cater to the new data traffic and performance expectations generated by new user devices and services in the next decade. The evolution towards "ultra-massive MIMO (UM-MIMO)" is not only about adding more antennas but will also uncover new propagation and hardware phenomena that can only be treated by jointly utilizing insights from the communication, electromagnetic (EM), and circuit theory areas. This article offers a comprehensive overview of the key benefits of the UM-MIMO technology and the associated challenges. It explores massive multiplexing facilitated by radiative near-field effects, characterizes the spatial degrees-of-freedom, and practical channel estimation schemes tailored for massive arrays. Moreover, we provide a tutorial on EM theory and circuit theory, and how it is used to obtain physically consistent antenna and channel models. Subsequently, the article describes different ways to implement massive and dense antenna arrays, and how to co-design antennas with signal processing. The main open research challenges are identified at the end.

A Novel Discrete Phase Shift Design for RIS-Assisted Multi-User MIMO

Reconfigurable intelligent surface (RIS) is a newly-emerged technology that might fundamentally change how wireless networks are operated. Though extensively studied in recent years, the practical limitations of RIS are often neglected when assessing the performance of RIS-assisted communication networks. One of these limitations is that each RIS element is restricted to incur a controllable phase shift to the reflected signal from a predefined discrete set. This paper studies an RIS-assisted multi-user multiple-input multiple-output (MIMO) system, where an RIS with discrete phase shifts assists in simultaneous uplink data transmission from multiple user equipments (UEs) to a base station (BS). We aim to maximize the sum rate by optimizing the receive beamforming vectors and RIS phase shift configuration. To this end, we transform the original sum-rate maximization problem into a minimum mean square error (MMSE) minimization problem and employ the block coordinate descent (BCD) technique for iterative optimization of the variables until convergence. We formulate the discrete RIS phase shift optimization problem as a mixed-integer least squares problem and propose a novel method based on sphere decoding (SD) to solve it. Through numerical evaluation, we show that the proposed discrete phase shift design outperforms the conventional nearest point mapping method, which is prevalently used in previous works.

Optimal Dual-Polarized Planar Arrays for Massive Capacity Over Point-to-Point MIMO Channels

Future wireless networks must provide ever higher data rates. The available bandwidth increases roughly linearly as we increase the carrier frequency, but the range shrinks drastically. This paper explores if we can instead reach massive capacities using spatial multiplexing over multiple-input multiple-output (MIMO) channels. In line-of-sight (LOS) scenarios, therank of the MIMO channel matrix depends on the polarization and antenna arrangement. We optimize the rank and condition number by identifying the optimal antenna spacing in dual-polarized planar antenna arrays with imperfect isolation. The result is sparely spaced antenna arrays that exploit radiative near-field properties. We further optimize the array geometry for minimum aperture length and aperture area, which leads to different configurations. Moreover, we prove analytically that for fixed-sized arrays, the MIMO rank grows quadratically with the carrier frequency in LOS scenarios, if the antennas are appropriately designed. Hence, MIMO technology contributes more to the capacity growth than the bandwidth. The numerical results show that massive data rates, far beyond 1 Tbps, can be reached both over fixed point-to-point links. It is also possible for a large base station to serve a practically-sized mobile device.

Broad Beam Reflection for RIS-Assisted MIMO Systems with Planar Arrays

While reconfigurable intelligent surface (RIS)-aided user-specific beamforming has been vastly investigated, the aspect of utilizing RISs for assisting cell-specific transmission has been largely unattended. Aiming to fill this gap, we study a downlink broadcasting scenario where a base station (BS) sends a cell-specific signal to all the users located in a wide angular area with the assistance of a dual-polarized RIS. We utilize the polarization degree of freedom offered by this type of RIS and design the phase configurations in the two polarizations in such a way that the RIS can radiate a broad beam, thereby uniformly covering all azimuth and elevation angles where the users might reside. Specifically, the per-polarization configuration matrices are designed in such a way that the total power-domain array factor becomes spatially flat over all observation angles implying that the RIS can preserve the broad radiation pattern of a single element while boosting its gain proportionally to its aperture size. We validate the mathematical analyses via numerical simulations.