MMSE Channel Estimation in Large-Scale MIMO: Improved Robustness with Reduced Complexity

Large-scale MIMO systems with a massive number N of individually controlled antennas pose significant challenges for minimum mean square error (MMSE) channel estimation, based on uplink pilots. The major ones arise from the computational complexity, which scales with $N^3$, and from the need for accurate knowledge of the channel statistics. This paper aims to address both challenges by introducing reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated. This is achieved by exploiting the inherent structure of the spatial correlation matrix induced by the array geometry. Specifically, we use a Kronecker decomposition for uniform planar arrays and a well-suited circulant approximation for uniform linear arrays. By doing so, a significantly lower computational complexity is achieved, scaling as $N\sqrt{N}$ and $N\log N$ for squared planar arrays and linear arrays, respectively.

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.

MMSE Design of RIS-aided Communications

Consider a communication system in which a single antenna user equipment exchanges information with a multi-antenna base station via a reconfigurable intelligent surface (RIS) in the presence of spatially correlated channels and electromagnetic interference (EMI). To exploit the attractive advantages of RIS technology, accurate configuration of its reflecting elements is crucial. In this paper, we use statistical knowledge of channels and EMI to optimize the RIS elements for i) accurate channel estimation and ii) reliable data transmission. In both cases, our goal is to determine the RIS coefficients that minimize the mean square error, resulting in the formulation of two non-convex problems that share the same structure. To solve these two problems, we present an alternating optimization approach that reliably converges to a locally optimal solution. The incorporation of the diagonally scaled steepest descent algorithm, derived from Newton's method, ensures fast convergence with manageable complexity. Numerical results demonstrate the effectiveness of the proposed method under various propagation conditions. Notably, it shows significant advantages over existing alternatives that depend on a sub-optimal configuration of the RIS and are derived on the basis of different criteria.

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.

Holographic MIMO Communications: What is the benefit of closely spaced antennas?

Holographic MIMO refers to an array (possibly large) with a massive number of antennas that are individually controlled and densely deployed. The aim of this paper is to provide further insights into the advantages (if any) of having closely spaced antennas in the uplink and downlink of a multi-user Holographic MIMO system. To this end, we make use of the multiport communication theory, which ensures physically consistent uplink and downlink models. We first consider a simple uplink scenario with two side-by-side half-wavelength dipoles, two users and single path line-of-sight propagation, and show both analytically and numerically that the channel gain and average spectral efficiency depend strongly on the directions from which the signals are received and on the array matching network used. Numerical results are then used to extend the analysis to more practical scenarios with a larger number of dipoles and users. The case in which the antennas are densely packed in a space-constrained factor form is also considered. It turns out that the spectral efficiency increases as the antenna distance reduces thanks to the larger number of antennas that allow to collect more energy, not because of the mutual coupling.

DFT-Based Channel Estimation for Holographic MIMO

Holographic MIMO (hMIMO) systems with a massive number of individually controlled antennas N make minimum mean square error (MMSE) channel estimation particularly challenging, due to its computational complexity that scales as $N^3$ . This paper investigates uniform linear arrays and proposes a low-complexity method based on the discrete Fourier transform (DFT) approximation, which follows from replacing the covariance matrix by a suitable circulant matrix. Numerical results show that, already for arrays with moderate size (in the order of tens of wavelengths), it achieves the same performance of the optimal MMSE, but with a significant lower computational load that scales as $N \log N$. Interestingly, the proposed method provides also increased robustness in case of imperfect knowledge of the covariance matrix.

Impact of Phase Noise on Uplink Cell-Free Massive MIMO OFDM

Cell-Free massive MIMO networks provide huge power gains and resolve inter-cell interference by coherent processing over a massive number of distributed instead of co-located antennas in access points (APs). Cost-efficient hardware is preferred but imperfect local oscillators in both APs and users introduce multiplicative phase noise (PN), which affects the phase coherence between APs and users even with centralized processing. In this paper, we first formulate the system model of a PN-impaired uplink Cell-Free massive MIMO orthogonal frequency division multiplexing network, and then propose a PN-aware linear minimum mean square error channel estimator and derive a PN-impaired uplink spectral efficiency expression. Numerical results are used to quantify the spectral efficiency gain of the proposed channel estimator over alternative schemes for different receiving combiners.

Spherical Wavefronts Improve MU-MIMO Spectral Efficiency When Using Electrically Large Arrays

Modern MIMO communication systems are almost exclusively designed under the assumption of locally plane wavefronts over antenna arrays. This is known as the far-field approximation and is soundly justified at sub-6-GHz frequencies at most relevant transmission ranges. However, when higher frequencies and shorter transmission ranges are used, the wave curvature over the array is no longer negligible, and arrays operate in the so-called radiative near-field region. This letter aims to show that the classical far-field approximation may significantly underestimate the achievable spectral efficiency of multi-user MIMO communications operating in the 30-GHz bands and above, even at ranges beyond the Fraunhofer distance. For planar arrays with typical sizes, we show that computing combining schemes based on the far-field model significantly reduces the channel gain and spatial multiplexing capability. When the radiative near-field model is used, interference rejection schemes, such as the optimal minimum mean-square-error combiner, appear to be very promising, when combined with electrically large arrays, to meet the stringent requirements of next-generation networks.

Cell-Free Massive MIMO for URLLC: A Finite-Blocklength Analysis

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low lantecy (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combing and precoding schemes. The framework is used to perform numerical experiments that clearly show the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, they provide the following novel insights into the optimal design of cell-free architectures for URLLC: i) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; ii) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; iii) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

Cooperative Hybrid Networks with Active Relays and RISs for B5G: Applications, Challenges, and Research Directions

Among the recent advances and innovations in wireless technologies, reconfigurable intelligent surfaces (RISs) have received much attention and are envisioned to be one of the enabling technologies for beyond 5G (B5G) networks. On the other hand, active (or classical) cooperative relays have played a key role in providing reliable and power-efficient communications in previous wireless generations. In this article, we focus on hybrid network architectures that amalgamate both active relays and RISs. The operation concept and protocols of each technology are first discussed. Subsequently, we present multiple use cases of cooperative hybrid networks where both active relays and RISs can coexist harmoniously for enhanced rate performance. Furthermore, a case study is provided which demonstrates the achievable rate performance of a communication network assisted by either an active relay, an RIS, or both, and with different relaying protocols. Finally, we provide the reader with the challenges and key research directions in this area.