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Line-of-Sight MIMO via Intelligent Reflecting Surface
Abstract
This paper deals with line-of-sight (LOS) MIMO communication via an intelligent reflecting surface (IRS). It is shown that the number of spatial degrees of freedom (DOF) afforded by this setting grows in proportion with the IRS aperture, as opposed to being dictated by the transmit and receive apertures; this buttresses the interest in IRS deployments at mmWave and terahertz frequencies, with wavelengths and transmission ranges small enough to enable LOS MIMO. Explicit and simple-to-implement IRS phase shifts are put forth that achieve, not only the maximum number of DOF, but the capacity, under a certain geometrical condition. The insights leading to the proposed phase shifts, and to the optimality condition itself, are asymptotic in nature, yet extensive simulations confirm that the performance is excellent for a broad range of settings and even if the optimality condition is not strictly met.
... Figure 5 illustrates the relationship between the position of the receiving array L p and its maximum K number when L s = 100λ, L p = 100λ, and λ = 0.01 m, where the center position of L p is described by (R, θ). "AK" represents the maximum value of the K number calculated using (17). "EK" denotes the K number calculated using numerical methods and then maximized by traversing all possible receiving directionsv. ...
... When θ = 0, i.e., when the transmitting and receiving arrays are directly facing each other, the maximum K number reaches its peak. Additionally, it is observed that the maximum K number calculated via (17) closely matches the maximum K number obtained numerically, particularly when R > 300λ. This validates the accuracy of the approximate expression for the K number provided by (16) and (17). ...
... Let the MIMO channel be represented by H ∈ C Nr×Nt . Considering the near-field spherical wavefront effect [5], [17], the complex gain between the n r -th receiving antenna and the n t -th transmitting antenna can be modeled as ...
This paper analyzes the spatial bandwidth of line-of-sight (LoS) channels in massive MIMO systems. For the linear large-scale antenna arrays (LSAA) of transceivers placed in random locations in 3D space, a simple but accurate closed-form expression is derived to characterize the spatial bandwidth. Subsequent analysis of the LSAA's spatial bandwidth properties is also provided, leading to the formulation of an approximate expression for the effective degrees of freedom (EDoF) of bilateral near-field channels. Interestingly, as proved in this work, when the transmit and receive arrays are coplanar, with the receive array positioned perpendicular to the axis joining the centroids of the transmit and receive arrays, the EDoF of the LoS channel is found to be approximately maximized.
... Recently, due to its low circuit cost and power consumption, intelligent reflecting surface (IRS) is becoming an extremely hot research topic and a very promising technique for future wireless networks like B5G and 6G [1]. It has the following several major advantages: extend coverage [2], improve rate [3], enhance security [4], and increase spatial degrees of freedom (DOF) [5], [6]. To achieve the above goals, IRS can be diversely combined with directional modulation networks [5], MIMO [7], and relay networks [8]. ...
... where φ h represents the phase of the direction channel complex gain h from BS to user. According to (6) and (20), the iterations of λ k and p are performed to reach convergence. ...
... (25) Plugging the solution p k to (25) in (6) gives the value of λ k at iteration k. Then, an alternate iteration between λ k and p k are performed until the terminal condition λ ...
Compared to passive intelligent reflecting surface (IRS), active IRS is viewed as a more efficient promising technique to combat the double-fading impact in IRS-aided wireless network. In this paper, in order to boost the achievable rate of user in such a wireless network, three enhanced-rate iterative beamforming methods are proposed by designing the amplifying factors and the corresponding phases at active IRS. The first method, called generalized maximum ratio reflection (GMRR), is presented with a closed-form expression, which is motivated by the maximum ratio combing. To further improve rate, maximize the simplified signal-to-noise ratio (Max-SSNR) is designed by omitting the cross-term in the definition of rate. Using the Rayleigh-Ritz (RR) theorem and the fractional programming (FP), two enhanced methods, Max-SSNR-RR and Max-SSNR-FP are proposed to iteratively optimize the norm of beamforming vector and its associated normalized vector. Simulation results indicate that the proposed three methods make an obvious rate enhancement over Max-reflecting signal-to-noise ratio (RSNR) and passive IRS, and are in increasing order of rate performance as follows: GMRR, Max-SSNR-RR, and Max-SSNR-FP.
... In this endeavor, it is anticipated to encompass the possibility of not only utilizing larger array apertures but also arrays with densely spaced antenna elements. This approach will be implemented over the millimeter-wave (mmWave) spectrum and even terahertz frequencies, offering more flexibility in manipulating the wireless environment [1]. ...
... Indeed, different representations of the far-field and near-field channels come from different approximations of the channel response. Specifically, these include the Fraunhofer approximation in the far-field [1], the Fresnel approximation in the near-field [5,8], and the Fourier plane-wave series approximation [4,5]. The Fourier plane-wave series approximation is determined by the plane waves characterized by different wavenumbers, exhibiting beneficial distance-independent properties. ...
This article conceives a unified representation for near-field and far-field holographic multiple-input multiple-output (HMIMO) channels, addressing a practical design dilemma: “Why does the angular-domain representation no longer function effectively?” To answer this question, we pivot from the angular domain to the wavenumber domain and present a succinct overview of its underlying philosophy. In re-examining the Fourier plane-wave series expansion that recasts spherical propagation waves into a series of plane waves represented by Fourier harmonics, we characterize the HMIMO channel employing these Fourier harmonics having different wavenumbers. This approach, referred to as the wavenumebr-domain representation, facilitates a unified view across the far-field and the near-field. Furthermore, the limitations of the DFT basis are demonstrated when identifying the sparsity inherent to the HMIMO channel, motivating the development of a wave-number-domain basis as an alternative. We then present some preliminary applications of the proposed wavenumber-domain basis in signal processing across both the far-field and near-field, along with several prospects for future HMIMO system designs based on the wavenumber domain.
... In this endeavor, it is anticipated to encompass the possibility of not only utilizing larger array apertures but also arrays with densely spaced antenna elements. This approach will be implemented over the millimeter-wave (mmWave) spectrum and even terahertz frequencies, offering more flexibility in manipulating the wireless environment [1]. ...
... Indeed, different representations of the far-field and near-field channels come from different approximations of the channel response. Specifically, these include the Fraunhofer approximation in the far-field [1], the Fresnel approximation in the nearfield [5], [8], and the Fourier plane-wave series approximation [4], [5]. The Fourier plane-wave series approximation is determined by the plane waves characterized by different wavenumbers, exhibiting beneficial distance-independent properties. ...
This article conceives a unified representation for near-field and far-field holographic multiple-input multiple-output (HMIMO) channels, addressing a practical design dilemma: "Why does the angular-domain representation no longer function effectively?" To answer this question, we pivot from the angular domain to the wavenumber domain and present a succinct overview of its underlying philosophy. In re-examining the Fourier plane-wave series expansion that recasts spherical propagation waves into a series of plane waves represented by Fourier harmonics, we characterize the HMIMO channel employing these Fourier harmonics having different wavenumbers. This approach, referred to as the wavenumebr-domain representation, facilitates a unified view across the far-field and the near-field. Furthermore, the limitations of the DFT basis are demonstrated when identifying the sparsity inherent to the HMIMO channel, motivating the development of a wavenumber-domain basis as an alternative. We then present some preliminary applications of the proposed wavenumber-domain basis in signal processing across both the far-field and near-field, along with several prospects for future HMIMO system designs based on the wavenumber domain.
... Furthermore, we can approximate the distance between the transmit and receive antennas using the first-order Taylor approximation as d m,k ≈ d + δm,k 2d , where δ m,k = (m − k) 2 ∆ 2 . Based on this Fresnel approximation, the MIMO channel matrix in (30) can be rewritten as ...
... Such a scenario Transmitter Receiver θ Extremely large aperture RIS is illustrated in Fig. 14, where the direct path between the transmitter and receiver is blocked but signals can be reflected off the RIS. If both the transmitter and receiver are in the radiative near-field, the RIS can create a high-rank channel between the transmitter and receiver [30]. The theory described earlier in this paper can be utilized to compute the 3 dB BW and BD of the beam produced by the RIS [10]. ...
In this article, we present our vision for how extremely large aperture arrays (ELAAs), equipped with hundreds or thousands of antennas, can play a major role in future 6G networks by enabling a remarkable increase in data rates through massive spatial multiplexing to both a single user and many simultaneous users. Specifically, with the quantum leap in the array aperture size, the users will be in the so-called radiative near-field region of the array, where previously negligible physical phenomena dominate the propagation conditions and give the channel matrices more favorable properties. This article presents the foundational properties of communication in the radiative near-field region and then exemplifies how these properties enable two unprecedented spatial multiplexing schemes: depth-domain multiplexing of multiple users and angular multiplexing of data streams to a single user. We also highlight research challenges and open problems that require further investigation.
... For a fixed aperture, a trade-off arises between array gain, increasing with antenna densification, and antenna selectivity, requiring larger structures as dictated by the uncertainty principle. • As the number of antennas grows with the electrical aperture, a plural multiplicity of λ max (HH H ) arises due to the eigenvalue polarization [37], [39], [40]. Then, low-SNR optimality entails multiple equal-power transmissions on each of those maximal-eigenvalue eigenvectors. ...
This paper presents a comprehensive framework for holographic multiantenna communication, a paradigm that integrates both wide apertures and closely spaced antennas relative to the wavelength. The presented framework is physically grounded, enabling information-theoretic analyses that inherently incorporate correlation and mutual coupling among the antennas. This establishes the combined effects of correlation and coupling on the information-theoretic performance limits across SNR levels. Additionally, it reveals that, by suitably selecting the individual antenna patterns, mutual coupling can be harnessed to either reinforce or counter spatial correlations as appropriate for specific SNRs, thereby improving the performance.
... It is often considered that the direct link between the base station (BS) and users is not available. For instance, in [16], the RIS-aided communication system was handled through MIMO transmission by considering an upper limit for the channel capacity of the RIS for the blocked direct link scenario. In [4], the hybrid beamforming design was proposed in the RIS-assisted point-to-point MIMO system without the consideration of the direct link. ...
A reconfigurable intelligent surface (RIS) has emerged as a promising solution for enhancing the capabilities of wireless communications. This paper presents a scalable beamforming design for maximizing the spectral efficiency (SE) of multi-RIS-aided communications through joint optimization of the precoder and RIS phase shifts in multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT). To address key challenges of the joint optimization problem, we first decompose it into two subproblems with deriving a proper lower bound. We then leverage a generalized power iteration (GPI) approach to identify a superior local optimal precoding solution. We further extend this approach to the RIS design using regularization; we set a RIS regularization function to efficiently handle the unitmodulus constraints, and also find the superior local optimal solution for RIS phase shifts under the GPI-based optimization framework. Subsequently, we propose an alternating optimization method. In particular, utilizing the block-diagonal structure of the matrices the GPI method, the proposed algorithm offers multi-RIS scalable beamforming as well as superior SE performance. Simulations validate the proposed method in terms of both the sum SE performance and the scalability.
... Those challenges are accompanied by significant opportunities. Leveraging the near-field effect, XL-arrays can unlock additional benefits that extend beyond their substantial beamforming gains, with a particular focus on line-of-sight multiplexing and capacity enhancement [21]. ...
Dynamic metasurface antennas (DMAs) represent a novel transceiver array architecture for extremely large-scale (XL) communications, offering the advantages of reduced power consumption and lower hardware costs compared to conventional arrays. This paper focuses on near-field channel estimation for XL-DMAs. We begin by analyzing the near-field characteristics of uniform planar arrays (UPAs) and introducing the Oblong Approx. model. This model decouples elevation-azimuth (EL-AZ) parameters for XL-DMAs, providing an effective means to characterize the near-field effect. It offers simpler mathematical expressions than the second-order Taylor expansion model, all while maintaining negligible model errors for oblong-shaped arrays. Building on the Oblong Approx. model, we propose an EL-AZ-decoupled estimation framework that involves near- and far-field parameter estimation for AZ/EL and EL/AZ directions, respectively. The former is formulated as a distributed compressive sensing problem, addressed using the proposed off-grid distributed orthogonal least squares algorithm, while the latter involves a straightforward parallelizable search. Crucially, we illustrate the viability of decoupled EL-AZ estimation for near-field UPAs, exhibiting commendable performance and linear complexity correlated with the number of metasurface elements. Moreover, we design an measurement matrix optimization method with the Lorentzian constraint on DMAs and highlight the estimation performance degradation resulting from this constraint.
... In conventional MIMO relaying, such as amplify-andforward (AF) [21] and decode-and-forward (DF) [22], the received radio signals are processed before being forwarded to the destination receiver. In contrast to conventional MIMO relaying, a RIM passively reflects the radio signal impinging on its elements without amplifications, while allowing control of the reflected signals' temporal and spatial characteristics. ...
Wireless networks are increasingly relying on machine learning (ML) paradigms to provide various services at the user level. Yet, it remains impractical for users to offload their collected data set to a cloud server for centrally training their local ML model. Federated learning (FL), which aims to collaboratively train a global ML model by leveraging the distributed wireless computation resources across users without exchanging their local information, is therefore deemed as a promising solution for enabling intelligent wireless networks in the data-driven society of the future. Recently, reconfigurable intelligent metasurfaces (RIMs) have emerged as a revolutionary technology, offering a controllable means for increasing signal diversity and reshaping transmission channels, without implementation constraints traditionally associated with multi-antenna systems. In this paper, we present a comprehensive survey of recent works on the applications of FL to RIM-aided communications. We first review the fundamental basis of FL with an emphasis on distributed learning mechanisms, as well as the operating principles of RIMs, including tuning mechanisms, operation modes, and deployment options. We then proceed with an in-depth survey of literature on FL-based approaches recently proposed for the solution of three key interrelated problems in RIM-aided wireless networks, namely: channel estimation (CE), passive beamforming (PBF) and resource allocation (RA). In each case, we illustrate the discussion by introducing an expanded FL (EFL) framework in which only a subset of active users partake in the distributed training process, thereby allowing to reduce transmission overhead. Lastly, we discuss some current challenges and promising research avenues for leveraging the full potential of FL in future RIM-aided extremely large-scale multiple-input-multiple-output (XL-MIMO) networks.
... Of late, nonregenerative relay technologies have revived with new flavors and brand-new names-reconfigurable intelligent surfaces (RISs) or intelligent reflecting surfaces [1]- [4]. The most contrasting features compared to their predecessor are that they lack radio-frequency chains and baseband processing, which potentially make them more economical than their competitors. ...
This paper presents an algorithm for finding the optimal configuration of active reconfigurable intelligent surface (RIS) when both transmitter and receiver are equipped with a single antenna each. The resultant configuration is globally optimal and it takes linear time for the computation. Moreover, there is a closed-form expression for the optimal configuration when the direct link vanishes, which enables further analysis.
... The reflection coefficients are given by the product of two focusing functions: one steering the RIS-aided signal towards the mid-point of the MIMO transmitter and one steering the RIS-aided signal towards the mid-point of the MIMO receiver. Notably, we prove that the proposed 1 During the review process of the present paper, we have found [40], wherein the authors obtain a similar result. ...
We consider a multiple‐input multiple‐output (MIMO) channel in the presence of a reconfigurable intelligent surface (RIS). Specifically, our focus is on analysing the spatial multiplexing gains in line‐of‐sight and low‐scattering MIMO channels in the near field. We prove that the channel capacity is achieved by diagonalising the end‐to‐end transmitter‐RIS‐receiver channel, and applying the water‐filling power allocation to the ordered product of the singular values of the transmitter‐RIS and RIS‐receiver channels. The obtained capacity‐achieving solution requires an RIS with a non‐diagonal matrix of reflection coefficients. Under the assumption of nearly‐passive RIS, that is, no power amplification is needed at the RIS, the water‐filling power allocation is necessary only at the transmitter. We refer to this design of RIS as a linear, nearly‐passive, reconfigurable electromagnetic object (EMO). In addition, we introduce a closed‐form and low‐complexity design for RIS, whose matrix of reflection coefficients is diagonal with unit‐modulus entries. The reflection coefficients are given by the product of two focusing functions: one steering the RIS‐aided signal towards the mid‐point of the MIMO transmitter and one steering the RIS‐aided signal towards the mid‐point of the MIMO receiver. We prove that this solution is exact in line‐of‐sight channels under the paraxial setup. With the aid of extensive numerical simulations in line‐of‐sight (free‐space) channels, we show that the proposed approach offers performance (rate and degrees of freedom) close to that obtained by numerically solving non‐convex optimization problems at a high computational complexity. Also, we show that it provides performance close to that achieved by the EMO (non‐diagonal RIS) in most of the considered case studies.
... This case study is motivated by the focusing function introduced in [20] and, later, studied in [21] and [22] for RISaided LoS channels. Similar to Scheme 3, we assume that the RIS is optimized only based on the LoS components of the channel. ...
In this paper, we study surface-based communication systems based on different levels of channel state information for system optimization. We analyze the system performance in terms of rate and degrees of freedom (DoF). We show that the deployment of a reconfigurable intelligent surface (RIS) results in increasing the number of DoF, by extending the near-field region. Over Rician fading channels, we show that an RIS can be efficiently optimized only based on the positions of the transmitting and receiving surfaces, while providing good performance if the Rician fading factor is not too small.
This paper proposes a reinforcement learning (RL) based intelligent reflecting surface (IRS) incremental control algorithm for a mmWave time-varying multi-user multiple-input single-output (MU-MISO) system. The research focuses on addressing the key challenge of near-field IRS design, which involves time-varying channels due to users’ mobility. In practice, the optimization becomes more challenging when the components of the concatenated channel are unknown. From a higher perspective, we leverage electromagnetic information theory and manifold theory to provide a unified description of the IRS-assisted MU-MISO system. We regard the communication system as a nonlinear dynamic system on reproducing kernel Hilbert space (RKHS), upon which the approximate evolution operator is defined as observables for system evolution. The IRS phase shift optimization problem is modeled as a nonlinear system eigenvalue maximization problem. Utilizing the geometric properties of the unitary evolution operator, we define a metric space where the geodesic-based distance function satisfies the Lipschitz condition, enabling efficient exploitation of channel similarities. We transform the complex non-convex optimization problem into a low-dimensional linear contextual bandit problem. The performance of the proposed GLinUCB algorithm is evaluated through numerical simulations in various scenarios, showing its effectiveness in achieving high sum rates with fast convergence speed.
The downlink non-orthogonal multiple access (NOMA) transmissions from a holographic multi-input multi-output surface (HMIMOS) transmitter to multiple single-antenna users are investigated in this work. And we focus on the power saving design when the HMIMOS has a massive number of elements. For single-cluster NOMA transmissions implemented by a single-RF-chain HMIMOS-based transmitter, the required transmit power to maintain the quality of service (QoS) of all users are derived and two holographic beamforming schemes aiming at minimizing the required transmit power are developed. For multi-cluster NOMA transmissions implemented by a multi-RF-chain HMIMOS-based transmitter, a two-layer partitioning problem is formulated and solved to minimize the power consumption. Numerical results are provided to validate our theoretical analysis. It is shown that the NOMA scheme has lower power consumption than orthogonal multiple access (OMA) based multi-user transmission schemes when the number of RF chains is limited, and our proposed holographic beamforming schemes achieve lower power consumption than other holographic beamforming schemes.
This paper studies the optimization of an active reconfigurable intelligent surface (RIS) under two power budget models. Two algorithms, one for each power constraint, for finding the optimal RIS configuration are proposed under the proviso that both the transmitter and receiver are equipped with a single antenna each. The computational complexities of these methods are linear in the number of RIS elements, and the resultant configurations are globally optimal.
This survey paper provides a comprehensive overview of integrating Multiple-Input Multiple- Output (MIMO) with Intelligent Reflecting Surfaces (IRS) in wireless communication systems. IRS is known as reconfigurable metasurfaces, have emerged as a transformative technology to enhance wireless communication performance by manipulating the propagation environment. This work delves into the fundamental concepts of MIMO and IRS technologies, exploring their benefits and applications. It subsequently investigates the synergies of resource allocation and energy efficiency that emerge when these technologies are combined, elucidating howIRS improves MIMO systems through signal manipulation and beamforming. Through an in-depth analysis of various techniques and cutting-edge algorithms in resource allocation and energy efficiency can explore the key research areas such as optimization techniques, beamforming strategies, and practical implementation consideration. Furthermore, it provides open research directions, individually addressing topics such as limitations of resource allocation and energy efficiency in the MIMO IRS system. This paper offers insights into MIMO-enabled IRS systems challenges and future trends. By presenting a consolidated view of the current state-of-the-art, this survey underscores their potential to revolutionize wireless communication paradigms, ushering in an era of enhanced connectivity, spectral efficiency, and improved coverage.
In this work, we investigate the joint visibility region (VR) detection and channel estimation (CE) problem for extremely large-scale multiple-input-multiple-output (XL-MIMO) systems considering both the spherical wavefront effect and spatial non-stationary (SnS) property. Unlike existing SnS CE methods that rely on the statistical characteristics of channels in the spatial or delay domain, we propose an approach that simultaneously exploits the antenna-domain spatial correlation and the wavenumber-domain sparsity of SnS channels. To this end, we introduce a two-stage VR detection and CE scheme. In the first stage, the belief regarding the visibility of antennas is obtained through a VR detection-oriented message passing (VRDO-MP) scheme, which fully exploits the spatial correlation among adjacent antenna elements. In the second stage, leveraging the VR information and wavenumber-domain sparsity, we accurately estimate the SnS channel employing the belief-based orthogonal matching pursuit (BB-OMP) method. Simulations show that the proposed algorithms lead to a significant enhancement in VR detection and CE accuracy as compared to existing methods, especially in low signal-to-noise ratio (SNR) scenarios.
With increasing frequencies, bandwidths, and array apertures, the phenomenon of beam squint arises as a serious impairment to beamforming. Fully digital arrays with true time delay per antenna element are a potential solution, but they require downconversion at each element. This paper shows that hybrid arrays can perform essentially as well as digital arrays once the number of radio-frequency chains exceeds a certain threshold that is far below the number of elements. This threshold is determined by only a few physical parameters—bandwidth, array size, and beamforming direction—and can be expressed in a remarkably simple closed form. The result is robust, holding also for suboptimum yet highly appealing beamspace architectures.
With the combination of extra-large arrays and high frequencies, near-field transmissions have become prevalent, challenging the validity of classical channel representations typically derived under the plane wavefront assumption. In this paper, we investigate the angular-domain representation of line-of-sight (LoS) extra-large MIMO (XL-MIMO) channels, considering the impact of spherical wavefront effects. First, we demonstrate the structured sparsity of LoS XL-MIMO channels in the angular domain. Leveraging this sparsity, we propose an effective spatial bandwidth channel representation method, which characterizes near-field LoS XL-MIMO channels as a superposition of multiple plane wave components, enabling us to capture the spherical wavefront effect in a low-dimensional angular channel. Subsequently, we introduce an angular-domain transceiver architecture based on this low-dimensional channel representation. This architecture could significantly facilitate the implementation of LoS XL-MIMO systems. Finally, simulation results confirm the effectiveness of the effective spatial bandwidth identification method and analyze the impact of various array geometries on the effective spatial bandwidth. Additionally, the availability of the angular-domain processing architecture is validated.
In this article, we present our vision for how extremely large aperture arrays (ELAAs), equipped with hundreds or thousands of antennas, can play a major role in future 6G networks by enabling a remarkable increase in data rates through spatial multiplexing of a massive number of data streams to both a single user and many simultaneous users. Specifically, with the quantum leap in the array aperture size, the users will be in the so-called radiative near-field region of the array, where previously negligible physical phenomena dominate the propagation conditions and give the channel matrices more favorable properties. This article presents the foundational properties of communication in the radiative near-field region and then exemplifies how these properties enable two unprecedented spatial multiplexing schemes: depth-domain multiplexing of multiple users and angular multiplexing of data streams to a single user. We also highlight research challenges and open problems that require further investigation.
Compared to passive intelligent reflecting surface (IRS), active IRS is viewed as a more efficient promising technique to combat the double-fading impact in IRS-aided wireless network. In this paper, in order to boost the achievable rate of user in such a wireless network, three enhanced-rate iterative beamforming methods are proposed by designing the amplifying factors and the corresponding phases at active IRS. The first method, maximizing the simplified signal-to-noise ratio (Max-SSNR) is designed by omitting the cross-term in the definition of rate. Using the Rayleigh-Ritz (RR) theorem, Max-SSNR-RR is proposed to iteratively optimize the norm of beamforming vector and its associated normalized vector. In addition, generalized maximum ratio reflection (GMRR) is presented with a closed-form expression, which is motivated by the maximum ratio combining. To further improve rate, maximizing SNR (Max-SNR) is designed by fractional programming (FP), which is called Max-SNR-FP. Simulation results show that the proposed three methods make an obvious rate enhancement over Max-reflecting signal-to-noise ratio (Max-RSNR), maximum ratio reflection (MRR), selective ratio reflecting (SRR), equal gain reflection (EGR) and passive IRS, and are in increasing order of rate performance as follows: Max-SSNR-RR, GMRR, and Max-SNR-FP.
Motivated by the widespread adoption of the parabolic wavefront model for line-of-sight (LOS) multiple-input multiple-output (MIMO) communication, this paper presents a comprehensive analysis of this model’s validity and simple conditions that ensure its applicability. Then, with the model’s scope clearly delineated, the paper expounds a number of properties of the channel that results from applying it. Connections are drawn among these properties under the umbrella of a Fourier interpretation, and their significance to LOS MIMO communication is substantiated.
An intelligent reflecting surface (IRS) at terahertz (THz) bands is expected to have a massive number of reflecting elements to compensate for the severe propagation losses. However, as the IRS size grows, the conventional far-field assumption starts becoming invalid and the spherical wavefront of the radiated waves should be taken into account. In this work, we consider a spherical wave channel model and pursue a comprehensive study of IRS-aided multiple-input multiple-output (MIMO) in terms of power gain and energy efficiency (EE). Specifically, we first analyze the power gain under beamfocusing and beamforming, and show that the latter is suboptimal even for multiple meters away from the IRS. To this end, we derive an approximate, yet accurate, closed-form expression for the loss in the power gain under beamforming. Building on the derived model, we next show that an IRS can significantly improve the EE of MIMO when it operates in the radiating near-field and performs beamfocusing. Numerical results corroborate our analysis and provide novel insights into the design and performance of IRS-assisted THz communication.
Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation in wireless networks and offers a great variety of possible performance and implementation gains. Motivated by this, we study the achievable rate optimization for multi-stream multiple-input multiple-output (MIMO) systems equipped with an RIS, and formulate a joint optimization problem of the covariance matrix of the transmitted signal and the RIS elements. To solve this problem, we propose an iterative optimization algorithm that is based on the projected gradient method (PGM). We derive the step size that guarantees the convergence of the proposed algorithm and we define a backtracking line search to improve its convergence rate. Furthermore, we introduce the total free space path loss (FSPL) ratio of the indirect and direct links as a first-order measure of the applicability of RISs in the considered communication system. Simulation results show that the proposed PGM achieves the same achievable rate as a state-of-the-art benchmark scheme, but with a significantly lower computational complexity. In addition, we demonstrate that the RIS application is particularly suitable to increase the achievable rate in indoor environments, as even a small number of RIS elements can provide a substantial achievable rate gain.
With the ratification of the IEEE 802.15.3d amendment to 802.15.3, a first step has been made to standardize consumer wireless communications in the sub-THz frequency band. IEEE 802.15.3d offers switched point-to-point connectivity with data rates of 100 Gb/s and higher at distances ranging from tens of centimeters up to a few hundred meters. In this article, we provide a detailed introduction to IEEE 802.15.3d and the key design principles beyond the developed standard. We particularly describe the target applications and usage scenarios, as well as the specifics of the IEEE 802.15.3d physical and medium access layers. Later, we present the results of the initial performance evaluation of IEEE 802.15.3d wireless communications. The obtained first-order performance predictions show non-incremental benefits compared to the characteristics of the fifth generation wireless systems, thus paving the way toward the sixth generation THz networks. We conclude the article by outlining the further standardization and regulatory activities on wireless networking in the THz frequency band.
Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.
Frequencies from 100 GHz to 3 THz are promising bands for the next generation of wireless communication systems because of the wide swaths of unused and unexplored spectrum. These frequencies also offer the potential for revolutionary applications that will be made possible by new thinking, and advances in devices, circuits, software, signal processing, and systems. This paper describes many of the technical challenges and opportunities for wireless communication and sensing applications above 100 GHz, and presents a number of promising discoveries, novel approaches, and recent results that will aid in the development and implementation of the sixth generation (6G) of wireless networks, and beyond. This paper shows recent regulatory and standard body rulings that are anticipating wireless products and services above 100 GHz and illustrates the viability of wireless cognition, hyper-accurate position location, sensing, and imaging. This paper also presents approaches and results that show how long distance mobile communications will be supported to above 800 GHz since the antenna gains are able to overcome air-induced attenuation, and present methods that reduce the computational complexity and simplify the signal processing used in adaptive antenna arrays, by exploiting the Special Theory of Relativity to create a cone of silence in over-sampled antenna arrays that improve performance for digital phased array antennas. Also, new results that give insights into power efficient beam steering algorithms, and new propagation and partition loss models above 100 GHz are given, and promising imaging, array processing, and position location results are presented. The implementation of spatial consistency at THz frequencies, an important component of channel modeling that considers minute changes and correlations over space, is also discussed. This paper offers the first in-depth look at the vast applications of THz wireless products and applications and provides approaches for how to reduce power and increase performance across several problem domains, giving early evidence that THz techniques are compelling and available for future wireless communications.
The use of large arrays might be the solution to the capacity problems in wireless communications. The signal-to-noise ratio (SNR) grows linearly with the number of array elements N when using Massive MIMO receivers and half-duplex relays. Moreover, intelligent reflecting surfaces (IRSs) have recently attracted attention since these can relay signals to achieve an SNR that grows as N2, which seems like a major benefit. In this paper, we use a deterministic propagation model for a planar array of arbitrary size, to demonstrate that the mentioned SNR behaviors, and associated power scaling laws, only apply in the far-field. They cannot be used to study the regime where N∞. We derive an exact channel gain expression that captures three essential near-field behaviors and use it to revisit the power scaling laws. We derive new finite asymptotic SNR limits but also conclude that these are unlikely to be approached in practice. We further prove that an IRS-aided setup cannot achieve a higher SNR than an equal-sized Massive MIMO setup, despite its faster SNR growth. We quantify analytically how much larger the IRS must be to achieve the same SNR. Finally, we show that an optimized IRS does not behave as an “anomalous” mirror but can vastly outperform that benchmark.
Future wireless networks are expected to evolve toward an intelligent and software reconfigurable paradigm enabling ubiquitous communications between humans and mobile devices. They will also be capable of sensing, controlling, and optimizing the wireless environment to fulfill the visions of low-power, high-throughput, massively-connected, and low-latency communications. A key conceptual enabler that is recently gaining increasing popularity is the HMIMOS that refers to a low-cost transformative wireless planar structure comprised of sub-wavelength metallic or dielectric scattering particles, which is capable of shaping electromagnetic waves according to desired objectives. In this article, we provide an overview of HMIMOS communications including the available hardware architectures for reconfiguring such surfaces, and highlight the opportunities and key challenges in designing HMIMOS-enabled wireless communications.
Intelligent reflecting surface (IRS) that enables the control of wireless propagation environment has recently emerged as a promising cost-effective technology for boosting the spectral and energy efficiency of future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming full signal reflection by each of its elements regardless of the phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection design. Based on the proposed model and considering an IRS-aided multiuser system with one IRS deployed to assist in the downlink communications from a multi-antenna access point (AP) to multiple single-antenna users, we formulate an optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit beamforming and the IRS reflect beamforming, subject to the users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Iterative algorithms are proposed to find suboptimal solutions to this problem efficiently by utilizing the alternating optimization (AO) as well as penalty-based optimization techniques. Moreover, to draw essential insight, we analyze the asymptotic performance loss of the IRS-aided system that employs practical phase shifters but assumes the ideal phase shift model for beamforming optimization, as the number of IRS elements goes to infinity. Simulation results unveil substantial performance gains achieved by the proposed beamforming optimization based on the practical phase shift model as compared to the conventional ideal model.
In this paper, we present a 300 GHz wireless link composed of a photonic uni-traveling-carrier diode transmitter and an active electronic receiver based on millimeterwave integrated circuits fabricated in an InGaAs metamorphic high electron mobility transistor technology. The input pseudo-random binary sequence is transmitted and analyzed offline using fast analog to digital converters. The data transmission reaches 100 Gbps over a distance of 15 meters. Complex modulation formats, like 32-Quadrature Amplitude Modulation and 64-Quadrature Amplitude Modulation, are successfully transmitted up to a symbol rate of 8 GBd. The system presents not only a high linearity but is also capable of transmitting high symbol rates, up to 40 GBd To the best of the authors' knowledge, this represents the highest ever reported transmission bandwidth as well as the highest spectral density symbol rate product for transmissions with center frequency in the terahertz band. Thus, the usage of such links in future bandwidth-hungry applications like data centers, data showers, front- and backhaul is proven feasible.
Intelligent reflecting surfaces can improve the communication between a source and a destination. The surface contains metamaterial that is configured to “reflect” the incident wave from the source towards the destination. Two incompatible pathloss models have been used in prior work. In this letter, we derive the far-field pathloss using physical optics techniques and explain why the surface consists of many elements that individually act as diffuse scatterers but can jointly beamform the signal in a desired direction with a certain beamwidth. We disprove one of the previously conjectured pathloss models.
The rate and energy efficiency of wireless channels can be improved by deploying software-controlled metasurfaces to reflect signals from the source to destination, especially when the direct path is weak. While previous works mainly optimized the reflections, this letter compares the new technology with classic decode-and-forward (DF) relaying. The main observation is that very high rates and/or large metasurfaces are needed to outperform DF relaying, both in terms of minimizing the total transmit power and maximizing the energy efficiency, which also includes the dissipation in the transceiver hardware.
The future of mobile communications looks exciting with the potential new use cases and challenging requirements of future 6th generation (6G) and beyond wireless networks. Since the beginning of the modern era of wireless communications, the propagation medium has been perceived as a randomly behaving entity between the transmitter and the receiver, which degrades the quality of the received signal due to the uncontrollable interactions of the transmitted radio waves with the surrounding objects. The recent advent of reconfigurable intelligent surfaces in wireless communications enables, on the other hand, network operators to control the scattering, reflection, and refraction characteristics of the radio waves, by overcoming the negative effects of natural wireless propagation. Recent results have revealed that reconfigurable intelligent surfaces can effectively control the wavefront, e.g., the phase, amplitude, frequency, and even polarization, of the impinging signals without the need of complex decoding, encoding, and radio frequency processing operations. Motivated by the potential of this emerging technology, the present article is aimed to provide the readers with a detailed overview and historical perspective on state-of-the-art solutions, and to elaborate on the fundamental differences with other technologies, the most important open research issues to tackle, and the reasons why the use of reconfigurable intelligent surfaces necessitates to rethink the communication-theoretic models currently employed in wireless networks. This article also explores theoretical performance limits of reconfigurable intelligent surface-assisted communication systems using mathematical techniques and elaborates on the potential use cases of intelligent surfaces in 6G and beyond wireless networks.
Electromagnetic waves undergo multiple uncontrollable alterations as they propagate within a wireless environment. Free space path loss, signal absorption, as well as reflections, refractions, and diffractions caused by physical objects within the environment highly affect the performance of wireless communications. Currently, such effects are intractable to account for and are treated as probabilistic factors. This article proposes a radically different approach, enabling deterministic, programmable control over the behavior of wireless environments. The key enabler is the so-called HyperSurface tile, a novel class of planar meta-materials that can interact with impinging electromagnetic waves in a controlled manner. The HyperSurface tiles can effectively re-engineer electromagnetic waves, including steering toward any desired direction, full absorption, polarization manipulation, and more. Multiple tiles are employed to coat objects such as walls, furniture, and overall, any objects in indoor and outdoor environments. An external software service calculates and deploys the optimal interaction types per tile to best fit the needs of communicating devices. Evaluation via simulations highlights the potential of the new concept.
Millimeter wave (mmWave) technology is expected to dominate the future 5G networks mainly due to large spectrum available at these frequencies. However, coverage deteriorates significantly at mmWave frequencies due to higher path loss, especially for the non-line-of-sight (NLOS) scenarios. In this work, we explore the use of passive reflectors for improving mmWave signal coverage in NLOS indoor areas. Measurements are carried out using the PXI-based mmWave transceiver platforms from National Instruments operating at 28 GHz, and the results are compared with the outcomes of ray tracing (RT) simulations in a similar environment. For both the measurements and RT simulations, different shapes of metallic passive reflectors are used to observe the coverage (signal strength) statistics on a receiver grid in an NLOS area. For a square metallic sheet reflector of size 24 by 24 in and 33 by 33 in , we observe a significant increase in the received power in the NLOS region, with a median gain of 20 dB when compared to no reflector case. The cylindrical reflector shows more uniform coverage on the receiver grid as compared to flat reflectors that are more directional.
In this paper, we consider the potential of data-transmission in a system with a massive number of radiating and sensing elements, thought of as a contiguous surface of electromagnetically active material. We refer to this as a large intelligent surface (LIS). The "LIS" is a newly proposed concept, which conceptually goes beyond contemporary massive MIMO technology, that arises from our vision of a future where man-made structures are electronically active with integrated electronics and wireless communication making the entire environment "intelligent". We consider capacities of single-antenna autonomous terminals communicating to the LIS where the entire surface is used as a receiving antenna array. Under the condition that the surface-area is sufficiently large, the received signal after a matched-filtering (MF) operation can be closely approximated by a sinc-function-like intersymbol interference (ISI) channel. We analyze the capacity per square meter (m^2) deployed surface, \hat{C}, that is achievable for a fixed transmit power per volume-unit, \hat{P}. Moreover, we also show that the number of independent signal dimensions per m deployed surface is 2/\lambda for one-dimensional terminal-deployment, and \pi/\lambda^2 per m^2 for two and three dimensional terminal-deployments. Lastly, we consider implementations of the LIS in the form of a grid of conventional antenna elements and show that, the sampling lattice that minimizes the surface-area of the LIS and simultaneously obtains one signal space dimension for every spent antenna is the hexagonal lattice. We extensively discuss the design of the state-of-the-art low-complexity channel shortening (CS) demodulator for data-transmission with the LIS.
By direct numerical-integration comparisons, it is established that the Fresnel approximation for collimated propagation is quite good (within about 2% in amplitude and 0.02 rad in phase) in every case, including that with the limit of a high Fresnel number. Moreover, the Fresnel approximation begins to break down in phase for spherical-wave propagation for beams faster than about f/12. It has been discovered, however, that if one also invokes the paraxial approximation, that is, replaces the spherical wave by a quadratic phase front, then the Fresnel approximation becomes valid for expanding (or diverging) beams as well. This result is substantiated through the use of stationary-phase arguments.
While the efficiency of MIMO transmissions in a rich scattering environment
has been demonstrated, less is known about the situation where the fading
matrix coefficients come from a line-of-sight model. In this paper, we study in
detail how this line-of-sight assumption affects the performance of distributed
MIMO transmissions between far away clusters of nodes in a wireless network.
Our analysis pertains to the study of a new class of random matrices.
In this paper we consider pure line-of-sight multiple-input multiple-output (MIMO) channels employing uniform linear antenna arrays. We investigate the influence of exact spherical wave propagation modeling versus approximate plane wave propagation modeling on the properties of the MIMO channel matrix. When the transmission distance increases, the properties of the singular values of the MIMO channel matrix given by the spherical wave model approach the properties given by the simpler plane wave model. We investigate this transition between the two channel models, which results in a new tool giving us analytical expressions describing when spherical wave modeling is necessary and when plane wave modeling gives sufficient modeling accuracy. The parameters of interest are the transmission distance, the frequency, the array orientation, and the array size. The tool introduced is general, in the sense that it supports different performance measures when deciding on the transition between the two models. As an example, we investigate underestimation of the mutual information in this paper. The results show that the spherical wave model should be applied e.g. in some practical WLAN scenarios where plane wave modeling is commonly applied today.
An alternative derivation is provided for the degrees of freedom (DOF) formula on line-of-sight (LOS) channels via Landau’s eigenvalue theorem for bandlimited signals. Compared to other approaches, Landau’s theorem provides a general framework to compute the DOF in arbitrary environments, this framework is herein specialized to LOS propagation. The development shows how the spatially bandlimited nature of the channel relates to its geometry under the paraxial approximation that applies to most LOS settings of interest.
In reconfigurable intelligent surfaces (RISs) aided communications, the existing passive beamforming (PB) design involves polynomial complexity in the number of reflecting elements, and thus is difficult to implement due to a massive number of reflecting elements. To overcome this difficulty, we propose a reflection-angle-based cascaded channel model by adopting the generalized Snell’s law, in which the dimension of the variable space involved in optimization is significantly reduced, resulting in a simplified hierarchical passive beamforming (HPB) design. We develop an efficient two-stage HPB algorithm, which exploits the angular domain property of the channel, to maximize the achievable rate of the target user. Simulation results demonstrate the appealing performance and low complexity of the proposed HPB design.
A relentless trend in wireless communications is the hunger for bandwidth, and fresh bandwidth is only to be found at ever higher frequencies. While 5G systems are seizing the mmWave band, the attention of researchers is shifting already to the terahertz range. In that distant land of tiny wavelengths, antenna arrays can serve for more than power-enhancing beamforming. Defying lower-frequency wisdom, spatial multiplexing becomes feasible even in line-of-sight conditions. This article reviews the underpinnings of this phenomenon, and it surveys recent results on the ensuing information-theoretic capacity. Reconfigurable array architectures are put forth that can closely approach such capacity, practical challenges are discussed, and supporting experimental evidence is presented.
The multiple intelligent reflecting surfaces (IRSs) are promising solutions to overcome the rank-deficiency of channel matrix by exploiting spatial multiplexing gains in high frequency communication. In this letter, we aim to maximize the capacity through optimizing the phase shifter matrices of multiple IRSs in pure line-of-sight multiple-input and multipleoutput (MIMO) channel. However, this optimization problem is not mathematically straightforward. To tackle this challenge, we propose a new IRS-assisted beamforming scheme. First, the problem of maximizing the determinant of channel matrix is formulated. The problem is reformulated by the inequality of arithmetic and geometric means, which generates a system of equations for the phase shift values.We can find the solution using the least square method. This scheme can be represented as a closed-form expression. Simulation results show that the proposed scheme can provide substantial capacity gains by increasing the rank of the channel matrix compared to the baseline schemes.
This work presents experimental results for a four-stream spatial multiplexing setup in a line-of-sight (LoS) wireless backhaul scenario at 60 GHz. With optimal antenna arrangement, a highly orthogonal wireless channel with a measured condition number of 1.42 is observed, whereby the channel tap distribution shows a dominant
LoS component. Two different equalizers, symbol-wise and block-wise adaptive, are presented and evaluated in terms of error vector magnitude (EVM) performance and bandwidth efficiency. For both approaches, an error-free transmission with a throughput of 14.08 Gbit/s is demonstrated, thus validating the practical suitability of
LoS MIMO for wireless backhaul applications.
This paper establishes an upper bound on the capacity of line-of-sight multiantenna channels over all possible antenna arrangements and shows that uniform linear arrays (ULAs) with an SNR-dependent rotation of transmitter and/or receiver can closely approach such capacity—and in fact achieve it at low and high SNR, and asymptotically in the numbers of antennas. Then, as an alternative to mechanically rotating ULAs, we propose to electronically select among multiple ULAs having a radial disposition at either transmitter or receiver, and we bound the shortfall from capacity as a function of the number of such ULAs. With only three ULAs, properly angled, 96% of the capacity can be achieved. Finally, we further introduce reduced-complexity precoders and linear receivers that capitalize on the structure of the channels spawned by these configurable ULA architectures.
Intelligent reflecting surfaces (IRSs) have the potential to transform wireless communication channels into smart reconfigurable propagation environments. To realize this new paradigm, the passive IRSs have to be large, especially for communication in far-field scenarios, so that they can compensate for the large end-to-end path-loss, which is caused by the multiplication of the individual path-losses of the transmitter-to-IRS and IRS-to-receiver channels. However, optimizing a large number of sub-wavelength IRS elements imposes a significant challenge for online transmission. To address this issue, in this article, we develop a physics-based model and a scalable optimization framework for large IRSs. The basic idea is to partition the IRS unit cells into several subsets, referred to as tiles, model the impact of each tile on the wireless channel, and then optimize each tile in two stages, namely an offline design stage and an online optimization stage. For physics-based modeling, we borrow concepts from the radar literature, model each tile as an
anomalous
reflector, and derive its impact on the wireless channel for a given phase shift by solving the corresponding integral equations for the electric and magnetic vector fields. In the offline design stage, the IRS unit cells of each tile are jointly designed for the support of different transmission modes, where each transmission mode effectively corresponds to a given configuration of the phase shifts that the unit cells of the tile apply to an impinging electromagnetic wave. In the online optimization stage, the best transmission mode of each tile is selected such that a desired quality-of-service (QoS) criterion is maximized. We consider an exemplary downlink system and study the minimization of the base station (BS) transmit power subject to QoS constraints for the users. Since the resulting mixed-integer programming problem for joint optimization of the BS beamforming vectors and the tile transmission modes is non-convex, we derive two efficient suboptimal solutions, which are based on alternating optimization and a greedy approach, respectively. We show that the proposed modeling and optimization framework can be used to efficiently optimize large IRSs comprising thousands of unit cells.
This paper analyzes the optimal communication involving large intelligent surfaces (LIS) starting from electromagnetic arguments. Since the numerical solution of the corresponding eigenfunctions problem is in general computationally prohibitive, simple but accurate analytical expressions for the link gain and available spatial degrees-of-freedom (DoF) are derived. It is shown that the achievable DoF and gain offered by the wireless link are determined only by geometric factors, and that the classical Friis’ formula is no longer valid in this scenario where the transmitter and receiver could operate in the near-field regime. Furthermore, results indicate that, contrarily to classical MIMO systems, when using LIS-based antennas DoF larger than 1 can be exploited even in strong line-of-sight (LOS) channel conditions, which corresponds to a significant increase in spatial capacity density, especially when working at millimeter waves.
This paper presents a literature review on recent applications and design aspects of the intelligent reflecting surface (IRS) in the future wireless networks. Conventionally, the network optimization has been limited to transmission control at two endpoints, i.e., end users and network controller. The fading wireless channel is uncontrollable and becomes one of the main limiting factors for performance improvement. The IRS is composed of a large array of scattering elements, which can be individually configured to generate additional phase shifts to the signal reflections. Hence, it can actively control the signal propagation properties in favor of signal reception, and thus realize the notion of a smart radio environment. As such, the IRS’s phase control, combined with the conventional transmission control, can potentially bring performance gain compared to wireless networks without IRS. In this survey, we first introduce basic concepts of the IRS and the realizations of its reconfigurability. Then, we focus on applications of the IRS in wireless communications. We overview different performance metrics and analytical approaches to characterize the performance improvement of IRS-assisted wireless networks. To exploit the performance gain, we discuss the joint optimization of the IRS’s phase control and the transceivers’ transmission control in different network design problems, e.g., rate maximization and power minimization problems. Furthermore, we extend the discussion of IRS-assisted wireless networks to some emerging use cases. Finally, we highlight important practical challenges and future research directions for realizing IRS-assisted wireless networks in beyond 5G communications.
Intelligent reflecting surface (IRS) is a promising solution to enhance the wireless communication capacity both cost-effectively and energy-efficiently, by properly altering the signal propagation via tuning a large number of passive reflecting units. In this paper, we aim to characterize the fundamental
capacity
limit of IRS-aided point-to-point multiple-input multiple-output (MIMO) communication systems with multi-antenna transmitter and receiver in general, by jointly optimizing the IRS reflection coefficients and the MIMO transmit covariance matrix. First, we consider narrowband transmission under frequency-flat fading channels, and develop an efficient
alternating optimization
algorithm to find a locally optimal solution by iteratively optimizing the transmit covariance matrix or one of the reflection coefficients with the others being fixed. Next, we consider capacity maximization for broadband transmission in a general MIMO orthogonal frequency division multiplexing (OFDM) system under frequency-selective fading channels, where transmit covariance matrices are optimized for different subcarriers while only one common set of IRS reflection coefficients is designed to cater to all the subcarriers. To tackle this more challenging problem, we propose a new alternating optimization algorithm based on convex relaxation to find a high-quality suboptimal solution. Numerical results show that our proposed algorithms achieve substantially increased capacity compared to traditional MIMO channels without the IRS, and also outperform various benchmark schemes. In particular, it is shown that with the proposed algorithms, various key parameters of the IRS-aided MIMO channel such as channel total power, rank, and condition number can be significantly improved for capacity enhancement.
Imagine an array with a massive (possibly uncountably infinite) number of antennas in a compact space. We refer to a system of this sort as Holographic MIMO. Given the impressive properties of Massive MIMO, one might expect a holographic array to realize extreme spatial resolution, incredible energy efficiency, and unprecedented spectral efficiency. At present, however, its fundamental limits have not been conclusively established. A major challenge for the analysis and understanding of such a paradigm shift is the lack of mathematically tractable and numerically reproducible channel models that retain some semblance to the physical reality. Detailed physical models are, in general, too complex for tractable analysis. This paper aims to take a closer look at this interdisciplinary challenge. Particularly, we consider the small-scale fading in the far-field, and we model it as a zero-mean, spatially-stationary, and correlated Gaussian scalar random field. Physically-meaningful correlation is obtained by requiring that the random field be consistent with the scalar Helmholtz equation. This formulation leads directly to a rather simple and exact description of the three-dimensional small-scale fading as a Fourier plane-wave spectral representation. Suitably discretized, this leads to a discrete representation for the field as a Fourier plane-wave series expansion, from which a computationally efficient way to generate samples of the small-scale fading over spatially-constrained compact spaces is developed. The connections with the conventional tools of linear systems theory and Fourier transform are thoroughly discussed.
IRS is a new and revolutionizing technology that is able to significantly improve the performance of wireless communication networks, by smartly reconfiguring the wireless propagation environment with the use of massive low-cost passive reflecting elements integrated on a planar surface. Specifically, different elements of an IRS can independently reflect the incident signal by controlling its amplitude and/or phase and thereby collaboratively achieve fine-grained 3D passive beamforming for directional signal enhancement or nulling. In this article, we first provide an overview of the IRS technology, including its main applications in wireless communication, competitive advantages over existing technologies, hardware architecture as well as the corresponding new signal model. We then address the key challenges in designing and implementing the new IRS-aided hybrid (with both active and passive components) wireless network, as compared to the traditional network comprising active components only. Finally, numerical results are provided to show the great performance enhancement with the use of IRS in typical wireless networks.
Metasurfaces, the two-dimensional counterpart of metamaterials, have caught great attention thanks to their powerful capabilities on manipulation of electromagnetic waves. Recent times have seen the emergence of a variety of metasurfaces exhibiting not only countless functionalities, but also a reconfigurable response. Additionally, digital or coding metasurfaces have revolutionized the field by describing the device as a matrix of discrete building block states, thus drawing clear parallelisms with information theory and opening new ways to model, compose, and (re)program advanced metasurfaces. This paper joins the reconfigurable and digital approaches, and presents a metasurface that leverages the tunability of graphene to perform beam steering at terahertz frequencies. A comprehensive design methodology is presented encompassing technological, unit cell design, digital metamaterial synthesis, and programmability aspects. By setting up and dynamically adjusting a phase gradient along the metasurface plane, the resulting device achieves beam steering at all practical directions. The proposed design is studied through analytical models and validated numerically, showing beam widths and steering errors well below 10 o and 5% in most cases. Finally, design guidelines are extracted through a scalability analysis involving the metasurface size and number of unit cell states.
In this paper, for the first time, a new generation of multi-bit graphene-based bias-encoded metasurfaces (MGBMs) is proposed for real-time reflected wavefront manipulation at terahertz (THz) frequencies. The architecture of the designed MGBM is composed of several meta-atoms whose operational status can be independently switched between eight digital states of “000” e “111” in a real-time manner. By mere changing the distribution of chemical potentials through an external electronic source, the occupying meta-atoms can be dynamically combined in different gradient, spiral-like, and spiral-parabola-like coding sequences. Different from earlier works, the proposed MGBM can be re-programmed for accomplishing multiple outlandish missions from generation of vortex wavefronts carrying a controllable amount of orbital angular momentum (OAM) toward emitting multiple arbitrarily-oriented pencil beams at the same time. By exploiting the addition theorem and convolutional principle, multi-type func- tionalities, such as multiple pencil beams, multiple vortex beams with different topological charges, and multiple pencil?vortex beams are simultaneously realized. The full control of reflected wavefronts is corroborated with numerical simulations and theoretical predictions. By offering new attractive degrees of freedom to EM waves, various future directions are expected for the proposed versatile MGBM such as controllable displays, modern information systems, moving target detection, etc.
Cambridge Core - Communications and Signal Processing - Foundations of MIMO Communication - by Robert W. Heath Jr
In this paper we present measurement results for pure line-of-sight MIMO links operating in the millimeter wave range. We show that the estimated condition numbers and capacities of the measured channels are in good agreement with the theory for various transmission distances and antenna setups. Furthermore, the results show that orthogonal channel vectors can be observed if the spacing criterion is fulfilled, thus facilitating spatial multiplexing and achieving high spectral efficiencies even over fairly long distances. Spacings generating ill-conditioned channel matrices show on the other hand significantly reduced performance.
The capacity of multiple input, multiple output (MIMO) wireless channels is computed for Ricean channels. The novelty is geometrical (ray-tracing) interpretation of the MIMO channel capacity formula to find array geometries which greatly enhance channel capacity compared to single input-single output (SISO) systems.
Functions I(k; α) defined by two-dimensional integrals of the form are considered. Here, α = (α1, α2) represents the position of the only stationary point of φ in a certain domain ∗ which contains . An asymptotic expansion of I(k; α) for k ⪢ 1 is obtained that remains uniformly valid for all values of α that lie in ∗. The case where α is a “center” (a maximum or minimum point) of φ yields a result that differs only slightly from the case where α is a saddle-point of φ. In both cases, it is shown that the uniform asymptotic expansion of I involves a single area integral which is significantly simpler than I itself and an infinite sequence of one-dimensional integrals. Moreover, it is found that the area integral is a two-dimensional generalization of the well-known Fresnel integral, and plays the same role in the present analysis as does the Fresnel integral in the uniform asymptotic expansion of certain one-dimensional integrals. It is further shown that several of the non-uniform expansions obtained by previous authors can be readily recovered from the uniform results.
Evaluation of the electromagnetic fields diffracted from plane apertures are, in the general case, highly problematic. Fortunately the exploitation of the Fresnel and more restricted Fraunhofer approximations can greatly simplify evaluation. In particular, the use of the fast Fourier transform algorithm when the Fraunhofer approximation is valid greatly increases the speed of computation. However, for specific applications it is often unclear which approximation is appropriate and the degree of accuracy that will be obtained. We build here on earlier work (Shimoji M 1995 Proc. 27th Southeastern Symp. on System Theory (Starkville, MS, March 1995) (Los Alamitos, CA: IEEE Computer Society Press) pp 520–4) that showed that for diffraction from a circular aperture and for a specific phase error, there is a specific curved boundary surface between the Fresnel and Fraunhofer regions. We derive the location of the boundary surface and the magnitude of the errors in field amplitude that can be expected as a result of applying the Fresnel and Fraunhofer approximations. These expressions are exact for a circular aperture and are extended to give the minimum limit on the domain of validity of the Fresnel approximation for plane arbitrary apertures.
We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multi-antenna systems over single-antenna systems is rather large under independenceassumptions for the fades and noises at different receiving antennas.
A method for computing the singular values and singular functions of real square-integrable kernels is presented. The analysis shows that a good discretization always yields a matrix whose singular value decomposition is closely related to the singular value expansion of the kernel. This relationship is important in connection with the solution of ill-posed problems since it shows that regularization of the algebraic problem, derived from an integral equation, is equivalent to regularization of the integral equation itself.Eine Methode zur Berechnung der singulren Werte und der singulren Funktionen von reellen, quadratisch-integrierbaren Kernen wird dargestellt. Die Analyse zeigt, da eine gute Diskretisierung immer eine Matrix ergibt, deren Singulrwert-Zerlegung mit der Singulrwert-Entwicklung der Kerne eng verbunden ist. Dieser Zusammenhang ist wesentlich, wenn schlecht gestellte Probleme zu lsen sind, weil er zeigt, da eine Regularisierung des von einer Integralgleichung hergeleiteten algebraischen Problems quivalent ist zu einer Regularisierung der Integralgleichung.
We consider a non-regenerative MIMO relay system where the source, relay and destination are all equipped with multiple antennas. The relay does not decode the packets but performs a multi-dimensional amplify-and-forward function (a relay matrix) on the baseband signals. Under the condition that the source is white, the relay matrix that maximizes the capacity between the source and the destination has been previously found. In this paper, we show a new result on how the source covariance matrix and the relay matrix can be jointly optimized to maximize the source-destination capacity. It is shown that the optimal coordinate system governed by the previously discovered relay matrix is still valid under the joint optimization, and the joint optimization yields a further capacity gain when the SNR at the relay is low
A scalable system architecture is proposed and demonstrated for spatial multiplexing over millimeter-wave line-of-sight communication links. This architecture provides increased data capacity without increasing the channel bandwidth. The modulation format is simple (BPSK or QPSK); this facilitates high-rate operation. The spatially multiplexed channels are separated at the receiver using broadband adaptive analog I/Q vector signal processing, a technique which should readily scale to data rates exceeding 10 Gb/s per channel. A control loop continuously tunes the channel separation electronics to correct for changes with time in either the propagation environment or the system components. Design and characterization of a four channel 60 GHz hardware prototype is presented.