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Joint Estimation of Direct and RIS-assisted Channels with Tensor Signal Modelling
... To find the elements of the FIM Υ, we need to calculate the second order partial derivatives (hessian matrix) of the loglikelihood function L(θ) with respect to each of the channel parameters θ as shown in (40), and take the expectation with respect to the corresponding noise tensor unfoldings. With (36) and (37), the partial derivatives of L(θ) in (38) and (39) with respect to a single channel parameter are: ...
Channel estimation is one of the main challenges for reconfigurable intelligent surface (RIS) assisted communication systems with passive reflective elements due to the high number of parameters to estimate. In this paper, we consider channel estimation for a MIMO FD RIS-assisted wireless communication system and use tensor (multidimensional array) signal modelling techniques to estimate all channel state information (CSI) involving the self-interference, direct-path, and the RIS assisted channel links. We model the received signal as a tensor composed of two CANDECOMP/PARAFAC (CP) decomposition terms for the non-RIS and the RIS assisted links. Based on this model we extend the alternating least squares algorithm to jointly estimate all channels, then derive the corresponding Cramér-Rao Bounds (CRB). Numerical results show that compared to recent previous works which estimate the non-RIS and RIS links during separate training stages, our method provides a more accurate estimate by efficiently using all pilots transmitted throughout the full training duration without turning the RIS off when comparing the same number of total pilots transmitted. For a sufficient number of transmitted pilots, the proposed method’s accuracy comes close to the CRB for the RIS channels and attains the CRB for the direct-path and self-interference channels.
The continuous evolution of wireless communication systems has driven the need for innovative signal processing and modeling techniques to enhance their performance, reliability, and scalability. This article explores the integration of advanced signal modeling and processing innovations within wireless communication systems, focusing on the contributions from the field of computer science. Tensor modeling, due to its ability to represent multi-dimensional data, offers a significant advantage in handling the complexities of modern communication systems, such as multi-path fading and interference. Furthermore, advanced signal processing techniques, including machine learning-based methods, are crucial in optimizing wireless networks. This article delves into the theoretical foundations of wireless communication, the application of multi-domain approaches, and the role of signal processing in improving system efficiency.
Tensor decomposition techniques have emerged as pivotal tools in multi-dimensional data analysis, enabling researchers to uncover latent structures and extract meaningful patterns from high-dimensional datasets. Among these methods, Alternating Least Squares (ALS) has gained prominence for its efficiency and adaptability across various applications, including signal processing, machine learning, and bioinformatics. This paper explores the fundamental principles of tensor decomposition, with a focus on the CANDECOMP/PARAFAC (CP) and Tucker models and evaluates the role of ALS in achieving computationally efficient solutions. Key challenges such as convergence issues, scalability, and optimization in noisy or sparse data environments are addressed, along with emerging innovations aimed at overcoming these limitations. By integrating theoretical insights and practical applications, this study highlights the transformative potential of ALS-driven tensor decomposition in enhancing the interpretability and utility of complex datasets, paving the way for advancements in multi-modal data fusion and real-time analytics.
Using reconfigurable intelligent surfaces (RISs) to improve the coverage and the data rate of future wireless networks is a viable option. These surfaces are constituted of a significant number of passive and nearly passive components that interact with incident signals in a smart way, such as by reflecting them, to increase the wireless system's performance as a result of which the notion of a smart radio environment comes to fruition. In this survey, a study review of RIS‐assisted wireless communication is supplied starting with the principles of RIS which include the hardware architecture, the control mechanisms, and the discussions of previously held views about the channel model and pathloss; then the performance analysis considering different performance parameters, analytical approaches and metrics are presented to describe the RIS‐assisted wireless network performance improvements. Despite its enormous promise, RIS confronts new hurdles in integrating into wireless networks efficiently due to its passive nature. Consequently, the channel estimation for, both full and nearly passive RIS and the RIS deployments are compared under various wireless communication models and for single and multi‐users. Lastly, the challenges and potential future study areas for the RIS aided wireless communication systems are proposed.
Reconfigurable Intelligent Surfaces (RISs) have been recently considered as an energy-efficient solution for future wireless networks due to their fast and low-power configuration, which has increased potential in enabling massive connectivity and low-latency communications. Accurate and low-overhead channel estimation in RIS-based systems is one of the most critical challenges due to the usually large number of RIS unit elements and their distinctive hardware constraints. In this paper, we focus on the uplink of a RIS-empowered multi-user Multiple Input Single Output (MISO) uplink communication systems and propose a channel estimation framework based on the parallel factor decomposition to unfold the resulting cascaded channel model. We present two iterative estimation algorithms for the channels between the base station and RIS, as well as the channels between RIS and users. One is based on alternating least squares (ALS), while the other uses vector approximate message passing to iteratively reconstruct two unknown channels from the estimated vectors. To theoretically assess the performance of the ALS-based algorithm, we derived its estimation Cramér-Rao Bound (CRB). We also discuss the downlink achievable sum rate computation with estimated channels and different precoding schemes for the base station. Our extensive simulation results show that our algorithms outperform benchmark schemes and that the ALS technique achieves the CRB. It is also demonstrated that the sum rate using the estimated channels always reach that of perfect channels under various settings, thus, verifying the effectiveness and robustness of the proposed estimation algorithms.
A realistic performance assessment of any wireless technology requires the use of a channel model that reflects its main characteristics. The independent and identically distributed Rayleigh fading channel model has been (and still is) the basis of most theoretical research on multiple antenna technologies in scattering environments. This letter shows that such a model is not physically appearing when using a reconfigurable intelligent surface (RIS) with rectangular geometry and provides an alternative physically feasible Rayleigh fading model that can be used as a baseline when evaluating RIS-aided communications. The model is used to revisit the basic RIS properties, e.g., the rank of spatial correlation matrices and channel hardening.
The exponential traffic growth of wireless communication
networks gives rise to both the insufficient network
capacity and excessive carbon emissions. Massive multiple-input multiple-output (MIMO) can improve the spectrum efficiency
(SE) together with the energy efficiency (EE) and has been
regarded as a promising technique for the next generation
wireless communication networks. Channel model reflects the
propagation characteristics of signals in radio environments and
is very essential for evaluating the performances of wireless communication
systems. The purpose of this paper is to investigate
the state of the art in channel models of massive MIMO. First,
the antenna array configurations are presented and classified,
which directly affect the channel models and system performance.
Then, measurement results are given in order to reflect the
main properties of massive MIMO channels. Based on these
properties, the channel models of massive MIMO are studied
with different antenna array configurations, which can be used
for both theoretical analysis and practical evaluation.
We consider the problem of channel estimation in a multiple-input-multiple-output (MIMO) full-duplex (FD) wireless communication system assisted by a reconfigurable intelligent surface (RIS) with hardware impairments (HI) occurring at the transceivers and RIS elements. We propose an unbiased channel estimator that requires knowledge of only the first and second order statistics of the HI, for which we derive closed form expressions. The proposed estimator reduces to the maximum likelihood estimator (MLE) in the case of ideal hardware. We also describe FD and HD orthogonal pilot schemes that minimize the mean square error of the MLE in the case of ideal hardware. We verify the performance of the estimator under varying conditions of transceiver and RIS HI via numerical simulations.
Intelligent reflecting surface (IRS) is a promising technology for the
generation of wireless systems, realizing the smart radio environment concept. This paper presents a novel tensor-based receiver for IRS-assisted multiple-input multipleoutput communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. A semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. We first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved-IRS-base station and user terminal-IRS-communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. We also formulate an enhanced two-stage semiblind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In particular, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Numerical results are proposed for performance evaluation in several system settings in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate, corroborating the merits of the proposed semi-blind receiver in comparison to competing methods.
Optimally extracting the advantages available from reconfigurable intelligent surfaces (RISs) in wireless communications systems requires estimation of the channels to and from the RIS. The process of determining these channels is complicated when the RIS is composed of passive elements without any sensing or data processing capabilities, and thus, the channels must be estimated indirectly by a noncolocated device, typically a controlling base station (BS). In this article, we examine channel estimation for passive RIS-based systems from a fundamental viewpoint. We study various possible channel models and the identifiability of the models as a function of the available pilot data and behavior of the RIS during training. In particular, we will consider situations with and without line-of-sight propagation, single-antenna and multi-antenna configurations for the users and BS, correlated and sparse channel models, single-carrier and wideband orthogonal frequency-division multiplexing (OFDM) scenarios, availability of direct links between the users and BS, exploitation of prior information, as well as a number of other special cases. We further conduct simulations of representative algorithms and comparisons of their performance for various channel models using the relevant Cramér-Rao bounds.
The reconfigurable intelligent surface (RIS) with low hardware cost and energy consumption has been recognized as a potential technique for future 6G communications to enhance coverage and capacity. To achieve this goal, accurate channel state information (CSI) in RIS assisted wireless communication system is essential for the joint beamforming at the base station (BS) and the RIS. However, channel estimation is challenging, since a large number of passive RIS elements cannot transmit, receive, or process signals. In the first part of this invited paper, we provide an overview of the fundamentals, solutions, and future opportunities of channel estimation in the RIS assisted wireless communication system. It is noted that a new channel estimation scheme with low pilot overhead will be provided in the second part of this letter.
Intelligent reflecting surface (IRS) is an emerging technology for future wireless communications including 5G and especially 6G. It consists of a large 2D array of (semi-)passive scattering elements that control the electromagnetic properties of radio-frequency waves so that the reflected signals add coherently at the intended receiver or destructively to reduce co-channel interference. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. In this paper, we address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach aiming at the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factor (PARAFAC) tensor modeling of the received signals. The first one has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel, by solving rank-1 matrix approximation problems, while the second on is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station-IRS and IRS-user terminal), which provides performance enhancements in comparison to competing methods that are based on unstructured LS estimates of the cascaded channel. Design recommendations for both methods that guide the choice of the system parameters are discussed. Numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions.
Intelligent reflecting surface (IRS) consisting of massive passive elements is a promising technology to save the hardware cost and energy consumption, but with a challenging channel estimation of IRS transmission links. In this letter, a low-complexity channel estimation method is first proposed for IRS-enhanced multi-user massive multiple-input and multiple-output systems, which can attain the separate channel state information (CSI) of the cascaded link. The acquisition of the separate CSI contributes to the flexibility of channel estimations for the multi-user case with user mobility. The proposed channel estimation consists of direction-of-arrival and path gain estimations, which are implemented by using the limited radio frequency chains and pilots, respectively. Besides, the computational complexity is analyzed for the proposed and existing methods for comparison. Numerical results show that the proposed method can achieve accurate channel estimation with a low complexity.
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N 3) have applications in psychomet- rics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank- one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
Unlike low-rank matrix decomposition, which is generically
nonunique for rank greater than one, low-rank three-and higher
dimensional array decomposition is unique, provided that the array rank
is lower than a certain bound, and the correct number of components
(equal to array rank) is sought in the decomposition. Parallel factor
(PARAFAC) analysis is a common name for low-rank decomposition of higher
dimensional arrays. This paper develops Cramer-Rao bound (CRB) results
for low-rank decomposition of three- and four-dimensional (3-D and 4-D)
arrays, illustrates the behavior of the resulting bounds, and compares
alternating least squares algorithms that are commonly used to compute
such decompositions with the respective CRBs. Simple-to-check necessary
conditions for a unique low-rank decomposition are also provided