The accurate approximation of multivariate functions is fundamental to high-dimensional data analysis. Among various strategies, tensor-based methods have been widely explored to address the curse of dimensionality for scalable and efficient approximation. While traditional techniques employ either structured tensor-product grid discretization or coefficient tensor factorization, they face two critical limitations: (1) limited adaptability to irregular data structures common in real-world applications and (2) dependence on manually designed basis functions that restrict flexibility and require substantial domain expertise. This paper introduces the Implicit Neural Functional Tensor Train (INFTT), which couples functional tensor–train decomposition with implicit neural representations to obtain continuous, low-rank approximations of multivariate functions. Specifically, instead of manual basis design, we parameterize each univariate core with a SIREN-based implicit network, preserving the chain structure while enabling adaptive, high-fidelity modeling. Our theoretical analysis demonstrates that INFTT inherently embeds low-rank structural priors and Lipschitz continuity, ensuring compact and smooth approximations. Extensive experiments on synthetic and real-world scientific datasets validate the superior accuracy and robustness of the proposed method compared to state-of-the-art approaches for both discretized and continuous representations.

Reconfigurable intelligent surface (RIS) is a recent low-cost and energy-efficient technology with potential applicability for future wireless communications. Performance gains achieved by employing RIS directly depend on accurate channel estimation (CE). It is common in the literature to assume channel reciprocity since it minimizes channel feedback, simplifies the beamforming design, and reduces the overall latency. However, in practice, due to hardware limitations at the RIS and transceivers, the channel non-reciprocity may occur naturally, so such behavior needs to be considered. In this paper, we focus on the CE problem in a non-reciprocal RIS-assisted multipleinput multiple-output (MIMO) wireless communication system. Making use of a novel closed-loop three-phase protocol for non-reciprocal CE estimation, we propose a two-stage fourthorder Tucker decomposition-based CE algorithm. In contrast to classical time-division duplexing (TDD) and frequency-division duplexing (FDD) approaches the proposed method concentrates all the processing burden for CE on the base station (BS) side, thereby freeing hardware-limited user terminal (UT) from this task. Our simulation results show that the proposed method has satisfactory performance in terms of CE accuracy compared to benchmark FDD LS-based and tensor-based techniques.

Recent research has focused on advanced architectures for reconfigurable intelligent surfaces (RIS) incorporating sensing capabilities. A notable development is the hybrid simultaneously sensing and reflecting RIS (HRIS), which integrates both sensing and reflecting meta-atoms. This design endows HRIS with signal processing abilities to tackle the channel estimation challenge. This work develops a closed-form semi-blind receiver pair for HRIS-assisted multiple-input multiple-output wireless communications, leveraging HRIS for joint symbol detection and channel estimation under a tensor space-time coding. By transmitting information symbols instead of pilots during the CE stage, our data-aided method reduces decoding delay while estimating symbols at a low computational cost. Simulation results show competitive performance in terms of normalized mean square error and symbol error rates compared to existing solutions, highlighting the effectiveness of enabling semi-blind estimation at both the HRIS and BS. Furthermore, data estimation directly at the HRIS opens new opportunities and use cases for HRIS/RISassisted communications.

In this paper, we consider a double-RIS (D-RIS)-aided flat-fading MIMO system and propose an interference-free channel training and estimation protocol, where the two single-reflection links and the one double-reflection link are estimated separately. Specifically, by using the proposed training protocol, the signal measurements of a particular reflection link can be extracted interference-free from the measurements of the superposition of the three links. We show that some channels are associated with two different components of the received signal.Exploiting the common channels involved in the single and double reflection links while recasting the received signals as tensors, we formulate the coupled tensor-based least square Khatri–Rao factorization (C-KRAFT) algorithm which is a closed-form solution and an enhanced iterative solution with less restrictions on the identifiability constraints, the coupled-alternating least square (C-ALS) algorithm. The C-KRAFT and C-ALS based channel estimation schemes are used to obtain the channel matrices in both single and double reflection links.We show that the proposed coupled tensor decomposition-based channel estimation schemes offer more accurate channel estimates under less restrictive identifiability constraints compared to competing channel estimation methods. Simulation results are provided showing the effectiveness of the proposedalgorithms.

This paper proposes a pilot decoupling-based two-dimensional channel parameter estimation method for intelligent reflecting surface (IRS)-assisted networks. We exploit the combined effect of Terahertz sparse propagation and the geometrical structure of arrays deployed at the base station, the IRS, and the user equipment to develop a low-complexity channel parameter estimation method. By means of a new pilot design along the horizontal and vertical directions, the overall channel parameter estimation problem is decoupled into different domains. Furthermore, with this decoupling, it is possible to simultaneously sense/estimate the channel parameters and to communicate with the sensed node. Specifically, we formulate two estimators by decoupling the global problem into sub-problems and exploiting the built-in tensor structure of the sensing/estimation problem by means of multiple rank-one approximations for rank-one and low-rank channels. The Cramér-Rao lower bound is derived to assess the performance of the proposed estimators. We show that our two proposed methods yield accurate parameter estimates and outperform state-of-the-art methods in terms of complexity. The tradeoffs between performance and complexity offered by the proposed methods are discussed and numerically assessed.

This paper addresses the direction-of-arrival (DOA) estimation problem of mixed coherent and uncorrelated signals using a sparse rectangular array, where tensor reconstruction is employed to preserve the structure of multi-dimensional array signals. In the proposed approach, we first estimate the DOAs of uncorrelated signals using the subspace algorithm. After eliminating the contribution of uncorrelated signals from the covariance tensor, a structural tensor decorrelation process is introduced to decorrelate the resulting coherent covariance tensor. The canonical polyadic decomposition method is employed to the decorrelated covariance tensor to detect the coherent signals. The conditions of signal resolvability are analyzed.

Despite the rapid advancements in 5G technology, accurately assessing the energy consumption of its Radio Ac-cess Networks (RANs) remains a challenge due to the diverse range of applicable technologies and implementation solutions. Designing a versatile power model for estimating the 5G RAN-specific power consumption requires extensive data collection and experimental studies to capture the diverse range of technolo-gies and implementation solutions. The objective is to outline a versatile energy model capable of estimating RAN-specific energy consumption, encompassing both mobile terminals and the physical layer (PHY) of base stations. In this paper, we focus on the computational complexity of the baseband part of the model. The developed (part of the) model is compared with the estimation of the number of cycles (and energy per cycle) used by a specific implementation (here a Matlab code ported on an Intel target), enabling the assessment of the model with the estimation of energy consumed on a real target. The study's results show a good agreement between the model and the implementation, even if some parts need to be refined to take specific algorithms into account. The key contribution is the development of an initial flexible energy model with finer granularity, enabling comparisons of energy use across various applications and contexts, and offering a comprehensive tool for optimizing 5G network energy consumption.

In this paper, we present a precoder design for multi-user multiple-input multiple-output (MU-MIMO) broadcast systems with rate splitting at the transmitter. The proposed scheme applies to both underloaded and overloaded communication systems and supports the transmission of multiple common and private streams. We show how the generalized singular value (GSVD) and multilinear generalized singular value (ML-GSVD) decompositions can be used to define the number of common and private streams and adjust the message split. Additionally, we present transmit precoding and receive combining designs that allow the simultaneous transmission of common and private streams but do not require successive interference cancellation (SIC) at the receivers and can be used in cases where the total number of streams does not exceed the number of transmit antennas.

Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a phenomenon known as the “curse of the dimensionality”. The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are known as the gold standard for computing the range span of the factor matrices of a Tucker Decomposition but also suffer from the curse. In this paper, we propose a new methodology with a similar estimation accuracy as the HOSVD with non-exploding computational and storage costs. If the noise-free data follows a Tucker decomposition, the corresponding Tensor Train (TT) decomposition takes a remarkable specific structure. More precisely, we prove that for a$Q$-order Tucker tensor, the corresponding TT decomposition is constituted by$Q-3$3-order TT-core tensors that follow a Constrained Canonical Polyadic Decomposition. Using this new formulation and the coupling property between neighboring TT-cores, we propose a JIRAFE-type scheme for the Tucker decomposition, called TRIDENT. Our numerical simulations show that the proposed method offers a drastically reduced complexity compared to the HOSVD and HOOI while outperforming the Fast Multilinear Projection (FMP) method in terms of estimation accuracy.

Hybrid analog/digital (A/D) beamforming architectures are low complexity alternatives to fully digital designs in large antenna setups. Recent research efforts have been set out to find low-complexity algorithms, which have low implementation complexity in the analog domain. In this paper, we propose a two-stage hybrid precoding design assuming hardware constraints that avoid the use of adaptive phase-shifters (PSs) by introducing a novel combination of Butler matrices (BMs) to feed a uniform planar array (UPA). With several fixed beams, we propose an algorithm to design the analog precoding matrix in the first stage, while in the second stage, hybrid-beamforming (HBF)-weighted minimum mean square error (WMMSE) is proposed for baseband precoding by taking into account the analog precoding matrix designed in the first stage. The proposed algorithm shows fast convergence, thanks to the analog precoder design, which helps the HBF-WMMSE algorithm to converge within a few iterations. Compared with the classical matched filter (MF) and minimum mean square error (MMSE) solutions, HBF-WMMSE outperforms the latter in terms of sum-rate, especially in the low signal-to-noise-ratio (SNR) regime. Simulation results further show that the partially connected Butler matrices (PCBMS) approach implemented with fixed-PSs exhibit superior energy-efficiency while maintaining higher spectral-efficiency as compared to the partially connected analog phase shifting (PCAPS) network implemented with variable-PSs.

Intelligent reconfigurable surface IRS are becoming an attractive component of cellular networks due to their ability to shape the propagation environment and thereby improve coverage. While IRS nodes incorporate a great number of phase-shifting elements and a controller entity, the phase shifts are typically determined by the cellular base station (BS) due to its computational capability. Since controlling a large number of phase shifts may become prohibitive in practice, it is important to reduce the control overhead between the BS and the IRS controller. To this end, in this paper, we propose a low-rank modeling approach for the IRS phase shifts. The key idea is to represent the IRS phase shift vector using a low-rank tensor approximation model, where each rank-one component is modeled as the Kronecker product of a predefined number of factors of smaller sizes, obtained via tensor decomposition algorithms. We show that the proposed low-rank models drastically reduce the required feedback requirements associated with the BS-IRS control links. Our simulation results indicate that the proposed method is especially attractive in scenarios with a strong line of sight component, in which case nearly the same spectral efficiency is reached as in the cases with near-optimal phase shifts, but with significantly lower feedback overhead.

In this paper, we propose a rank-one tensor modeling approach that yields a compact representation of the optimum intelligent reconfigurable surface (IRS) phase-shift vector for reducing the feedback overhead. The main idea consists of factorizing the IRS phase-shift vector as a Kronecker product of smaller vectors, namely factors. The proposed phase-shift model allows the network to trade-off between achievable data rate and feedback reduction by controling the factorization parameters. Our simulations show that the proposed phase-shift factorization drastically reduces the feedback overhead, while improving the data rate in some scenarios, compared to the state-of-the-art schemes.

Reconfigurable intelligent surfaces (RISs) have been proposed recently as new technology to tune the wireless propagation channels in real-time. However, most of the current works assume single-RIS (S-RIS)-aided systems, which can be limited in some application scenarios where a transmitter might need a multi-RIS-aided channel to communicate with a receiver. In this paper, we consider a double-RIS (D-RIS)-aided MIMO system and propose an alternating least-squares-based channel estimation method by exploiting the Tucker2 tensor structure of the received signals. Using the proposed method, the cascaded MIMO channel parts can be estimated separately, up to trivial scaling factors. Compared with the S-RIS systems, we show that if the RIS elements of an S-RIS system are distributed carefully between the two RISs in a D-RIS system, the training overhead can be reduced and the estimation accuracy can also be increased. Therefore, D-RIS systems can be seen as an appealing approach to further increase the coverage, capacity, and efficiency of future wireless networks compared to S-RIS systems.

In this paper, a coarray tensor completion-based direction-of-arrival (DOA) estimation method is proposed for coprime planar array. To perform Nyquist-matched coarray signal processing, the completion of the coarray tensor corresponding to an augmented discontinuous virtual array is pursued. However, it is difficult to impose a low-rank regularization on the incomplete coarray tensor with slices of missing elements for its completion. To solve this problem, a structural tensorization approach is designed to reshape the incomplete coarray tensor into one with distributed missing elements. As such, a coarray tensor completion problem based on tensor nuclear norm minimization is formulated to complete these missing elements. By exploiting the filled virtual array obtained from the completed coarray tensor, a super-resolution DOA estimation can be achieved in closed-form.

Conventional tensor direction-of-arrival (DOA) estimation methods for sparse arrays apply canonical polyadic decomposition (CPD) to the high-order coarray covariance tensor for retrieving angle information. However, due to the low convergence rate of CPD-based algorithms for high-order tensors, these methods suffer from a high computation cost. To address this issue, a sub-Nyquist tensor train decomposition (SubTTD)-based DOA estimation method is proposed for a three-dimensional (3-D) sparse array, where an augmented virtual array is derived from the sub-Nyquist tensor statistics. To reduce computational complexity of processing the 6-D coarray covariance tensor, the proposed SubTTD model efficiently decomposes it into a train of head matrix, 3-D core tensors, and tail matrix. Based on that, a core tensor decomposition and a change-of-basis transformation for the head matrix are designed to retrieve canonical polyadic factors of the coarray covariance tensor for DOA estimation. The computational efficiency of the proposed method is theoretically analyzed, and its effectiveness is verified via simulations.

Existing works concluded that coherent transmission outperforms non-coherent transmission in the downlink of cell-free systems when the fronthaul links have unlimited capacity. Since the capacity of the fronthaul links of cell-free networks is typically limited, in this paper we ask the question whether this conclusion holds under more realistic assumptions on the fronthaul capacity. To answer this question, we study and compare the performance of these transmission strategies by formulating novel energy efficiency (EE) maximization problems for both strategies, where we explicitly consider realistic fronthaul capacity and power consumption constraints. Despite the non-convexity of these problems, we derive closed-form equations to find suboptimal solutions of both problems using a unified framework that combines successive convex approximation and the Dinkelbach algorithm. Numerical results show that the performance of coherent transmission is severely impacted by limited fronthaul capacities, power consumption on the fronthaul links, user-centric cluster size and the number of antennas at the access points, such that in many cases non-coherent transmission achieves higher EE than coherent transmission. Based on these results, we provide deployment guidelines on when to use coherent or non-coherent transmission to maximize the EE of cell-free systems with limited fronthauls.

In this work, we propose a two-stage tensor-based receiver for joint channel, phase-noise (PN), and data estimation in MIMO-OFDM systems. First, we cast the received signal at the pilot subcarriers as a third-order PARAFAC model. Based on this model, we propose a closed-form algorithm based on the LS-KRF (Least Squares - Khatri-Rao Factorization) that estimates the channel gains and the phase-noise terms through multiple rank-one factorizations. From the estimated channel, the second stage of the receiver consists of data estimation based on a ZF (Zero-Forcing) receiver that capitalizes on the tensor structure of the received signal at the data subcarriers via a Selective Kronecker Product (SKP) approach. Our numerical simulations show that the proposed receiver achieves an improved performance compared to the state-of-art receivers.

We consider the channel estimation problem in point-to-point reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) MIMO systems. By exploiting the low-rank nature of mmWave channels in the angular domains, we propose a non-iterative Two-stage RIS-aided Channel Estimation (TRICE) framework, where every stage is formulated as a multidimensional direction-of-arrival (DOA) estimation problem. As a result, our TRICE framework is very general in the sense that any efficient multidimensional DOA estimation solution can be readily used in every stage to estimate the associated channel parameters. Numerical results show that the TRICE framework has a lower training overhead and a lower computational complexity, as compared to benchmark solutions.

In this paper, a novel two-dimensional parameter estimation method is proposed for frequency-selective millimeter-wave (mmWave) channels by probing a limited number of Kronecker products of discrete Fourier transform (DFT) beams, which are efficiently implemented in the analog domain by a novel combination of Butler matrices. The proposed strategy firstly estimates the channel parameters by using a modified parameter estimation via interpolation based on a DFT grid (PREIDG) algorithm. In a second step, high-resolution channel parameter estimation is achieved even in the low signal-to-noise-ratio (SNR) using the space-alternating generalized expectation-maximization (SAGE) algorithm. The proposed modified PREIDG algorithm outperforms state-of-the-art methods, e.g., the auxiliary beam pair (ABP) method while the SAGE algorithm achieves the derived Cramér-Rao lower bound (CRLB). Numerical results demonstrate that excellent estimation performance can be achieved for angle of departure (AoD) azimuth and elevation with addition to delay and complex path gain of each path even in the low SNR regime.

Channel estimation in hybrid analog-digital massive MIMO systems is a challenging problem due to the high channel dimension, low signal-to-noise ratio before beamforming, and reduced number of radio-frequency chains. Compressed sensing based algorithms have been adopted to address these challenges by leveraging the sparse nature of millimeter-wave MIMO channels. In compressed sensing-based methods, the training vectors should be designed carefully to guarantee recoverability. Although using random vectors has an overwhelming recoverability guarantee, it has been recently shown that an optimized update, which could be obtained so that the mutual coherence of the resulting sensing matrix is minimized, can improve the recoverability guarantee. In this paper, we propose an openloop hybrid analog-digital beam-training framework, where a given sensing matrix is decomposed into analog and digital beamformers. The given sensing matrix can be designed efficiently offline to reduce computational complexity. Simulation results show that the proposed training method achieves a lower mutual coherence and an improved channel estimation performance than the other benchmark methods.

In this paper, we propose a new Multilinear Generalized Singular Value Decomposition (ML-GSVD) which allows to jointly factorize a set of matrices with one common dimension. The ML-GSVD is an extension of the Generalized Singular Value Decomposition (GSVD) for more than two matrices. In comparison with other approaches that extend the GSVD, the proposed tensor decomposition preserves the essential properties of the original GSVD, such as orthogonality of the second mode factor matrices. In this work, we introduce two algorithms to compute the ML-GSVD. In addition, we present an application of the ML-GSVD to compute the beamforming matrices for the multi-user MIMO downlink channel with more than two users in wireless communications.

Over the last two decades, tensor‐based methods have received growing attention in the signal processing community. In this work, the authors proposed a comprehensive overview of tensor‐based models and methods for multisensor signal processing. They presented for instance the Tucker decomposition, the canonical polyadic decomposition, the tensor‐train decomposition (TTD), the structured TTD, including nested Tucker train, as well as the associated optimisation strategies. More precisely, they gave synthetic descriptions of state‐of‐the‐art estimators as the alternating least square (ALS) algorithm, the high‐order singular value decomposition (HOSVD), and of more advanced algorithms as the rectified ALS, the TT‐SVD/TT‐HSVD and the Joint dImensionally Reduction and Factor retrieval Estimator scheme. They illustrated the efficiency of the introduced methodological and algorithmic concepts in the context of three important and timely signal processing‐based applications: the direction‐of‐arrival estimation based on sensor arrays, multidimensional harmonic retrieval and multiple‐input–multiple‐output wireless communication systems.

To achieve a reliable communication with short data blocks, we propose a novel decoding strategy for Kronecker-structured constant modulus signals that provides low bit error ratios (BERs) especially in the low energy per bit to noise power spectral density ratio (Eb/No). The encoder exploits the fact that any M-PSK constellation can be factorized as Kronecker products of lower or equal order PSK constellation sets. A construction of two types of schemes is first derived. For such Kronecker-structured schemes, a conceptually simple decoding algorithm is proposed, referred to as Kronecker-RoD (rank-one detector). The decoder is based on a rank-one approximation of the “tensorized” received data block, has a built-in noise rejection capability and a smaller implementation complexity than state-of-the-art detectors. Compared with convolutional codes with hard and soft Viterbi decoding, Kronecker-RoD outperforms the latter in BER performance at same spectral efficiency.

Channel state information (CSI) estimation in hybrid analog-digital (HAD) millimeter-wave (mmWave) massive MIMO systems is a challenging problem due to the high channel dimension and reduced number of radio-frequency chains. However, exploiting the channel sparsity, several methods have been proposed leveraging the compressed sensing (CS) tools. Most of the prior works consider an approximate CS formulation by assuming that the channel parameters lie perfectly on a finite grid neglecting the grid mismatch effect. To resolve this issue, we propose a gridless CS approach that exploits the antenna array geometry. The proposed algorithm is based on an alternating optimization technique and is guaranteed to converge to a local minimum. Simulation results are provided to evaluate the effectiveness of the proposed algorithm.

Millimeter wave multiple-input-multiple-output (MIMO) achieves the best performance when reliable channel state information is used to design the beams. Most channel estimation methods proposed in the literature, however, ignore practical hardware impairments such as carrier frequency offset (CFO) and may fail under such impairment. In this paper, we present a joint CFO and channel estimation method based on tensor modeling and compressed sensing. Simulation results indicate that the proposed method yields better channel recovery performance than the benchmark and that it is more robust to a small number of channel measurements.

This study proposes a semi‐blind receivers for two‐way multiple‐input multiple‐output (MIMO) relaying systems capable of jointly estimating the channels and symbols in a direct‐data approach. Resorting to a Khatri‐Rao coding scheme applied at both uplink and downlink transmission phases, the authors show that the signals received at the relay and user node are third‐order tensors satisfying the parallel factor (PARAFAC) and PARATUCK2 models, respectively. Combining these two tensor models, a semi‐blind receiver based on an integrated alternating least squares algorithm is proposed to estimate the channels and symbols transmitted by the user nodes without training sequences. The effectiveness of the proposed semi‐blind receiver is corroborated with numerical results, which show that the proposed semi‐blind receiver outperforms state‐of‐the‐art two‐stage training sequence estimator, while operating close to the tensor‐based channel estimator.

Future cellular systems will likely employ massive bi‐dimensional arrays to improve performance by large array gain and more accurate spatial filtering, motivating the design of low‐complexity signal‐processing methods. The authors propose optimising a Kronecker‐separable beamforming filter that takes advantage of the bi‐dimensional array geometry to reduce computational costs. The Kronecker factors are obtained using two strategies: alternating optimisation and sub‐array minimum mean square error (MMSE) beamforming with Tikhonov regularisation. According to the simulation results, the proposed methods are computationally efficient but come with source recovery degradation, which becomes negligible when the sources are sufficiently separated in space.

In this letter, we present two closed-form semiblind receivers for a two-way amplify-and-forward relaying system. The proposed receivers jointly estimate the symbol and channel matrices involved in the two-way relaying system by exploiting tensor structures of the received signals at the relay and the destination, and without using training sequences, in contrast to previous works. Differently from competing receivers, one of the proposed receivers does not require channel reciprocity between uplink and downlink phases, which can be of interest in frequency division duplexing relaying systems. Parameter identifiability and computational complexity are analyzed, and simulation results are provided to corroborate the effectiveness of the proposed semiblind receivers in scenarios with and without channel reciprocity.

In this paper, we address the problem of joint downlink (DL) and uplink (UL) channel estimation for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. Assuming a closed-loop and multifrequency-based channel training framework in which pilot signals received by multiple antenna mobile stations (MSs) are coded and spread in the frequency domain via multiple adjacent subcarriers, we propose two tensor-based semiblind receivers by capitalizing on the multilinear structure and sparse feature of the received signal at the BS equipped with a hybrid analog-digital beamforming (HB) architecture. As a first processing stage, the joint estimation of the compressed DL and UL channel matrices can be obtained in an iterative way by means of an alternating least squares (ALS) algorithm that capitalizes on a parallel factors model for the received signals. Alternatively, for more restricted scenarios, a closed-form solution is also proposed. From the estimated effective channel matrices, the users’ channel parameters such as angles of departure (AoD), angles of arrival (AoA), and path gains are then estimated in a second processing stage by solving independent compressed sensing (CS) problems (one for each MS). In contrast to the classical approach in the literature, in which the DL and UL channel estimation problems are usually considered as two separate problems, our idea is to jointly estimate both the DL and UL channels as a single problem by concentrating most of the processing burden for channel estimation at the BS side. Simulation results demonstrate that the proposed receivers achieve a performance close to the classical approach that is applied on DL and UL communication links separately, with the advantage of avoiding complex computations for channel estimation at the MS side as well as dedicated feedback channels for each MS, which are attractive features for massive MIMO systems.

Applications of direction of arrival (DoA) techniques have dramatically increased in various areas ranging from the traditional wireless communication systems and rescue operations to GNSS systems and drone tracking. Particularly, police forces and security companies have drawn their attention to drone tracking devices, in order to provide the safeness of citizens and of clients, respectively. In this paper, we propose a low cost antenna array based drone tracking device for outdoor environments. The proposed solution is divided into hardware and software parts. The hardware part of the proposed device is based on off-the-shelf components such as an omnidirectional antenna array, a 4-channel software defined radio (SDR) platform with carrier frequency ranging from 70 MHz to 6 GHz, a FPGA motherboard, and a laptop. The software part includes algorithms for calibration, model order selection (MOS), and DoA estimation, including specific preprocessing steps and a tensor-based estimator to increase the DoA accuracy. We evaluate the performance of our proposed low cost solution in outdoor scenarios. According to our measurement campaigns, we show that when the array is in the front fire position, i.e., with a DoA ranging from -60° to 60° , the maximum and the average DoA errors are 6° and 1,9°, respectively.

Tensor contraction is a multilinear algebra operator that defines an inner product between two tensors with compatible dimensions. In this work, we show that the MIMO-OFDM (Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing) received signal can be modeled by means of the tensor contraction operator. This tensor model is obtained without requiring additional spreading and provides a new, compact, and flexible formulation of a MIMO-OFDM system. Moreover, exploiting it at the receiver side facilitates the design of several types of receivers based on iterative LS (Least Squares) or recursive LS. We compare the proposed iterative and recursive LS based receivers with and without enumeration and show their advantages over the traditional ZF -FFT (Zero Forcing - Fast Fourier Transform) receiver for MIMO OFDM. This structured tensor model also opens new research directions. Moreover, our generalized tensor contraction formulation can be extended to different multi-carrier MIMO systems.

Massive multiple-input multiple-output (MIMO) theoretical performance results have attracted the attention of the community due to the possibility of increasing the spectral efficiency in wireless communications. The performance potential is mainly conditioned to the use of digital beamforming techniques which demand one radio-frequency (RF) chain per antenna element. For large arrays, this implementation may result in high complexity, power consumption, and cost. To reduce the number of RF chains, we use a hybrid beamforming (HB) architecture of an analog beamformer implemented by using phase-shifters and a low-dimensional digital beamformer. The performance of the HB depends on the resolution of the phase-shifters. However, very few works in the literature take into account finite phase-shifters. In this paper, we address the problem of designing HB in frequency selective channels using finite-resolution phase-shifters. The strategy is to exploit the second-order statistics of the channel and a least-square formulation to obtain the discrete phase of each phase-shifter. The digital part is derived based on analog solution to maximize the single-user MIMO system sum-rate. This solution requires a number of RF chains compared to the rank of the spatial covariance matrix which is far lower than ones demanded to implement the full digital beamforming. The simulation results show that the proposed technique can achieve a sum-rate performance very close to that of the digital beamforming assuming low-rank channels.

In this letter, we present a sequential closed-form semiblind receiver for a one-way multihop amplify-and-forward relaying system. Assuming Khatri-Rao space-time coding at each relay, it is shown that the system with K relays can be modeled by means of a generalized nested PARAFAC model. Decomposing this model into K + 1 third-order PARAFAC models, we develop a closed-form semiblind receiver for jointly estimating the information symbols and the individual channels, at the destination node. Each step consists of a Khatri-Rao factorization. Parameter identifiability conditions are given, and simulation results are provided to illustrate the effectiveness of the proposed semiblind receiver.

In the past few years, multidimensional array processing emerged as the generalization of classic array signal processing. Tensor methods exploiting array multidimensionality provided more accurate parameter estimation and consistent modeling. In this paper, multilinear translation invariant arrays are studied. An M-dimensional translation invariant array admits a separable representation in terms of a reference subarray and a set of M - 1 translations, which is equivalent to a rank-1 decomposition of an Mth order array manifold tensor. We show that such a multilinear translation invariant property can be exploited to design tensor beamformers that operate multilin-early on the subarray level instead of the global array level, which is usually the case with a linear beamforming. An important reduction of the computational complexity is achieved with the proposed tensor beamformer with a negligible loss in performance compared to the classical minimum mean square error (MMSE) beamforming solution.

Massive multiple‐input multiple‐output technology has been considered a breakthrough in wireless communication systems. It consists of equipping a base station with a large number of antennas to serve many active users in the same time–frequency block. Among its underlying advantages is the possibility to focus transmitted signal energy into very short‐range areas, which will provide huge improvements in terms of system capacity. However, while this new concept renders many interesting benefits, it brings up new challenges that have called the attention of both industry and academia: channel state information acquisition, channel feedback, instantaneous reciprocity, statistical reciprocity, architectures, and hardware impairments, just to mention a few. This paper presents an overview of the basic concepts of massive multiple‐input multiple‐output, with a focus on the challenges and opportunities, based on contemporary research.

We propose a noniterative algorithm, called SeROAP,1 to estimate a rank-1 approximation of a tensor in the real or complex field. Our algorithm is based on a sequence of singular value decompositions followed by a sequence of projections onto Kronecker vectors. For three-way tensors, we show that our algorithm is always at least as good as the state-of-the-art truncation algorithm, ST-HOSVD,2in terms of approximation error. Thus, it gives a good starting point to iterative rank-1 tensor approximation algorithms. By means of computational experiments, it also turns out that for fourth order tensors, SeROAP yields a better approximation with high probability when compared to the standard THOSVD3algorithm.

In this letter, we consider a one-way two-hop AF relaying scheme employing two independent Khatri-Rao space-time (KRST) codings at the source and relay nodes. The signals received at destination form a fourth-order tensor whose dimensions correspond to four signal diversities, and which satisfies a nested PARAFAC model. Exploiting this nested structure, we derive two matrix unfoldings expressed in terms of two Khatri-Rao products which are used to propose a closed-form semi-blind receiver allowing to jointly estimate the information symbols and the individual channels. A numerical analysis shows that this new receiver achieves a substantial computational complexity reduction over an iterative (ALS-based) semi-blind receiver, especially in presence of a great number of source and/or relay antennas.

The Canonical Polyadic (CP) tensor decomposition has become an attractive mathematical tool these last ten years in various fields. Yet, efficient algorithms are still lacking to compute the full CP decomposition, whereas rank-one approximations are rather easy to compute. We propose a new deflation-based iterative algorithm allowing to compute the full CP decomposition, by resorting only to rank-one approximations. An analysis of convergence issues is included, as well as computer experiments. Our theoretical and experimental results show that the algorithm converges almost surely.

We propose a novel joint channel estimator for a relaying MIMO communication system. Considering a three-hop relaying protocol, our combined alternating least squares (Comb-ALS) algorithm obtains cooperative diversity by fully exploiting the tensor algebraic structures of the available cooperative MIMO links. This is achieved by coupling the tensor data for the different relay-assisted links to iteratively estimate the channel matrices. Simulation results corroborate the effectiveness of the proposed tensor-based joint channel estimator in comparison with a sequential tensor-based method and a sequential LS estimator.

Canonical Polyadic Decomposition (CPD), also known as PARAFAC, is a useful tool for tensor factorization. It has found application in several domains including signal processing and data mining. With the deluge of data faced in our societies, large-scale matrix and tensor factorizations become a crucial issue. Few works have been devoted to large-scale tensor factorizations. In this paper, we introduce a fully distributed method to compute the CPD of a large-scale data tensor across a network of machines with limited computation resources. The proposed approach is based on collaboration between the machines in the network across the three modes of the data tensor. Such a multi-modal collaboration allows an essentially unique reconstruction of the factor matrices in an efficient way. We provide an analysis of the computation and communication cost of the proposed scheme and address the problem of minimizing communication costs while maximizing the use of available computation resources.

In this paper, we consider a wireless communication scenario where M sources simultaneously transmit towards a base station equipped with an array of K sensors. A new method is proposed to solve the spatial signature estimation problem without resorting to training sequences and without knowledge of sources' covariance structure. By assuming that the sources' amplitudes vary between successive time blocks, a fourth-order tensor decomposition of the multimode spatio-temporal data covariance is proposed, from which an iterative algorithm is formulated to estimate sources' spatial signatures. A distinguishing feature of the proposed tensor method is its efficiency in treating the case where the sources' covariance matrix is non-diagonal and unknown, which generally happens when working with sample data covariances computed from a reduced number of snapshots.

Orthogonal frequency division multiplexing (OFDM) is considered as a key technology for future wireless communication systems. One of the main disadvantages of OFDM systems is the high peak‐to‐average power ratio (PAPR) of the transmitted signals. When a non‐linear power amplifier (PA) is present, the high PAPR may cause the introduction of non‐linear distortions. On the other hand, cooperative communications have emerged as a promising technology for wireless networks. A theoretical analysis of an amplify‐and‐forward OFDM system taking into consideration the non‐linear distortions introduced by a PA is done. More specifically, approximate analytical expressions for the outage probability and average symbol error rate (SER) are derived and studied under several special situations. The performance analysis sheds light on the influence of PA non‐linearity on the outage probability and the average SER of an OFDM system. Particularly, it is shown that the non‐linear PA has a more significant effect over the average SER for medium and high signal‐to‐noise ratio (SNR) values and for small‐order constellations. The analytical results are validated by means of computer simulations for different system configurations and SNR levels.

A closed-loop multiple-input multiple-output (MIMO) transceiver combining space–time multilayer precoding and transmit selection is proposed. The transmitter design consists in optimizing the number of space–time transmit layers as well as the partitioning of the transmit antennas into the selected number of space–time layers. We show that this problem can be translated into jointly selecting, from a finite alphabet, two transmit matrices that define, respectively, the multilayer space–time code and the antenna mapping to be used. The parametrization of the proposed design takes into account all possible space–time layering schemes in between spatial multiplexing and transmit diversity for a fixed number of transmit antennas and linear precoder structure. Sufficient conditions for solution existence using a linear space–time zero forcing receiver are discussed. Simulation results compare the proposed transceiver with some MIMO schemes and corroborate the benefits of closed-loop multilayer selection in terms of capacity and bit error rates. Copyright © 2012 John Wiley & Sons, Ltd.

Wireless sensor networks are evolving to hybridnetworks in which static and mobile sensor nodes cooperate in order to address challenging requirements imposed by new emerging applications. However, due to the ad hoc nature of the network and especially to resources constraints of the sensor nodes, this cooperation is not trivial, requiring a number of retransmissions thus wasting precious resources. In this paper the use of cooperative multiple input multiple output (MIMO) techniques is proposed to overcome transmission problems, ensuring a reliable and more efficient communication link with less retransmissions. Extensive simulation experiments support the proposal, and the results highlight the benefits in using MIMO to deliver messages from static to mobile nodes in wireless sensor networks.

This paper presents a comparative analysis between a bilinear decomposition (Principal Component Analysis - PCA) and a multilinear decomposition (Parallel Factor - PARAFAC) on the data obtained by the students' evaluation of teaching effectiveness in an engineering course. It is known that the teaching and learning relationship is a nonlinear process related to many fundamental subjects, which are highlighted into students' evaluation of the teaching effectiveness methodology. The comparison was made in order to know which additional knowledge is obtained when the analysis takes into account the multilinear process model of this. The results shown the importance of the latent characteristics in a students' professional formation in accordance with the results presented in the application of PARAFAC decomposition, that has been reveled as a powerful tool for data analysis in the assessment area.

Processes and evaluation methods are gaining prominence in the social and educational contexts. In this context, it is proposed to contribute to the improvement of the higher education quality, through the analysis of information obtained in six engineering courses offered by the Federal University of Ceará. The study seeks to strengthen the interface among data analysis methods typically used of engineering contexts in order to allow the analysis of the relationship between academic management processes of engineering courses and outcomes from external evaluations. This discussion aims to propose a mathematical model to support the academic management, based on multivariate analysis (MVA) and data processing, such as Principal Component Analysis (PCA). The instrument created aims to identify professors' point of view about the management practices developed in their academic courses where they work. The application of the reliability tests revealed the suitability of the sample for the application of PCA. In the PCA application, we observed the formation of three responses' clusters, that has been well characterized by the similarity of their factor loadings that are related to students' academic education, academic formation processes and institutional environment. It should stand out even that the application of MVA showed strong evidence for a relationship among the methods of management in higher education, through the manifestation of latent variables in order to define a mathematical model based on MVA academic management support.

There is a considerable number of engineering courses that suffer with failure rates and high withdrawal of students in their first year, especially in fundamental discipline areas like mathematics and science. In order to detect the educational quality indicators, a study was conducted to validate the application of Students' Evaluation of Educational Quality (SEEQ) instrument in an engineering course, using Factor Analysis (FA). The choice of FA to validate the instrument is that this method has been used to validate the SEEQ instrument from the students' point of view but using this structure does not allowed us analyze the disciplines in focus, then we need to validate this same instrument into our research context according to a latent structure performed by the disciplines. We validate the application of the factor analysis by the Kaiser-Meyer-Olkin (KMO) and Bartletts' tests that investigate the sample adequacy. After the validation of the sample adequacy, the factor analysis validate the structure of the questionnaire, and we can state that the SEEQ instrument is valid for application in a teleinformatics engineering context to analyze the disciplines. As a final result of this procedure, we guarantee the consistency of the instrument for the application to analyze different disciplines under different criterions that can possibility a deeper analysis of the curriculum structure.

This work considers a collaborative wireless sensor network where nodes locally exchange coded informative data before transmitting the combined data towards a remote fusion center equipped with an antenna array. For this communication scenario, a new blind estimation algorithm is developed for jointly recovering network transmitted data and connection topology at the fusion center. The proposed algorithm is based on a two-stage approach. The first stage is concerned with the estimation of the channel gains linking the nodes to the fusion center antennas. The second stage performs a joint estimation of network data and connection topology matrices by exploiting a constrained (PARALIND) tensor model for the collected data at the fusion center. Illustrative simulation results evaluate the performance of the proposed algorithm for some system configurations and network topologies.

We first introduce a new class of tensor models for fourth-order tensors, referred to as “nested PARAFAC models.” Then, we present a space-time-frequency (STF) coding scheme for multiple antenna orthogonal frequency division multiplexing systems. This scheme, called double Khatri-Rao STF (D-KRSTF) coding, combines time-domain spreading with space-frequency precoding and provides an extension of Khatri-Rao space-time (KRST) coding . We show that the received signals define a fourth-order tensor satisfying two nested PARAFAC models, and a semi-blind receiver is then derived using a two-step alternating least squares algorithm for joint channel and symbol estimation. Simulation results show that our receiver offers superior performance compared with previously proposed tensor-based solutions and operates close to the zero forcing receiver with perfect channel state information.

We consider the uplink of a cooperative DS-CDMA communication system, where each user communicates with the base station through a direct link and with the help of relays. A multiuser detection approach for the joint estimation of spatial signatures, channel gains and transmitted symbols of all the users is proposed. Such an approach is derived from a trilinear tensor model for the received signal that combines the source-destination and relay-destination links. The proposed multiuser receiver provides an extension of the traditional trilinear DS-CDMA receiver to cooperative relaying systems, by including the users' relay-assisted links into the trilinear model. Moreover, in contrast to a previous work by the authors, where the relays of a cluster transmit over orthogonal channels, the proposed receiver operates in a more attractive scenario where all the relays simultaneously transmit towards the base station without requiring orthogonal codes. Simulation results illustrate the performance of the proposed receiver in comparison with alternative approaches.

In this letter, we present new blind receivers for uplink multiuser cooperative diversity systems. Considering amplify-and-forward (AF), fixed decode-and-forward (FDF), and selective decode-and-forward (SDF) relaying protocols, the proposed receivers exploits a unified formulation of the received signal as a CANDECOMP/PARAFAC (CP) model with dimensions$receive\ antenna\times cooperative\ branch\times symbol\ period$. Under the assumption that channel state information (CSI) is not available neither at the relays nor at the base station, the proposed receiver jointly and blindly estimates the transmitted symbols and channel parameters. In addition to avoiding the use of pilots symbols, the CP-based receiver can operate with less base station antennas than users or, alternatively, with a single relay per user.

This work formulates a new receiver for the blind decoding of multi-layered space-frequency codes (MLSFC) in multiple input multiple output (MIMO) systems based on orthogonal frequency division multiplexing (OFDM). We introduce a slight modification on the standard MLSFC transmit structure with linear constellation precoding, which consists in extending the constellation rotation across multiple OFDM symbols. Thanks to this added feature, we formulate the received signal as a three-way array following a parallel factor (PARAFAC) model exploiting the powerful uniqueness property of this tensor model, blind MLSFC decoding is guaranteed under mild conditions using an alternating least squares estimation algorithm. Our preliminary numerical results illustrate the bit error rate (BER) performance of the proposed receiver in comparison with the non-blind zero-forcing based MLSFC receiver that assumes perfect channel knowledge.

Modern wireless communications systems fall on the use of multiple antennas at both link ends in order to achieve increased spectral efficiency and high data rates. Recent works have studied the interaction between the antenna array model and the wave propagation scenario in order to provide insight into spatial degrees of freedom of multiple-antenna communication systems. This paper presents a polarization-sensitive MIMO channel decomposition model using spherical harmonics expansion. This approach allows the separation of co- and cross-polarized end-to-end MIMO channel responses into three components: transmit antennas' response, multipath propagation, and receive antennas' response. Besides the inclusion of polarization in the modeling, the novelty is the presence of time delay. Computer simulations are provided to evaluate the correlation and capacity of practical mobile phone antenna setups in conjunction with the WINNER II channel model, exploring the usability of the improved model.

In 3rd. Generation Partnership Project (3GPP) Long Term Evolution (LTE) systems, when no resources has been assigned in the uplink to a given user, the control information associated with Layers 1 and 2 in the protocol stack is conveyed back to the LTE base station (also known as eNodeB) through the so-called Physical Uplink Control Channel (PUCCH). In this work we consider the Format 2 of LTE PUCCH which conveys information about the channel status. At the eNodeB, conventional receivers generally resort to reference signals (RS), or pilot symbols, to perform channel estimation prior to symbol detection. In this paper, we propose a tensor modeling approach for a Data-Aided (DA) channel estimation in PUCCH. First, we formulate the practical channel estimation problem in PUCCH using the Parallel Factor (PARAFAC) tensor model. Based in this model, we resort to the Alternating Least Squares (ALS) algorithm as a DA-based channel estimator. Contrary to conventional RS-based channel estimation operating only on reference signals, the proposed algorithm also simultaneously exploits the energy of the data symbols of all the users, which is contained in PUCCH slots in order to iteratively estimate the user channel coefficients. As will be shown in our simulation results, improved channel estimation accuracy is obtained.

This paper presents a multiple-access MIMO wireless transceiver combining space- and frequency-domain spreadings with a frequency-domain block-coding strategy. Spreading across space (transmit antennas) and frequency (subcarriers) adds resilience against deep channel fades while providing space and frequency diversities, and block-coding enables multiple-access transmission. The merits of the proposed MIMO transceiver using a Zero Forcing (ZF) receiver is confirmed by means of some computer simulation results.

In this paper, we perform an experimental MIMO wireless channel characterization in an outdoor environment. We use the data acquired during wideband channel measurement campaigns made in Kista, Stockholm, Sweden. In order to predict the impact of DOA distribution and polarization diversity on the channel capacity, we have chosen specific measurement routes and locations as well as different MIMO antenna array configurations.

In this paper, we propose a new multi-user receiver processing for PUCCH LTE that counteracts the ICI in a non-cooperative multi-cell architecture. Using the fact that the received signal in PUCCH signaling follows a constrained tensor model, a multi-user receiver based on an iterative joint channel/code estimation and symbol detection is proposed. The interest in such a challenging setting relies on the overhead reduction among neighboring cells. Simulation results show remarkable performance gains of the proposed receiver compared to the conventional time-frequency decorrelator based receiver under the same conditions. We also show a performance comparison with the cooperative version of such a tensor receiver.

Multiple input multiple output (MIMO) wireless communication systems have been intensely investigated in the past years. In order to understand the fundamental limitations of antennas and propagation models on the performance of MIMO systems, the use of spherical harmonics theory allows to decouple the effects of the antennas and the propagation medium. In this work, we make use of spherical harmonics expansion to perform a spherical mode analysis of MIMO systems including the effect of different transmit/receive antennas. Two antenna models are used for evaluating the capacity behavior as a function of their associated spherical harmonics expansion. The first antenna is a theoretical dipole antenna, whose spherical harmonics coefficients have uniform distribution. The second is a a real-world patch antenna, whose coefficients were obtained from practical RF measurements. Both antennas are simulated in a rich-scattering propagation scenario (i.i.d. channel). Our results illustrate how channel capacity is dependent on the number and distribution of the antennas' spherical modes.

In this work we propose a new method for estimation of multipath parameters in the context of mobile communications. The proposed method is an effective way to exploit the fact that the paths amplitudes are fast-varying while angles and delays are slowly-varying over multiple time-slots. By relying on such a multislot invariance of angles and delays and by periodically extending a training sequence over multiple time-slots, we show that the received signal can be modeled as a third-order (3D) tensor, which follows a parallel factor (PARAFAC) model. An accelerated alternating least squares (ALS) algorithm is used for a joint estimation of the angles of arrival, delays and fading amplitudes of the multipaths. Numerical results from computer simulations show that the proposed PARAFAC-based estimator is capable of estimating the multipath channel parameters with good accuracy using short training sequences and with fewer receiver antennas than multipaths

A new approach to space-time-frequency coding for Multiple-Input Multiple-Output (MIMO) systems based on Orthogonal Frequency Division Multiplexing (OFDM) is presented. Tensor-based Space-Time-Multiplexing (TSTM) codes combine multi-stream spatial multiplexing and transmit diversity, and are based on a tensor modeling of the transmitted/received signals. The proposed codes are designed to offer some transmission flexibility by allowing a simple multiplexing-diversityrate control as well as to achieve full space and multipath diversities in a frequency-selective channel. We show that the received signal has a tensor structure and this tensor modeling is exploited for blind separation/decoding of the transmitted information. Simulation results illustrate the performance of some TSTM codes with blind detection.

The use of antenna arrays at both ends of the link has attracted significant attention of the researches on space-time equalization and coding techniques for so called multiple-input-multiple-output (MIMO) channels. The presence of strong co-channel interference (CCI) in addition to inter-symbol interference (ISI) in current wireless (mobile) communication systems places a significant challenge to MIMO space-time equalizers. We assess the performance of BLAST/MIMO on frequency-selective MIMO channel model in the presence of CCI. Space-time processing is used in order to deal with the frequency selectivity and to provide more degrees of freedom to deal with cochannel interference. We consider two non-linear space-time processing-based receivers. The first one is a MIMO space-time decision feedback equalizer (MIMO ST-DFE) and the second one is a space-time delayed decision feedback sequence estimator (MIMO ST-DDFSE) with actual adaptive algorithms for channel acquisition. Noise-limited as well as interference-limited situations are evaluated.

Transmission diversity schemes have recently emerged in wireless systems as an attractive solution in order to mitigate fading effects. Space-time block codes (STBC) with two antennas can provide similar order diversity as maximal-ratio receiver combining (MARC). In this paper a transmit diversity scheme using STBC with two and four antennas is applied for the EDGE/EGPRS system and its results are evaluated in a interference-limited scenario. We jointly compare this strategy of multiple antennas with incremental redundancy (IR), a technique for link quality control (LQC) in EDGE.

This work aims at investigating the performance of a decoupled space-time processing structure based on a delayed decision-feedback sequence estimator (D-ST-DDFSE), in the context of the Enhanced Data rates for GSM Evolution (EDGE) system. The main idea in using decoupled space-time (D-ST) processing structures is to separate co-channel interference (CCI) reduction from intersymbol interference (ISI) suppression. Consequently, all degrees of freedom of a space-time (ST) front-end are dedicated to treat CCI, leaving ISI to be suppressed by a temporal equalizer. Due to the 8-PSK modulation and the large delay spread values compared to the symbol period, optimum detection becomes too complex in the EDGE system, which makes DDFSE a promising scheme for ISI suppression. The performance of D-ST-DDFSE is analyzed through link-level simulations under the context of COST 259 channel models for typical urban (TU) and bad urban (BU) propagation scenarios. Improved performance of this D-ST technique over a space-time linear equalizer is observed.

In studying the possibility of increasing wireless system capacity, we evaluate the performance of some algorithms that make use of sub-space techniques to estimate the covariance matrix, and compare these results to those obtained through traditional methods, such as the direct matrix inversion-maximum signal-to-noise ratio and maximal ratio combining. Illustrative simulation results demonstrate that the minimum mean square error-signal sub-space and the weighted sub-space algorithms may lead to a better performance than full-rank conventional algorithms. Furthermore, a more elaborate system-level simulation in a TDMA IS-136 context is performed and it shows that such benefits also appear in a more practical scenario.