arXiv subjects

Andre L. F. de Almeida

Publications and source records attributed to Andre L. F. de Almeida.

11 recordsLinked to original sources

arXiv2026

Simultaneous Direct and Indirect Channel Estimation for RIS-Assisted MIMO Communications

This paper introduces an enhanced channel estimation method for reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) communications. Considering the presence of both the direct link from the base station (BS) to the user equipment (UE) and the indirect link \textit{via} the RIS, we formulate a tensor-based receiver for joint direct and indirect channel estimation called the TenDICE algorithm. The proposed receiver relies on an extended parallel factor analysis (PARAFAC) tensor model for the received pilot signals, from which the involved (direct and indirect link) channels are estimated using a simple alternating least squares scheme. The proposed TenDICE method is compared with the state-of-the-art least squares (LS) method, Khatri-Rao factorization (KRF) method, enhanced trilinear alternating least squares (E-TALS), and the theoretical Cramér-Rao lower bound (CRLB) based on normalized mean square error (NMSE) and spectral efficiency (SE). The proposed TenDICE outperforms the LS and E-TALS methods and performs similarly to the KRF methods while estimating the direct channel.

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arXiv2026

Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability

Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is underexploited by the conventional matrix-centric view. Tensor decompositions and tensor networks provide a principled algebraic language for this structure, yet the literature often treats them as isolated compression mechanisms. This survey organizes tensor methods for LLMs through two complementary views: a seven-stage lifecycle taxonomy covering tokenization, embeddings, pre-training, adaptation, compression, inference, and interpretability, and a component view covering embeddings, attention, and feed-forward networks. We provide unified notation and theoretical foundations, analyze tensorization strategies for individual Transformer components, and compare methods at each lifecycle stage while making differences in evaluation protocols and model scales explicit. We further connect tensor methods to neighboring efficiency techniques and probabilistic tensor networks. Finally, we synthesize open challenges and introduce $ρ_{\rm gap}$, a metric for the compression-realization gap between theoretical memory reduction and measured system-level speedup. By treating tensorization as a common structural principle, the survey provides a structured entry point to tensorized language models and clarifies when parameter savings can plausibly translate into memory efficiency, computational efficiency, or interpretability. The GitHub page dedicated to this paper is accessible at \href{https://github.com/ma-tt-a/awesome-tensor-methods-for-llms}{this https URL}.

cs.LG↗

arXiv2026

Fast randomized Kronecker tensor decomposition: algorithms and error analysis

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD) by replacing the sequence of deterministic SVDs in the TTr1SVD framework with randomized SVDs incorporating oversampling and power iterations. The proposed algorithms can decompose a given tensor into the KTD format significantly faster than existing state-of-the-art deterministic methods. Our principal idea is to use randomization to reduce computational complexity while maintaining controlled accuracy. A detailed theoretical analysis is presented, including a recursive error bound that accounts for error propagation through the TTr1SVD tree structure. We prove that the expected Frobenius norm error is bounded by a sum of tail energies multiplied by factors that decay exponentially with the number of power iterations. Extensive simulations on synthetic and real-world datasets demonstrate several orders of magnitude acceleration compared to the deterministic approach, with applications to tensor completion, video/image compression, image denoising, and image super-resolution.

math.NA↗

arXiv2026

Randomized block Krylov method for approximation of truncated tensor SVD

This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental experiments using synthetics and real-world data are conducted to verify the efficiency and feasibility of the proposed randomized approach, and the numerical results show that the proposed method provides promising results. Applications of the proposed approach to data completion and data compression are presented.

math.NA↗

arXiv2025

Least-Squares Khatri-Rao Factorization of a Polynomial Matrix

The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis. Many applications require a least-squares (LS) Khatri-Rao factorization. In broadband sensor array problems, polynomial matrices effectively model frequency-dependent behaviors, necessitating extensions of conventional linear algebra techniques. This paper generalizes LS Khatri-Rao factorization from ordinary to polynomial matrices by applying it to the discrete Fourier transform (DFT) samples of polynomial matrices. Phase coherence across bin-wise Khatri-Rao factors is ensured via a phasesmoothing algorithm. The proposed method is validated through broadband angle-of-arrival (AoA) estimation for uniform planar arrays (UPAs), where the steering matrix is a polynomial matrix, which can be represented as a Khatri-Rao product between steering matrix in azimuth and elevation directions.

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arXiv2025

Mobility Management in Integrated Sensing and Communications Networks

The performance of the integrated sensing and communication (ISAC) networks is considerably affected by the mobility of the transceiver nodes, user equipment devices (UEs) and the passive objects that are sensed. For instance, the sensing efficiency is considerably affected by the presence or absence of a line-of-sight connection between the sensing transceivers and the object; a condition that may change quickly due to mobility. Moreover, the mobility of the UEs and objects may result in dynamically varying communication-to-sensing and sensing-to communication interference, deteriorating the network performance. In such cases, there may be a need to handover the sensing process to neighbor nodes. In this article, we develop the concept of mobility management in ISAC networks. Here, depending on the mobility of objects and/or the transceiver nodes, the data traffic, the sensing or communication coverage area of the transceivers, and the network interference, the transmission and/or the reception of the sensing signals may be handed over to neighbor nodes. Also, the ISAC configuration and modality - that is, using monostatic or bistatic sensing - are updated accordingly, such that the sensed objects can be continuously sensed with low overhead. We show that mobility management reduces the sensing interruption and boosts the communication and sensing efficiency of ISAC networks.

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arXiv2024

Tensor-Based Receivers for the Bistatic Sensing and Communication Scenario

We propose receivers for bistatic sensing and communication that exploit a tensor modeling of the received signals. We consider a hybrid scenario where the sensing link knows the transmitted data to estimate the target parameters while the communication link operates semi-blindly in a direct data decoding approach without channel knowledge. We show that the signals received at the sensing receiver and communication receiver follow PARATUCK and PARAFAC tensor models, respectively. These models are exploited to obtain accurate estimates of the target parameters (at the sensing receiver) and the transmitted symbols and channels (at the user equipment). We discuss uniqueness conditions and provide some simulation results to evaluate the performance of the proposed receivers. Our experiments show that the sensing parameters are well estimated at moderate signal-to-noise ratio (SNR) while keeping good symbol error rate (SER) and channel normalized mean square error (NMSE) results for the communication link.

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arXiv2024

Enhanced channel estimation for double RIS-aided MIMO systems using coupled tensor decomposition

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 proposed algorithms.

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arXiv2024

Semi-Blind Channel Estimation for Beyond Diagonal RIS

The channel estimation problem has been widely discussed in traditional reconfigurable intelligent surface assisted multiple-input multiple-output. However, solutions for channel estimation adapted to beyond diagonal RIS need further study, and few recent works have been proposed to tackle this problem. Moreover, methods that avoid or minimize the use of pilot sequences are of interest. This work formulates a data-driven (semi-blind) joint channel and symbol estimation algorithm for beyond diagonal RIS that avoids a prior pilot-assisted stage while providing decoupled estimates of the involved communication channels. The proposed receiver builds upon a PARATUCK tensor model for the received signal, from which a trilinear alternating estimation scheme is derived. Preliminary numerical results demonstrate the proposed method's performance for selected system setups. The symbol error rate performance is also compared with that of a linear receiver operating with perfect knowledge of the cascaded channel.

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arXiv2019

Adaptive Modulation and Coding based on Reinforcement Learning for 5G Networks

We design a self-exploratory reinforcement learning (RL) framework, based on the Q-learning algorithm, that enables the base station (BS) to choose a suitable modulation and coding scheme (MCS) that maximizes the spectral efficiency while maintaining a low block error rate (BLER). In this framework, the BS chooses the MCS based on the channel quality indicator (CQI) reported by the user equipment (UE). A transmission is made with the chosen MCS and the results of this transmission are converted by the BS into rewards that the BS uses to learn the suitable mapping from CQI to MCS. Comparing with a conventional fixed look-up table and the outer loop link adaptation, the proposed framework achieves superior performance in terms of spectral efficiency and BLER.

cs.NI↗

arXiv2016

Joint Channel Estimation / Data Detection in MIMO-FBMC/OQAM Systems - A Tensor-Based Approach

Filter bank-based multicarrier (FBMC) systems are currently being considered as a prevalent candidate for replacing the long established cyclic prefix (CP)-based orthogonal frequency division multiplexing (CP-OFDM) in the physical layer of next generation communications systems. In particular, FBMC/OQAM has received increasing attention due to, among other features, its potential for maximum spectral efficiency. It suffers, however, from an intrinsic self-interference effect, which complicates signal processing tasks at the receiver, including synchronization, channel estimation and equalization. In a multiple-input multiple-output (MIMO) configuration, the multi-antenna interference has also to be taken into account. (Semi-)blind FBMC/OQAM receivers have been little studied so far and mainly for single-antenna systems. The problem of joint channel estimation and data detection in a MIMO-FBMC/OQAM system, given limited or no training information, is studied in this paper through a tensor-based approach in the light of the success of such techniques in OFDM applications. Simulation-based comparisons with CP-OFDM are included, for realistic transmission models.

cs.IT↗