Bayesian Estimation and Tuning-Free Rank Detection for Probability Mass Function Tensors

Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor that admits a low-rank canonical polyadic decomposition (CPD) has enabled the development of efficient PMF estimation algorithms. However, these algorithms require the rank (model order) of the tensor to be specified beforehand. In real-world applications, the true rank is unknown. Therefore, an appropriate rank is usually selected from a candidate set either by observing validation errors or by computing various likelihood-based information criteria, a procedure which is computationally expensive for large datasets. This paper presents a novel Bayesian framework for estimating the joint PMF and automatically inferring its rank from observed data. We specify a Bayesian PMF estimation model and employ appropriate prior distributions for the model parameters, allowing for tuning-free rank inference via a single training run. We then derive a deterministic solution based on variational inference (VI) to approximate the posterior distributions of various model parameters. Additionally, we develop a scalable version of the VI-based approach by leveraging stochastic variational inference (SVI) to arrive at an efficient algorithm whose complexity scales sublinearly with the size of the dataset. Numerical experiments involving both synthetic data and real movie recommendation data illustrate the advantages of our VI and SVI-based methods in terms of estimation accuracy, automatic rank detection, and computational efficiency.

Near-Field Signal Processing: Unleashing the Power of Proximity

After nearly a century of specialized applications in optics, remote sensing, and acoustics, the near-field (NF) electromagnetic propagation zone is experiencing a resurgence in research interest. This renewed attention is fueled by the emergence of promising applications in various fields such as wireless communications, holography, medical imaging, and quantum-inspired systems. Signal processing within NF sensing and wireless communications environments entails addressing issues related to extended scatterers, range-dependent beampatterns, spherical wavefronts, mutual coupling effects, and the presence of both reactive and radiative fields. Recent investigations have focused on these aspects in the context of extremely large arrays and wide bandwidths, giving rise to novel challenges in channel estimation, beamforming, beam training, sensing, and localization. While NF optics has a longstanding history, advancements in NF phase retrieval techniques and their applications have lately garnered significant research attention. Similarly, utilizing NF localization with acoustic arrays represents a contemporary extension of established principles in NF acoustic array signal processing. This article aims to provide an overview of state-of-the-art signal processing techniques within the NF domain, offering a comprehensive perspective on recent advances in diverse applications.

Gridless Parameter Estimation in Partly Calibrated Rectangular Arrays

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing challenges for large antennas. In contrast, sparsity-based approaches outperform subspace methods, especially in scenarios with limited snapshots or correlated sources. This study focuses on direction-of-arrival (DOA) estimation using a partly calibrated rectangular array with fully calibrated subarrays. A gridless sparse formulation leveraging shift invariances in the array is developed, yielding two competitive algorithms under the alternating direction method of multipliers (ADMM) and successive convex approximation frameworks, respectively. Numerical simulations show the superior error performance of our proposed method, particularly in highly correlated scenarios, compared to the conventional subspace-based methods. It is demonstrated that the proposed formulation can also be adopted in the fully calibrated case to improve the robustness of the subspace-based methods to the source correlation. Furthermore, we provide a generalization of the proposed method to a more challenging case where a part of the sensors is unobservable due to failures.

Joint Sparse Estimation with Cardinality Constraint via Mixed-Integer Semidefinite Programming

The multiple measurement vectors (MMV) problem refers to the joint estimation of a row-sparse signal matrix from multiple realizations of mixtures with a known dictionary. As a generalization of the standard sparse representation problem for a single measurement, this problem is fundamental in various applications in signal processing, e.g., spectral analysis and direction-of-arrival (DOA) estimation. In this paper, we consider the maximum a posteriori (MAP) estimation for the MMV problem, which is classically formulated as a regularized least-squares (LS) problem with an $\ell_{2,0}$-norm constraint, and derive an equivalent mixed-integer semidefinite program (MISDP) reformulation. The proposed MISDP reformulation can be exactly solved by a generic MISDP solver, which, however, becomes computationally demanding for problems of extremely large dimensions. To further reduce the computation time in such scenarios, a relaxation-based approach can be employed to obtain an approximate solution of the MISDP reformulation, at the expense of a reduced estimation performance. Numerical simulations in the context of DOA estimation demonstrate the improved error performance of our proposed method in comparison to several popular DOA estimation methods. In particular, compared to the deterministic maximum likelihood (DML) estimator, which is often used as a benchmark, the proposed method applied with a state-of-the-art MISDP solver exhibits a superior estimation performance at a significantly reduced running time. Moreover, unlike other nonconvex approaches for the MMV problem, including the greedy methods and the sparse Bayesian learning, the proposed MISDP-based method offers a guarantee of finding a global optimum.

SALSA: A Sequential Alternating Least Squares Approximation Method For MIMO Channel Estimation

In this paper, we consider the channel estimation problem in sub-6 GHz uplink wideband MIMO-OFDM communication systems, where a user equipment with a fully-digital beamforming structure is communicating with a base station having a hybrid analog-digital beamforming structure. A novel channel estimation method called Sequential Alternating Least Squares Approximation (SALSA) is proposed by exploiting a hidden tensor structure in the uplink measurement matrix. Specifically, by showing that any MIMO channel matrix can be approximately decomposed into a summation of R factor matrices having a Kronecker structure, the uplink measurement matrix can be reshaped into a 3-way tensor admitting a Tucker decomposition. Exploiting the tensor structure, the MIMO channel matrix is estimated sequentially using an alternating least squares method. Detailed simulation results are provided showing the effectiveness of the proposed SALSA method as compared to the classical least squares method.

The Perfect Match: RIS-enabled MIMO Channel Estimation Using Tensor Decomposition

The deployment of reconfigurable intelligent surfaces (RISs) in a communication system provides control over the propagation environment, which facilitates the augmentation of a multitude of communication objectives. As these performance gains are highly dependent on the applied phase shifts at the RIS, accurate channel state information at the transceivers is imperative. However, not only do RISs traditionally lack signal processing capabilities, but their end-to-end channels also consist of multiple components. Hence, conventional channel estimation (CE) algorithms become incompatible with RIS-aided communication systems as they fail to provide the necessary information about the channel components, which are essential for a beneficial RIS configuration. To enable the full potential of RISs, we propose to use tensor-decomposition-based CE, which facilitates smart configuration of the RIS by providing the required channel components. We use canonical polyadic (CP) decomposition, that exploits a structured time domain pilot sequence. Compared to other state-of-the-art decomposition methods, the proposed Semi-Algebraic CP decomposition via Simultaneous Matrix Diagonalization (SECSI) algorithm is more time efficient as it does not require an iterative process. The benefits of SECSI for RIS-aided networks are validated with numerical results, which show the improved individual and end-to-end CE accuracy of SECSI.

Combining AI/ML and PHY Layer Rule Based Inference -- Some First Results

In 3GPP New Radio (NR) Release 18 we see the first study item starting in May 2022, which will evaluate the potential of AI/ML methods for Radio Access Network (RAN) 1, i.e., for mobile radio PHY and MAC layer applications. We use the profiling method for accurate iterative estimation of multipath component parameters for PHY layer reference, as it promises a large channel prediction horizon. We investigate options to partly or fully replace some functionalities of this rule based PHY layer method by AI/ML inferences, with the goal to achieve either a higher performance, lower latency, or, reduced processing complexity. We provide first results for noise reduction, then a combined scheme for model order selection, compare options to infer multipath component start parameters, and, provide an outlook on a possible channel prediction framework.

Transfer Learning Capabilities of Untrained Neural Networks for MIMO CSI Recreation

Machine learning (ML) applications for wireless communications have gained momentum on the standardization discussions for 5G advanced and beyond. One of the biggest challenges for real world ML deployment is the need for labeled signals and big measurement campaigns. To overcome those problems, we propose the use of untrained neural networks (UNNs) for MIMO channel recreation/estimation and low overhead reporting. The UNNs learn the propagation environment by fitting a few channel measurements and we exploit their learned prior to provide higher channel estimation gains. Moreover, we present a UNN for simultaneous channel recreation for multiple users, or multiple user equipment (UE) positions, in which we have a trade-off between the estimated channel gain and the number of parameters. Our results show that transfer learning techniques are effective in accessing the learned prior on the environment structure as they provide higher channel gain for neighbouring users. Moreover, we indicate how the under-parameterization of UNNs can further enable low-overhead channel state information (CSI) reporting.

Machine Learning for CSI Recreation Based on Prior Knowledge

Knowledge of channel state information (CSI) is fundamental to many functionalities within the mobile wireless communications systems. With the advance of machine learning (ML) and digital maps, i.e., digital twins, we have a big opportunity to learn the propagation environment and design novel methods to derive and report CSI. In this work, we propose to combine untrained neural networks (UNNs) and conditional generative adversarial networks (cGANs) for MIMO channel recreation based on prior knowledge. The UNNs learn the prior-CSI for some locations which are used to build the input to a cGAN. Based on the prior-CSIs, their locations and the location of the desired channel, the cGAN is trained to output the channel expected at the desired location. This combined approach can be used for low overhead CSI reporting as, after training, we only need to report the desired location. Our results show that our method is successful in modelling the wireless channel and robust to location quantization errors in line of sight conditions.

Compressed Sensing Constant Modulus Constrained Projection Matrix Design and High-Resolution DoA Estimation Methods

This paper proposes a compressed sensing-based high-resolution direction-of-arrival estimation method called gradient orthogonal matching pursuit (GOMP). It contains two main steps: a sparse coding approximation step using the well-known OMP method and a sequential iterative refinement step using a newly proposed gradient-descent method. To enhance the recoverability, we further propose an efficient projection matrix design method, which considers the constant modulus constraints imposed by the projection matrix hardware components. Simulation results show the effectiveness of the proposed methods as compared to benchmark algorithms.