Martin Haardt

Florian Roemer, Martin Haardt

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we derive an explicit first-order expansion of the Higher- Order SVD (HOSVD)-based subspace estimate. Secondly, we show how to obtain explicit first-order expansions of the estimation error of ESPRIT-type algorithms and provide the expressions for matrix-based and tensor-based Standard ESPRIT and Unitary ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, we only need the noise to be zero mean and possess finite second order moments. Fourthly, we investigate the effect of using Structured Least Squares (SLS) to solve the overdetermined shift invariance equations in ESPRIT and provide an explicit first-order expansion as well as a closed-form MSE expression. Finally, we simplify the MSE for the special case of a single source and compute the asymptotic efficiency of the investigated ESPRIT-type algorithms in compact closed-form expressions which only depend on the array size and the effective SNR. Our results are more general than existing results on the performance analysis of ESPRIT-type algorithms since (a) we do not need any assumptions about the noise except for the mean to be zero and the second-order moments to be finite (in contrast to earlier results that require Gaussianity or second-order circular symmetry); (b) our results are asymptotic in the effective SNR, i.e., we do not require the number of samples to be large; (c) we present a framework that incorporates various ESPRIT-type algorithms in one unified manner.

Brenda Vilas Boas, Wolfgang Zirwas, Martin Haardt

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.

Bruno Sokal, André L. F. de Almeida, Martin Haardt

We address joint active and passive beamforming for uplink RIS-assisted multi-user multi-stream MIMO systems with joint detection. The coupled design of the receive combiner, block-diagonal user precoders, and RIS phase vector is formulated through a third-order composite channel tensor. Exploiting this multilinear structure, we propose a multi-stream tensor alternating optimization method that updates the combiner, user precoders, and RIS coefficients via low-dimensional tensor projections. Simulations show that the proposed method approaches a multi-start alternating-optimization benchmark while reducing computational complexity and improving large-RIS scaling.

Wesley S. Leite, Rodrigo C. de Lamare, Yuriy Zakharov et al.

In this work, we introduce a variable window size (VWS) spatial smoothing framework that enhances coarray-based direction of arrival (DOA) estimation for sparse linear arrays. By compressing the smoothing aperture, the proposed VWS Coarray MUSIC (VWS-CA-MUSIC) and VWS Coarray root-MUSIC (VWS-CA-rMUSIC) algorithms replace part of the perturbed rank-one outer products in the smoothed coarray data with unperturbed low-rank additional terms, increasing the separation between signal and noise subspaces, while preserving the signal subspace span. We also derive the bounds that guarantees identifiability, by limiting the values that can be assumed by the compression parameter. Simulations with sparse geometries reveal significant performance improvements and complexity savings relative to the fixed-window coarray MUSIC method.

Mustafa Musab, Joseph K. Chege, Arie Yeredor et al.

Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns. However, conventional density estimators based on uniform histograms often fail to capture local variations, especially when the underlying distribution is highly nonuniform. Furthermore, the inherent discontinuity of histograms poses challenges for tasks requiring smooth derivatives, such as gradient-based optimization, clustering, and nonparametric discriminant analysis. In this work, we present a novel non-parametric approach for multivariate probability density function (PDF) estimation that utilizes minimum description length (MDL)-based binning with quantile cuts. Our approach builds upon tensor factorization techniques, leveraging the canonical polyadic decomposition (CPD) of a joint probability tensor. We demonstrate the effectiveness of our method on synthetic data and a challenging real dry bean classification dataset.

Brenda Vilas Boas, Wolfgang Zirwas, Martin Haardt

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.

Brenda Vilas Boas, Wolfgang Zirwas, Martin Haardt

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.

Brenda Vilas Boas, Wolfgang Zirwas, Martin Haardt

A variety of wireless channel estimation methods, e.g., MUSIC and ESPRIT, rely on prior knowledge of the model order. Therefore, it is important to correctly estimate the number of multipath components (MPCs) which compose such channels. However, environments with many scatterers may generate MPCs which are closely spaced. This clustering of MPCs in addition to noise makes the model order selection task difficult in practice to currently known algorithms. In this paper, we exploit the multidimensional characteristics of MIMO orthogonal frequency division multiplexing (OFDM) systems and propose a machine learning (ML) method capable of determining the number of MPCs with a higher accuracy than state of the art methods in almost coherent scenarios. Moreover, our results show that our proposed ML method has an enhanced reliability.

Khaled Ardah, Martin Haardt, Tianyi Liu et al.

This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning.

Brenda Vilas Boas, Wolfgang Zirwas, Martin Haardt

Massive MIMO is one of the main features of 5G mobile radio systems. However, it often leads to high cost, size and power consumption. To overcome these issues, the use of constrained radio frequency (RF) frontends has been proposed, as well as novel precoders, e.g., a multi-antenna, greedy, iterative and quantized precoding algorithm (MAGIQ). Nevertheless, the best performance of MAGIQ assumes accurate channel knowledge per antenna element, for example, from uplink sounding reference signals. In this context, we propose an efficient uplink channel estimator by applying machine learning (ML) algorithms. In a first step a conditional generative adversarial network (cGAN) predicts the radio channels from a limited set of full resolution RF chains to the rest of the low resolution RF chain antenna elements. A long-short term memory (LSTM) neural network extracts further phase information from the low resolution RF chain antenna elements. Our results indicate that our proposed approach is competitive with traditional Unitary tensor-ESPRIT in scenarios with various closely spaced multipath components (MPCs).