arXiv subjects

Martin Haardt

Publications and source records attributed to Martin Haardt.

At least 37 records · Page 2Linked to original sources

arXiv2021

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.

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arXiv2021

Robust Multi-dimensional Model Order Estimation Using LineAr Regression of Global Eigenvalues (LaRGE)

The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank data is corrupted by additive noise. In this paper, we present a novel robust method for model order estimation of noise-corrupted multi-dimensional low-rank data based on the LineAr Regression of Global Eigenvalues (LaRGE). The LaRGE method uses the multi-linear singular values obtained from the HOSVD of the measurement tensor to construct global eigenvalues. In contrast to the Modified Exponential Test (EFT) that also exploits the approximate exponential profile of the noise eigenvalues, LaRGE does not require the calculation of the probability of false alarm. Moreover, LaRGE achieves a significantly improved performance in comparison with popular state-of-the-art methods. It is well suited for the analysis of biomedical data. The excellent performance of the LaRGE method is illustrated via simulations and results obtained from EEG recordings.

stat.ME↗

arXiv2021

Double-RIS Versus Single-RIS Aided Systems: Tensor-Based MIMO Channel Estimation and Design Perspectives

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-squared-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 a 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.

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arXiv2021

Machine Learning for Model Order Selection in MIMO OFDM Systems

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.

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arXiv2021

Recovery under Side Constraints

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.

cs.IR↗

arXiv2021

Fully Digital and Hybrid Beamforming Design For Millimeter-Wave MIMO-OFDM Two-Way Relaying Systems

In this work, we consider the design of hybrid analog-digital (HAD) multi-carrier MIMO-OFDM two-way relaying systems, where the relay station is equipped with a HAD amplify-and-forward architecture and every mobile station is equipped with a fully-digital beamforming architecture. We propose a sub-optimal solution by reformulating the original non-convex problem as a constrained Tucker2 decomposition with the objective of minimizing the sum Euclidean-norm between the HAD amplification matrices and their fully-digital counterparts. For the fully-digital amplification matrix design, we use a Frobenius-norm maximization of the effective channels on every subcarrier and propose an effective solution applicable for multi-stream communication scenarios. After that, we propose an alternating maximization (AltMax) HAD solution by exploiting the tensor structure of the reformulated problem. Simulation results are provided, where we show that the proposed fully-digital and AltMax-based HAD amplification matrix designs outperform some benchmark methods, especially for multi-stream communication scenarios.

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arXiv2021

Machine Learning Prediction of Time-Varying Rayleigh Channels

Channel state information (CSI) rapidly becomes outdated in high mobility scenarios, degrading the performance of wireless communication systems. In these cases, time series prediction techniques can be applied to combat the effects of outdated CSI. Recently, it has been shown that recurrent neural networks (RNNs) exhibit outstanding performance in time series prediction tasks. In this paper, we investigate the performance of RNN and long short term memory (LSTM) predictors in a simple Rayleigh flat-fading channel. We conduct numerical experiments to evaluate whether these machine-learning (ML)-based predictors can outperform the optimal linear minimum mean square error Wiener predictor. Our simulation results indicate that the considered neural network predictors outperform the Wiener predictor for small observation window lengths and are more robust under weak channel correlation as well as in the presence of noise. Furthermore, we show that simple shallow RNNs are sufficient to model Rayleigh channels over a wide range of Doppler shifts.

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arXiv2021

Low-Complexity Zero-Forcing Precoding for XL-MIMO Transmissions

Deploying antenna arrays with an asymptotically large aperture will be central to achieving the theoretical gains of massive MIMO in beyond-5G systems. Such extra-large MIMO (XL-MIMO) systems experience propagation conditions which are not typically observed in conventional massive MIMO systems, such as spatial non-stationarities and near-field propagation. Moreover, standard precoding schemes, such as zero-forcing (ZF), may not apply to XL-MIMO transmissions due to the prohibitive complexity associated with such a large-scale scenario. We propose two novel precoding schemes that aim at reducing the complexity without losing much performance. The proposed schemes leverage a plane-wave approximation and user grouping to obtain a low-complexity approximation of the ZF precoder. Our simulation results show that the proposed schemes offer a possibility for a performance and complexity trade-off compared to the benchmark schemes.

cs.IT↗

arXiv2021

TRICE: A Channel Estimation Framework for RIS-Aided Millimeter-Wave MIMO Systems

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.

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arXiv2021

Two-step Machine Learning Approach for Channel Estimation with Mixed Resolution RF Chains

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).

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arXiv2020

Low-Complexity Massive MIMO Tensor Precoding

We present a novel and low-complexity massive multiple-input multiple-output (MIMO) precoding strategy based on novel findings concerning the subspace separability of Rician fading channels. Considering a uniform rectangular array at the base station, we show that the subspaces spanned by the channel vectors can be factorized as a tensor product between two lower dimensional subspaces. Based on this result, we formulate tensor maximum ratio transmit and zero-forcing precoders. We show that the proposed tensor precoders exhibit lower computational complexity and require less instantaneous channel state information than their linear counterparts. Finally, we present computer simulations that demonstrate the applicability of the proposed tensor precoders in practical communication scenarios.

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arXiv2020

The Extended "Sequentially Drilled" Joint Congruence Transformation and its Application in Gaussian Independent Vector Analysis

Independent Vector Analysis (IVA) has emerged in recent years as an extension of Independent Component Analysis (ICA) into multiple sets of mixtures, where the source signals in each set are independent, but may depend on source signals in the other sets. In a semi-blind IVA (or ICA) framework, information regarding the probability distributions of the sources may be available, giving rise to Maximum Likelihood (ML) separation. In recent work we have shown that under the multivariate Gaussian model, with arbitrary temporal covariance matrices (stationary or non-stationary) of the source signals, ML separation requires the solution of a "Sequentially Drilled" Joint Congruence (SeDJoCo) transformation of a set of matrices, which is reminiscent of (but different from) classical joint diagonalization. In this paper we extend our results to the IVA problem, showing how the ML solution for the Gaussian model (with arbitrary covariance and cross-covariance matrices) takes the form of an extended SeDJoCo problem. We formulate the extended problem, derive a condition for the existence of a solution, and propose two iterative solution algorithms. In addition, we derive the induced Cramér-Rao Lower Bound (iCRLB) on the resulting Interference-to-Source Ratios (ISR) matrices, and demonstrate by simulation how the ML separation obtained by solving the extended SeDJoCo problem indeed attains the iCRLB (asymptotically), as opposed to other separation approaches, which cannot exploit prior knowledge regarding the sources' distributions.

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arXiv2020

Performance Analysis of the Gaussian Quasi-Maximum Likelihood Approach for Independent Vector Analysis

Maximum Likelihood (ML) estimation requires precise knowledge of the underlying statistical model. In Quasi ML (QML), a presumed model is used as a substitute to the (unknown) true model. In the context of Independent Vector Analysis (IVA), we consider the Gaussian QML Estimate (QMLE) of the demixing matrices set and present an (approximate) analysis of its asymptotic separation performance. In Gaussian QML the sources are presumed to be Gaussian, with covariance matrices specified by some "educated guess". The resulting quasi-likelihood equations of the demixing matrices take a special form, recently termed an extended "Sequentially Drilled" Joint Congruence (SeDJoCo) transformation, which is reminiscent of (though essentially different from) classical joint diagonalization. We show that asymptotically this QMLE, i.e., the solution of the resulting extended SeDJoCo transformation, attains perfect separation (under some mild conditions) regardless of the sources' true distributions and/or covariance matrices. In addition, based on the "small-errors" assumption, we present a first-order perturbation analysis of the extended SeDJoCo solution. Using the resulting closed-form expressions for the errors in the solution matrices, we provide closed-form expressions for the resulting Interference-to-Source Ratios (ISRs) for IVA. Moreover, we prove that asymptotically the ISRs depend only on the sources' covariances, and not on their specific distributions. As an immediate consequence of this result, we provide an asymptotically attainable lower bound on the resulting ISRs. We also present empirical results, corroborating our analytical derivations, of three simulation experiments concerning two possible model errors - inaccurate covariance matrices and sources' distribution mismodeling.

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arXiv2020

Rank-one Detector for Kronecker-Structured Constant Modulus Constellations

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 $(E_b/N_0)$. 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.

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arXiv2020

Using Double Contractions to Derive the Structure of Slice-Wise Multiplications of Tensors with Applications to Semi-Blind MIMO OFDM

The slice-wise multiplication of two tensors is required in a variety of tensor decompositions (including PARAFAC2 and PARATUCK2) and is encountered in many applications, including the analysis of multidimensional biomedical data (EEG, MEG, etc.) or multi-carrier MIMO systems. In this paper, we propose a new tensor representation that is not based on a slice-wise (matrix) description, but can be represented by a double contraction of two tensors. Such a double contraction of two tensors can be efficiently calculated via generalized unfoldings. It leads to new tensor models of the investigated system that do not depend on the chosen unfolding and reveal the tensor structure of the data model (such that all possible unfoldings can be seen at the same time). As an example, we apply this new concept to the design of new receivers for multi-carrier MIMO systems in wireless communications. In particular, we consider MIMO OFDM systems with and without Khatri-Rao coding. The proposed receivers exploit the channel correlation between adjacent subcarriers, require the same amount of training symbols as traditional OFDM techniques, but have an improved performance in terms of the symbol error rate. Furthermore, we show that the spectral efficiency of the Khatri-Rao coded MIMO-OFDM can be increased by introducing "random coding" such that the "coding matrix" also contains useful information symbols. Considering this transmission technique, we derive a tensor model and two types of receivers for randomly coded MIMO-OFDM systems using the double contraction of two tensors.

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arXiv2017

First-Order Perturbation Analysis of the SECSI Framework for the Approximate CP Decomposition of 3-D Noise-Corrupted Low-Rank Tensors

The Semi-Algebraic framework for the approximate Canonical Polyadic (CP) decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient tool for the computation of the CP decomposition. The SECSI framework reformulates the CP decomposition into a set of joint eigenvalue decomposition (JEVD) problems. Solving all JEVDs, we obtain multiple estimates of the factor matrices and the best estimate is chosen in a subsequent step by using an exhaustive search or some heuristic strategy that reduces the computational complexity. Moreover, the SECSI framework retains the option of choosing the number of JEVDs to be solved, thus providing an adjustable complexity-accuracy trade-off. In this work, we provide an analytical performance analysis of the SECSI framework for the computation of the approximate CP decomposition of a noise corrupted low-rank tensor, where we derive closed-form expressions of the relative mean square error for each of the estimated factor matrices. These expressions are obtained using a first-order perturbation analysis and are formulated in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. Simulation results exhibit an excellent match between the obtained closed-form expressions and the empirical results. Moreover, we propose a new Performance Analysis based Selection (PAS) scheme to choose the final factor matrix estimate. The results show that the proposed PAS scheme outperforms the existing heuristics, especially in the high SNR regime.

cs.IT↗

arXiv2016

Performance analysis of multi-dimensional ESPRIT-type algorithms for arbitrary and strictly non-circular sources with spatial smoothing

Spatial smoothing is a widely used preprocessing scheme to improve the performance of high-resolution parameter estimation algorithms in case of coherent signals or if only a small number of snapshots is available. In this paper, we present a first-order performance analysis of the spatially smoothed versions of R-D Standard ESPRIT and R-D Unitary ESPRIT for sources with arbitrary signal constellations as well as R-D NC Standard ESPRIT and R-D NC Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Moreover, no assumptions on the noise statistics are required apart from a zero-mean and finite SO moments. We show that both R-D NC ESPRIT-type algorithms with spatial smoothing perform asymptotically identical in the high effective SNR regime. Generally, the performance of spatial smoothing based algorithms depends on the number of subarrays, which is a design parameter and needs to be chosen beforehand. In order to gain more insights into the optimal choice of the number of subarrays, we simplify the derived analytical R-D mean square error (MSE) expressions for the special case of a single source. The obtained MSE expression explicitly depends on the number of subarrays in each dimension, which allows us to analytically find the optimal number of subarrays for spatial smoothing. Based on this result, we additionally derive the maximum asymptotic gain from spatial smoothing and explicitly compute the asymptotic efficiency for this special case. All the analytical results are verified by simulations.

cs.IT↗

arXiv2015

Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. In this paper, as a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain for two sources. Our analysis is supported by extensive simulation results.

cs.IT↗