Browsing by Author "Vorobyov, Sergiy A."

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  • An Accelerated Composite Gradient Method for Large-scale Composite Objective Problems
    (2019-01-15) Florea, Mihai I.; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Various signal processing applications can be expressed as large-scale optimization problems with a composite objective structure, where the Lipschitz constant of the smooth part gradient is either not known, or its local values may only be a fraction of the global value. The smooth part may be strongly convex as well. The algorithms capable of addressing this problem class in its entirety are black-box accelerated first-order methods, related to either Nesterov's Fast Gradient Method or the Accelerated Multistep Gradient Scheme, which were developed and analyzed using the estimate sequence mathematical framework. In this paper, we develop the augmented estimate sequence framework, a relaxation of the estimate sequence. When the lower bounds incorporated in the augmented estimate functions are hyperplanes or parabolae, this framework generates a conceptually simple gap sequence. We use this gap sequence to construct the Accelerated Composite Gradient Method (ACGM), a versatile first-order scheme applicable to any composite problem. Moreover, ACGM is endowed with an efficient dynamic Lipschitz constant estimation (line-search) procedure. We also introduce the wall-clock time unit (WTU), a complexity measure applicable to all first-order methods that accounts for variations in per-iteration complexity and more consistently reflects the running time in practical applications. When analyzed using WTU, ACGM has the best provable convergence rate on the composite problem class, both in the strongly and non-strongly convex cases. Our simulation results confirm the theoretical findings and show the superior performance of our new method.
  • AdaBoost-Based Efficient Channel Estimation and Data Detection in One-Bit Massive MIMO
    (2024) Esfandiari, Majdoddin; Vorobyov, Sergiy A.; Heath, Robert W.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    The use of one-bit analog-to-digital converter (ADC) has been considered as a viable alternative to high resolution counterparts in realizing and commercializing massive multiple-input multiple-output (MIMO) systems. However, the issue of discarding the amplitude information by one-bit quantizers has to be compensated. Thus, carefully tailored methods need to be developed for one-bit channel estimation and data detection as the conventional ones cannot be used. To address these issues, the problems of one-bit channel estimation and data detection for MIMO orthogonal frequency division multiplexing (OFDM) system that operates over uncorrelated frequency selective channels are investigated here. We first develop channel estimators that exploit Gaussian discriminant analysis (GDA) classifier and approximate versions of it as the so-called weak classifiers in an adaptive boosting (AdaBoost) approach. Particularly, the combination of the approximate GDA classifiers with AdaBoost offers the benefit of scalability with the linear order of computations, which is critical in massive MIMO-OFDM systems. We then take advantage of the same idea for proposing the data detectors. Numerical results validate the efficiency of the proposed channel estimators and data detectors compared to other methods. They show comparable/better performance to that of the state-of-the-art methods, but require dramatically lower computational complexities and run times.
  • ADMM-Based Solution for mmWave UL Channel Estimation with One-Bit ADCs via Sparsity Enforcing and Toeplitz Matrix Reconstruction
    (2023) Esfandiari, Majdoddin; Vorobyov, Sergiy A.; Heath, Robert W.
     A4 Artikkeli konferenssijulkaisussa
    Low-power millimeter wave (mmWave) multi-input multi-output communication systems can be enabled with the use of one-bit analog-to-digital converters. Owing to the extreme quantization, conventional signal processing tasks such as channel estimation are challenging, making uplink (UL) multiuser receivers difficult to implement. To address this issue, we first reformulate the UL channel estimation problem, and then combine the idea of ℓ1 regularized logistic regression classification and Toeplitz matrix reconstruction in a properly designed optimization problem. Our new method is referred to as ℓ1 regularized logistic regression with Toeplitz matrix reconstruction (L1-RLR-TMR). In addition, we develop a computationally efficient alternating direction method of multi-pliers (ADMM)-based implementation for the L1-RLR-TMR method. Numerical results demonstrate the performance of the L1-RLR-TMR method in comparison with other existing methods.
  • Advances in DOA Estimation and Source Localization
    (2017) Aboutanios, Elias; Hassanien, Aboulnasr; El-Keyi, Amr; Nasser, Youssef; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
  • Algebraic Geometry Based Design for Generalized Sidelobe Canceler
    (2019-11) Morency, Matthew W.; Vorobyov, Sergiy A.
     A4 Artikkeli konferenssijulkaisussa
    Generalized sidelobe canceler (GSC) uses a two step procedure in order to produce a beampattern with a fixed mainlobe and suppressed sidelobes. In the first step, a beampattern with a fixed response in the look direction is produced by convolving a vector of constraints with a normalized beamforming vector with the desired mainlobe response. In the second step, the signals in the look direction are blocked out using so-called blocking matrix, while the output power is minimized. Observing that for Griffiths-Jim GSC the beamforming vector contains the coefficients of a polynomial with at least one root at 1, we find here that all rows of a blocking matrix should be the coefficients of polynomials from the polynomial ideal with a root at 1. This allows us to reveal and exploit the underlying algebraic structure for GSC blocking matrix design using methods from computational algebraic geometry. It also allows to arrive to and prove several generalized statements. For example, the necessary and sufficient condition for a signal to be blocked can be easily found. The condition to a row-space of blocking matrix for blocking multiple signals impinging upon the array from multiple directions can also be easily formulated. The linear independence of rows of blocking matrix implies that all the corresponding polynomial share a single root. In general, understanding the algebraic structure that GSC's blocking matrix has to satisfy makes the GSC's design simpler and more intuitive.
  • Attention Neural Network for Downlink Cell-Free Massive MIMO Power Control
    (2023-03-07) Kocharlakota, Atchutaram K.; Vorobyov, Sergiy A.; Heath, Robert W.
     A4 Artikkeli konferenssijulkaisussa
    The downlink power control is challenging in a cell-free massive multiple-input multiple-output (CFmMIMO) system because of the non-convexity of the problem. This paper proposes a computationally efficient deep-learning algorithm to solve the max-min power control optimization problem subject to power constraints. To solve this problem, it presents an attention neural network(ANN) composed using the masked multi-head attention network modules, which are building blocks of the popular transformer neural network. The ANN solves the downlink power control problem of CFmMIMO in the presence of pilot contamination (non-orthogonal pilot sequences). The paper first translates the constrained optimization problem to an unconstrained one parameterized by the weights of the ANN. These weights are trained in an unsupervised fashion. The performance of the ANN power control algorithm is demonstrated using numerical simulations. The paper also provides a computational complexity analysis of the method.
  • Beamforming Design for Integrated Sensing, Over-the-Air Computation, and Communication in Internet of Robotic Things
    (2024) Dong, Kai; Vorobyov, Sergiy A.; Yu, Hao; Taleb, Tarik
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    The integration of communication and radar systems could enhance the robustness of future communication systems to support advanced application demands, e.g., target sensing, data exchange, and parallel computation. In this article, we investigate the beamforming design for integrated sensing, computing, and communication (ISCC) in the Internet of Robotic Things (IoRT) scenario. Specifically, we assume that each robot uploads its preprocessed sensing information to the access point (AP). Meanwhile, leveraging the additive features of the spatial wireless channels between robots and AP, over-the-air computation (AirComp) through multirobot cooperation could bolster system performance, particularly in tasks like target localization through sensing. To get a full picture of the effects of antenna array structures and beampatterns on the ISCC system, we evaluate the performance by considering the shared and separated antenna structures, as well as the omnidirectional and directional beampatterns. Based on these setups, the nonconvex optimization problems for the performance tradeoff between sensing and AirComp are formulated to minimize the mean-squared error (MSE) of AirComp and sensing. To efficiently solve these optimization problems, we designed the gradient descent augmented Lagrangian (GDAL) algorithm, which involves dynamically adjusting the step sizes while updating the variables. Simulation results show that the separated antenna structure achieves a lower AirComp MSE than the shared antenna setup because it has greater beam steering Degrees of Freedom. Moreover, the beampattern types have almost no effect on the AirComp MSE for the given antenna structure setup. This comprehensive investigation provides useful guidelines for ISCC framework implementation in IoRT applications.
  • A Combined Waveform-Beamforming Design for Millimeter-Wave Joint Communication-Radar
    (2019-11) Kumari, Preeti; Myers, Nitin Jonathan; Vorobyov, Sergiy A.; Heath, Robert W.
     A4 Artikkeli konferenssijulkaisussa
    Millimeter-wave (mmWave) joint communication-radar (JCR) simultaneously realizes a high data rate communication and a high-resolution radar sensing for applications such as autonomous driving. Prior JCR systems that are based on the state-of-the-art mmWave communications hardware, however, suffer from a limited angular field-of-view (FoV) and low detection rate for radars due to the employed directional beam. To address this limitation, we propose an adaptive and fast combined waveform-beamforming design for mmWave JCR with a phased-array architecture. We present a JCR beamformer design algorithm that permits a trade-off between communication data rate and radar successful recovery rate in the angular domain. We show that distinct radar measurements can be obtained with circulant shifts of the designed JCR beamformer for compressed radar sensing. Numerical results demonstrate that our JCR design enables the angle-of-arrival/departure estimation of short-range radar targets with a high successful recovery rate and a wide FoV at the expense of a slight loss in the communication rate.
  • Convolutional Simultaneous Sparse Approximation with Applications to RGB-NIR Image Fusion
    (2023-03-07) Veshki, Farshad G.; Vorobyov, Sergiy A.
     A4 Artikkeli konferenssijulkaisussa
    Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple correlated input signals. In this paper, we propose algorithms for convolutional SSA (CSSA) based on the alternating direction method of multipliers. Specifically, we address the CSSA problem with different sparsity structures and the convolutional feature learning problem in multimodal data/signals based on the SSA model. We evaluate the proposed algorithms by applying them to multimodal and multifocus image fusion problems.
  • Correlation-based Graph Smoothness Measures In Graph Signal Processing
    (2023) Miettinen, Jari; Vorobyov, Sergiy A.; Ollila, Esa; Wang, Xinjue
     A4 Artikkeli konferenssijulkaisussa
    Graph smoothness is an important prior used for designing sampling strategies for graph signals as well as for regularizing the problem of graph learning. Additionally, smoothness is an appropriate assumption for graph signal processing (GSP) tasks such as filtering or signal recovery from samples. The most popular measure of smoothness is the quadratic form of the Laplacian, which naturally follows from the factor analysis approach. This paper presents a novel smoothness measure based on the graph correlation. The proposed measure enhances the applicability of graph smoothness measures across a variety of GSP tasks, by facilitating interoperability and generalizing across shift operators.
  • Coupled Feature Learning Via Structured Convolutional Sparse Coding for Multimodal Image Fusion
    (2022) Veshki, Farshad G.; Vorobyov, Sergiy A.
     A4 Artikkeli konferenssijulkaisussa
    A novel method for learning correlated features in multimodal images based on convolutional sparse coding with applications to image fusion is presented. In particular, the correlated features are captured as coupled filters in convolutional dictionaries. At the same time, the shared and independent features are approximated using separate convolutional sparse codes and a common dictionary. The resulting optimization problem is addressed using alternating direction method of multipliers. The coupled filters are fused based on a maximum-variance rule, and a maximum-absolute-value rule is used to fuse the sparse codes. The proposed method does not entail any prelearning stage. The experimental evaluations using medical and infrared-visible image datasets demonstrate the superiority of our method compared to state-of-the-art algorithms in terms of preserving the details and local intensities as well as improving objective metrics.
  • DOA Estimation for Transmit Beamspace MIMO Radar via Tensor Decomposition with Vandermonde Factor Matrix
    (2022) Xu, Feng; Morency, Mathew W.; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general higher-order tensor model that enables computationally efficient DOA estimation is designed. Whereas other tensor decomposition-based methods treat all factor matrices as arbitrary, the essence of the proposed DOA estimation method is to fully exploit the Vandermonde structure of the factor matrices to take advantage of the shift-invariance between and within different transmit subarrays. Specifically, the received signal of TB MIMO radar is expressed as a higher-order tensor. A computationally efficient tensor decomposition method is proposed to decompose the Vandermonde factor matrices of this signal tensor. The generators of the Vandermonde factor matrices are computed to estimate the phase rotations between subarrays, which can be utilized as a look-up table for finding targets DOA. The proposed tensor signal model as well as the DOA estimation algorithm are also straightforwardly applicable for the one-dimensional TB MIMO radar case. It is further shown that our proposed approach can be used in a more general scenario where the transmit subarrays with arbitrary but identical configuration can be non-uniformly displaced. We also show that both the tensor rank of the signal tensor and the matrix rank of a particular matrix derived from the signal tensor are identical to the number of targets. Thus, the number of targets can be estimated via matrix rank determination. Simulation results illustrate the performance improvement of the proposed DOA estimation method as compared to other tensor decomposition-based techniques for TB MIMO radar.
  • Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model
    (2024) Wang, Xinjue; Ollila, Esa; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Graph Neural Networks (GNNs), particularly Graph Convolutional Neural Networks (GCNNs), have emerged as pivotal instruments in machine learning and signal processing for processing graph-structured data. This paper proposes an analysis framework to investigate the sensitivity of GCNNs to probabilistic graph perturbations, directly impacting the graph shift operator (GSO). Our study establishes tight expected GSO error bounds, which are explicitly linked to the error model parameters, and reveals a linear relationship between GSO perturbations and the resulting output differences at each layer of GCNNs. This linearity demonstrates that a single-layer GCNN maintains stability under graph edge perturbations, provided that the GSO errors remain bounded, regardless of the perturbation scale. For multilayer GCNNs, the dependency of system's output difference on GSO perturbations is shown to be a recursion of linearity. Finally, we exemplify the framework with the Graph Isomorphism Network (GIN) and Simple Graph Convolution Network (SGCN). Experiments validate our theoretical derivations and the effectiveness of our approach.
  • Graph Error Effect on Graph Neural Networks: Theoretical Bounds
    (2022-08-22) Wang, Xinjue
     Sähkötekniikan korkeakoulu | Master's thesis
    Graph neural networks (GNNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GNNs. In this thesis, the effect on the performance of GNNs is studied when the adjacency matrix is estimated with errors, namely, it is assumed to be perturbed by a probabilistic graph error model. It is proven that the error as measured by the difference in the spectral norm of the true adjacency matrix and the mislearned adjacency matrix under the error model is bounded, and the error upper bound is a function of graph size and error probability parameters regarding erroneously adding or deleting edges from the graph topology. A similar error upper bound regarding the normalized adjacency matrix with self-loop added is also derived. Diverse numerical experiments in the thesis illustrate the derived error bounds on a synthetic dataset and study the error sensitivity of a simple graph convolutional neural network under the probabilistic error model.
  • Graph Neural Network Sensitivity Under Probabilistic Error Model
    (2022) Wang, Xinjue; Ollila, Esa; Vorobyov, Sergiy A.
     A4 Artikkeli konferenssijulkaisussa
    Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.
  • Impact of Pilot Overhead and Channel Estimation on the Performance of Massive MIMO
    (2021-12-01) Kocharlakota, Atchutaram K.; Upadhya, Karthik; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    This paper studies the impact of additional pilot overhead for covariance matrix estimation in a time-division duplexed (TDD) massive multiple-input multiple-output (MIMO) system. We choose average uplink (UL) and downlink (DL) spectral efficiencies (SEs) as performance metrics for the massive MIMO system, and derive closed form expressions for them in terms of the additional pilot overhead. The expressions are derived by considering linear minimum mean squared error (LMMSE)-type and element-wise LMMSE-type channel estimates that represent LMMSE and element-wise LMMSE with estimated covariance matrices, respectively. Using these expressions, a detailed theoretical analysis of SE behavior as a function of pilot overhead for both LMMSE-type and element-wise LMMSE-type channel estimation are presented, followed by simulations, which also demonstrate and validate theoretical results.
  • Improved Proportionate Least Mean Square/Fourth Based Channel Equalization for Underwater Acoustic Communications
    (2023) Tian, Ya-nan; Han, Xiao; Vorobyov, Sergiy A.; Li, Weizhe
     A4 Artikkeli konferenssijulkaisussa
    An improved proportionate least mean square/fourth (IPLMS/F) equalizer is proposed in this paper, and applied to underwater acoustic communications in real experiment. In addition to improving the performance of least mean squares (LMS) equalizer, the proposed IPLMS/F equalizer maintains the simplicity and stability of LMS. The advantage of the proposed IPLMS/F equalizer is due to introduction of a proportional update matrix. The diagonal elements of this matrix are determined by the equalizer tap magnitudes to improve the sparsity level estimate, and thus, further improve the equalizer performance. The performance of IPLMS/F is verified by applying it to the experimental data from the 9th Chinese National Arctic Research Expedition. The results show that IPLMS/F exhibits fastest convergence speed and it has the lowest bit error rate compared with LMS and LMS/F, indicating its effectiveness and reliability in practical applications.
  • Joint design of radar transmit waveform and mismatched filter with low sidelobes
    (2020) Jing, Yang; Liang, Junli; Vorobyov, Sergiy A.; Fan, Xuhui; Zhou, Deyun
     A4 Artikkeli konferenssijulkaisussa
    The paper focuses on joint design of transmit waveform and mismatched filter to achieve low sidelobe level for improving the resolution of pulse compression (PC). An Lp-norm, p = 1, of the power ratio of sidelobe to mainlobe levels is used in the corresponding PC optimization problem as a metric. The use of Lp-norm minimization contains as special cases the integrated sidelobe level and peak sidelobe level (PSL) minimization problems which corresponds to specific selections of different p values. The main contribution of this work is the development of a new iterative algorithm to solve the aforementioned optimization problem. It is based on using Dinkelbach's scheme together with majorization minimization method. The computational complexity of the proposed algorithm is also analyzed. Numerical examples demonstrate that waveforms and mismatched filters designed by using the proposed method produce lower PSL than the existing counterparts.
  • Joint DOD and DOA Estimation in Slow-Time MIMO Radar via PARAFAC Decomposition
    (2020-01-01) Xu, Feng; Vorobyov, Sergiy A.; Yang, Xiaopeng
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We develop a new tensor model for slow-time multiple-input multiple-output (MIMO) radar, and apply it for joint direction-of-departure (DOD), and direction-of-arrival (DOA) estimation. This tensor model aims to exploit the independence of phase modulation matrix, and receive array in the received signal for slow-time MIMO radar. Such tensor can be decomposed into two tensors of different ranks, one of which has identical structure to that of the conventional tensor model for MIMO radar, and the other contains all phase modulation values used in the transmit array. We then develop a modification of the alternating least squares algorithm to enable parallel factor decomposition of tensors with extra constants. The Vandermonde structure of the transmit, and receive steering matrices (if both arrays are uniform, and linear) is then utilized to obtain angle estimates from factor matrices. The multi-linear structure of the received signal is maintained to take advantage of tensor-based angle estimation algorithms, while the shortage of samples in Doppler domain for slow-time MIMO radar is mitigated. As a result, the joint DOD, and DOA estimation performance is improved as compared to existing angle estimation techniques for slow-time MIMO radar. Simulation results verify the effectiveness of the proposed method.
  • Lossless Dimension Reduction for Integer Least Squares with Application to Sphere Decoding
    (2020) Neinavaie, Mohammad; Derakhtian, Mostafa; Vorobyov, Sergiy A.
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-Achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) linearly detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE linearly detected point has a vital difference at low SNRs. By exploiting the information provided by the MMSE of linear method, we prove the existence of a lossless dimension reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless dimension reduction-Aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.