arXiv subjects

Mats Viberg

Publications and source records attributed to Mats Viberg.

12 recordsLinked to original sources

arXiv2026

Statistical Analysis of the Extensive Cancellation Algorithm for Passive Radar Using an Imperfect Reference Signal

Passive radar systems have received tremendous attention over the past few decades, due to their low cost and ability to remain covert during operation. Such systems rely on a so-called Illuminator-of-Opportunity (IO), for example, a commercial TV station. We consider a network of Receiving Nodes (RN) without spatial resolution capability, which receives the direct signal and reflections from both stationary objects (clutter) and possible targets. After suitable preprocessing, the RNs transmit information to a Fusion Center (FC) that performs the final target detection, localization and tracking. Several methods for target localization have been proposed in the literature, and our focus is on the seminal Extensive Cancellation Algorithm (ECA). In this approach, each RN collects information about target parameters, while canceling interference using a projection. This is done by exploiting a separate Reference Channel (RC), which captures the IO signal without interference apart from receiver noise. We derive the statistical properties of the ECA parameter estimates under the assumption of a high Signal-to-Noise Ratio (SNR), and we give a sufficient condition for the SNR in the RC to enable statistically efficient estimates. The theoretical results are corroborated through computer simulations, which indicate that the theory agrees well with empirical results under practical operating conditions. The contributions of this paper can be used, for example, to design experimental setups for feasibility studies and to inform system design for achieving a desired localization accuracy.

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arXiv2026

Separable Delay And Doppler Estimation In Passive Radar

In passive radar, a network of distributed sensors exploit signals from so-called Illuminators-of-Opportunity to detect and localize targets. We consider the case where the IO signal is available at each receiver node through a reference channel, whereas target returns corrupted by interference are collected in a separate surveillance channel. The problem formulation is similar to an active radar that uses a noise-like waveform, or an integrated sensing and communication application. The available data is first split into batches of manageable size. In the direct approach, the target's time-delay and Doppler parameters are estimated jointly by incoherently combining the batch-wise data. We propose a new method to estimate the time-delay separately, thus avoiding a costly 2-D search. Our approach is designed for slowly moving targets, and the accuracy of the time-delay estimate is similar to that of the full batch-wise 2-D method. Given the time-delay, the coherency between batches can be restored when estimating the Doppler parameter. Thereby, the separable approach is found to yield superior Doppler estimates over a wide parameter range. In addition to reducing computational complexity, the proposed separable estimation technique also significantly reduces the communication overhead in a distributed radar setting.

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arXiv2025

Statistical Analysis of Target Parameter Estimation Using Passive Radar

A passive radar system uses one or more so-called Illuminators of Opportunity (IO) to detect and localize targets. In such systems, a reference channel is often used at each receiving node to capture the transmitted IO signal, while targets are detected using the main surveillance channel. The purpose of the present contribution is to analyze a method for estimating the target parameters in such a system. Specifically, we quantify the additional error contribution due to not knowing the transmitted IO waveform perfectly. A sufficient condition for this error to be negligible as compared to errors due to clutter and noise in the surveillance channel is then given.

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arXiv2022

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.

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arXiv2017

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.

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arXiv2016

Transmission Strategies for Remote Estimation with an Energy Harvesting Sensor

We consider the remote estimation of a time-correlated signal using an energy harvesting (EH) sensor. The sensor observes the unknown signal and communicates its observations to a remote fusion center using an amplify-and-forward strategy. We consider the design of optimal power allocation strategies in order to minimize the mean-square error at the fusion center. Contrary to the traditional approaches, the degree of correlation between the signal values constitutes an important aspect of our formulation. We provide the optimal power allocation strategies for a number of illustrative scenarios. We show that the most majorized power allocation strategy, i.e. the power allocation as balanced as possible, is optimal for the cases of circularly wide-sense stationary (c.w.s.s.) signals with a static correlation coefficient, and sampled low-pass c.w.s.s. signals for a static channel. We show that the optimal strategy can be characterized as a water-filling type solution for sampled low-pass c.w.s.s. signals for a fading channel. Motivated by the high-complexity of the numerical solution of the optimization problem, we propose low-complexity policies for the general scenario. Numerical evaluations illustrate the close performance of these low-complexity policies to that of the optimal policies, and demonstrate the effect of the EH constraints and the degree of freedom of the signal.

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arXiv2016

Performance Bounds for Remote Estimation under Energy Harvesting Constraints

Remote estimation with an energy harvesting sensor with a limited data and energy buffer is considered. The sensor node observes an unknown Gaussian field and communicates its observations to a remote fusion center using the energy it harvested. The fusion center employs minimum mean-square error (MMSE) estimation to reconstruct the unknown field. The distortion minimization problem under the online scheme, where the sensor has access to only the statistical information for the future energy packets is considered. We provide performance bounds on the achievable distortion under a slotted block transmission scheme, where at each transmission time slot, the data and the energy buffer are completely emptied. Our bounds provide insights to the trade-offs between the buffer sizes, the statistical properties of the energy harvesting process and the achievable distortion. In particular, these trade-offs illustrate the insensitivity of the performance to the buffer sizes for signals with low degree of freedom and suggest performance improvements with increasing buffer size for signals with relatively higher degree of freedom. Depending only on the mean, variance and finite support of the energy arrival process, these results provide practical insights for the battery and buffer sizes for deployment in future energy harvesting wireless sensing systems.

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arXiv2015

Performance Analysis of Parameter Estimation Using LASSO

The Least Absolute Shrinkage and Selection Operator (LASSO) has gained attention in a wide class of continuous parametric estimation problems with promising results. It has been a subject of research for more than a decade. Due to the nature of LASSO, the previous analyses have been non-parametric. This ignores useful information and makes it difficult to compare LASSO to traditional estimators. In particular, the role of the regularization parameter and super-resolution properties of LASSO have not been well-understood yet. The objective of this work is to provide a new insight into this context by introducing LASSO as a parametric technique of a varying order. This provides us theoretical expressions for the LASSO-based estimation error and false alarm rate in the asymptotic case of high SNR and dense grids. For this case, LASSO is compared to maximum likelihood and conventional beamforming. It is found that LASSO loses performance due to the regularization term, but the amount of loss is practically negligible with a proper choice of the regularization parameter. Thus, we provide suggestions on the selection of the regularization parameter. Without loss of generality, we present the comparative numerical results in the context of Direction of Arrival (DOA) estimation using a sensor array.

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arXiv2015

A Novel Sparsity-Based Approach to Recursive Estimation of Dynamic Parameter Sets

We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the observations are not reliable or the parameters evolve rapidly. Inspired by the sparsity based techniques, we introduce a novel Bayesian model for the problems of interest and study its associated recursive Bayesian filter. We propose an algorithm approximating the Bayesian filter, maintaining a reasonable amount of calculations. We compare by numerical evaluation the resulting technique to state-of-the-art algorithms in different scenarios. In a scenario with a low SNR, the proposed method outperforms other complex techniques.

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arXiv2014

Wideband Waveform Design for Robust Target Detection

Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is developed. The context is optimal detection of a single object with partially unknown parameters. The waveforms are robust in the sense that, for a single transmission, detection capability is maintained over an interval of time-delay and time-scaling (Doppler) parameters. A solution framework is derived, approximated, and formulated as an optimization by means of basis expansion. In terms of probabilities of detection and false alarm, numerical evaluation shows the efficiency of the proposed method when compared with a Linear Frequency Modulated signal and a Gaussian pulse.

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arXiv2012

A robust l_1 penalized DOA estimator

The SPS-LASSO has recently been introduced as a solution to the problem of regularization parameter selection in the complex-valued LASSO problem. Still, the dependence on the grid size and the polynomial time of performing convex optimization technique in each iteration, in addition to the deficiencies in the low noise regime, confines its performance for Direction of Arrival (DOA) estimation. This work presents methods to apply LASSO without grid size limitation and with less complexity. As we show by simulations, the proposed methods loose a negligible performance compared to the Maximum Likelihood (ML) estimator, which needs a combinatorial search We also show by simulations that compared to practical implementations of ML, the proposed techniques are less sensitive to the source power difference.

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arXiv2010

A Wideband Spectrum Sensing Method for Cognitive Radio using Sub-Nyquist Sampling

Spectrum sensing is a fundamental component in cognitive radio. A major challenge in this area is the requirement of a high sampling rate in the sensing of a wideband signal. In this paper a wideband spectrum sensing model is presented that utilizes a sub-Nyquist sampling scheme to bring substantial savings in terms of the sampling rate. The correlation matrix of a finite number of noisy samples is computed and used by a subspace estimator to detect the occupied and vacant channels of the spectrum. In contrast with common methods, the proposedmethod does not need the knowledge of signal properties that mitigates the uncertainty problem. We evaluate the performance of this method by computing the probability of detecting signal occupancy in terms of the number of samples and the SNR of randomly generated signals. The results show a reliable detection even in low SNR and small number of samples.

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