arXiv subjects

Sergiy A. Vorobyov

Publications and source records attributed to Sergiy A. Vorobyov.

At least 73 records · Page 4Linked to original sources

arXiv2016

An Algebraic Approach to a Class of Rank-Constrained Semi-Definite Programs With Applications

A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink beamforming design in MIMO communications, generalized sidelobe canceller design, phase retrieval, etc., is presented. The essence of the approach is the use of underlying algebraic structure enforced in such problems by other practical constraints such as, for example, null shaping constraint. According to this approach, instead of relaxing the non-convex rankconstrained SDP problem to a feasible set of positive semidefinite matrices, we restrict it to a space of polynomials whose dimension is equal to the desired rank. The resulting optimization problem is then convex as its solution is required to be full rank, and can be efficiently and exactly solved. A simple matrix decomposition is needed to recover the solution of the original problem from the solution of the restricted one. We show how this approach can be applied to solving some important signal processing problems that contain null-shaping constraints. As a byproduct of our study, the conjugacy of beamfoming and parameter estimation problems leads us to formulation of a new and rigorous criterion for signal/noise subspace identification. Simulation results are performed for the problem of rank-constrained beamforming design and show an exact agreement of the solution with the proposed algebraic structure, as well as significant performance improvements in terms of sidelobe suppression compared to the existing methods.

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arXiv2015

Joint Robust Transmit/Receive Adaptive Beamforming for MIMO Radar Using Probability-Constrained Optimization

A joint robust transmit/receive adaptive beamforming for multiple-input multipleoutput (MIMO) radar based on probability-constrained optimization approach is developed in the case of Gaussian and arbitrary distributed mismatch present in both the transmit and receive signal steering vectors. A tight lower bound of the probability constraint is also derived by using duality theory. The formulated probability-constrained robust beamforming problem is nonconvex and NP-hard. However, we reformulate its cost function into a bi-quadratic function while the probability constraint splits into transmit and receive parts. Then, a block coordinate descent method based on second-order cone programming is developed to address the biconvex problem. Simulation results show an improved robustness of the proposed beamforming method as compared to the worst-case and other existing state-of-the-art joint transmit/receive robust adaptive beamforming methods for MIMO radar.

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arXiv2015

Ambiguity Function of the Transmit Beamspace-Based MIMO Radar

In this paper, we derive an ambiguity function (AF) for the transmit beamspace (TB)-based multipleinput multiple-output (MIMO) radar for the case of far-field targets and narrow-band waveforms. The effects of transmit coherent processing gain and waveform diversity are incorporated into the AF definition. To cover all the phase information conveyed by different factors, we introduce the equivalent transmit phase centers. The newly defined AF serves as a generalized AF form for which the phased-array (PA) and traditional MIMO radar AFs are important special cases. We establish relationships among the defined TB-based MIMO radar AF and the existing AF results including the Woodward's AF, the AFs defined for the traditional colocated MIMO radar, and also the PA radar AF, respectively. Moreover, we compare the TB-based MIMO radar AF with the square-summation-form AF definition and identify two limiting cases to bound its 'clear region' in Doppler-delay domain that is free of sidelobes. Corresponding bounds for these two cases are derived, and it is shown that the bound for the worst case is inversely proportional to the number of transmitted waveforms K, whereas the bound for the best case is independent of K. The actual 'clear region' of the TB-based MIMO radar AF depends on the array configuration and is in between of the worst- and best-case bounds. We propose a TB design strategy to reduce the levels of the AF sidelobes, and show in simulations that proper design of the TB matrix leads to reduction of the relative sidelobe levels of the TB-based MIMO radar AF.

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arXiv2015

Cramer-Rao Bound for Sparse Signals Fitting the Low-Rank Model with Small Number of Parameters

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.

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arXiv2015

Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size

Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods are exposed to performance breakdown, as the sample covariance matrix can largely deviate from the true covariance matrix. In this paper, the problem of DOA estimation performance breakdown is investigated. We consider the structure of the sample covariance matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, the subspace leakage is theoretically derived. We also propose a two-step method which improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced. Furthermore, we introduce a phenomenon named as root-swap which occurs in the root-MUSIC algorithm in the low sample size region and degrades the performance of the DOA estimation. A new method is then proposed to alleviate this problem. Numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods. Moreover, the proposed algorithms are combined with the pseudo-noise resampling method to further improve the performance.

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arXiv2014

Performance Limits of Segmented Compressive Sampling: Correlated Samples versus Bits

This paper gives performance limits of the segmented compressive sampling (CS) which collects correlated samples. It is shown that the effect of correlation among samples for the segmented CS can be characterized by a penalty term in the corresponding bounds on the sampling rate. Moreover, this penalty term is vanishing as the signal dimension increases. It means that the performance degradation due to the fixed correlation among samples obtained by the segmented CS (as compared to the standard CS with equivalent size sampling matrix) is negligible for a high-dimensional signal. In combination with the fact that the signal reconstruction quality improves with additional samples obtained by the segmented CS (as compared to the standard CS with sampling matrix of the size given by the number of original uncorrelated samples), the fact that the additional correlated samples also provide new information about a signal is a strong argument for the segmented CS.

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arXiv2014

On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

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arXiv2014

Permutation Enhanced Parallel Reconstruction with A Linear Compressive Sampling Device

In this letter, a permutation enhanced parallel reconstruction architecture for compressive sampling is proposed. In this architecture, a measurement matrix is constructed from a block-diagonal sensing matrix and the sparsifying basis of the target signal. In this way, the projection of the signal onto the sparsifying basis can be divided into several segments and all segments can be reconstructed in parallel. Thus, the computational complexity and the time for reconstruction can be reduced significantly. This feature is especially appealing for big data processing. Furthermore, to reduce the number of measurements needed to achieve the desired reconstruction error performance, permutation is introduced for the projection of the signal. It is shown that the permutation can be performed implicitly by using a pre-designed measurement matrix. Thus, the permutation enhanced parallel reconstruction can be achieved with a linear compressive sampling device.

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arXiv2014

How Many Beamforming Vectors Generate the Same Beampattern?

In this letter, we address the fundamental question of how many beamforming vectors exist which generate the same beampattern? The question is relevant to many fields such as, for example, array processing, radar, wireless communications, data compression, dimensionality reduction, and biomedical engineering. The desired property of having the same beampattern for different columns of a beamspace transformation matrix (beamforming vectors) often plays a key importance in practical applications. The result is that at most 2^{M-1}-1 beamforming vectors with the same beampattern can be generated from any given beamforming vector. Here M is the dimension of the beamforming vector. At the constructive side, the answer to this question allows for computationally efficient techniques for the beamspace transformation design. Indeed, one can start with a single beamforming vector, which gives a desired beampattern, and generate a number of other beamforming vectors, which give absolutely the same beampattern, in a computationally efficient way. We call the initial beamforming vector as the mother beamforming vector. One possible procedure for generating all possible new beamforming vectors with the same beampattern from the mother beamforming vector is proposed. The application of the proposed analysis to the transmit beamspace design in multiple-input multiple-output radar is also given.

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arXiv2014

Simple Semi-Distributed Lifetime Maximizing Strategy via Power Allocation in Collaborative Beamforming for Wireless Sensor Networks

Energy-efficient communication is an important issue in wireless sensor networks (WSNs) consisting of large number of energy-constrained sensor nodes. Indeed, sensor nodes have different energy budgets assigned to data transmission at individual nodes. Therefore, without energy-aware transmission schemes, energy can deplete from sensor nodes with smaller energy budget faster than from the rest of the sensor nodes in WSNs. This reduces the coverage area as well as the lifetime of WSNs. Collaborative beamforming (CB) has been proposed originally to achieve directional gain, however, it also inherently distributes the corresponding energy consumption over the collaborative sensor nodes. In fact, CB can be seen as a physical layer solution (versus the media access control/network layer solution) to balance the lifetimes of individual sensor nodes and extend the lifetime of the whole WSN. However, the introduction of energy-aware CB schemes is critical for extending the WSNs lifetime. In this paper, CB with power allocation (CB-PA) is developed to extend the lifetime of a cluster of collaborative sensor nodes by balancing the individual sensor node lifetimes. A novel strategy is proposed to utilize the residual energy information available at each sensor node. It adjusts the energy consumption rate at each sensor node while achieving the required average signal-to-noise ratio (SNR) at the destination. It is a semi-distributed strategy and it maintains average SNR. Different factors affecting the energy consumption are studied as well. Simulation results show that CB-PA outperforms CB with Equal Power Allocation (CB-EPA) in terms of extending the lifetime of a cluster of collaborative nodes.

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arXiv2014

Equivalent Codes, Optimality, and Performance Analysis of OSTBC: Textbook Study

An equivalent model for a multi-input multi-output (MIMO) communication system with orthogonal space-time block codes (OSTBCs) is proposed based on a newly revealed connection between OSTBCs and Euclidean codes. Examples of distance spectra, signal constellations, and signal coordinate diagrams of Euclidean codes equivalent to simplest OSTBCs are given. A new asymptotic upper bound for the symbol error rate (SER) of OSTBCs, based on the distance spectra of the introduced equivalent Euclidean codes is derived, and new general design criteria for signal constellations of the optimal OSTBC are proposed. Some bounds relating distance properties, dimensionality, and cardinality of OSTBCs with constituent signals of equal energy are given, and new optimal signal constellations with cardinalities M = 8 and M = 16 for Alamouti's code are designed. Using the new model for MIMO communication systems with OSTBCs, a general methodology for performance analysis of OSTBCs is developed. As an example of the application of this methodology, an exact evaluation of the SER of any OSTBC is given. Namely, a new expression for the SER of Alamouti's OSTBC with binary phase shift keying (BPSK) signals is derived.

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arXiv2014

Reweighted l1-norm Penalized LMS for Sparse Channel Estimation and Its Analysis

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l1-norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l0-pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l1-norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l1-norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l1-norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l1-norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.

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arXiv2014

Efficient Strategies for Single/Multi-Target Jamming on MIMO Gaussian Channels

The problem of jamming on multiple-input multiple-output (MIMO) Gaussian channels is investigated in this paper. In the case of a single target legitimate signal, we show that the existing result based on the simplification of the system model by neglecting the jamming channel leads to losing important insights regarding the effect of jamming power and jamming channel on the jamming strategy. We find a closed-form optimal solution for the problem under a positive semi-definite (PSD) condition without considering simplifications in the model. If the condition is not satisfied and the optimal solution may not exist in closed-form, we find the optimal solution using a numerical method and also propose a suboptimal solution in closed-form as a close approximation of the optimal solution. Then, the possibility of extending the results to solve the problem of multi-target jamming is investigated for four scenarios, i.e., multiple access channel, broadcasting channel, multiple transceiver pairs with orthogonal transmissions, and multiple transceiver pairs with interference, respectively. It is shown that the proposed numerical method can be extended to all scenarios while the proposed closed-form solutions for jamming may be applied in the scenarios of the multiple access channel and multiple transceiver pairs with orthogonal transmissions. Simulation results verify the effectiveness of the proposed solutions.

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arXiv2013

Spectral Estimation from Undersampled Data: Correlogram and Model-Based Least Squares

This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum into a number of segments and estimates the average power within each spectral segment. We derive the bias and the variance of the spectrum estimator, and show that there is a tradeoff between the accuracy of the estimation and the frequency resolution. The asymptotic behavior of the estimator is also investigated, and it is proved that this spectrum estimator is consistent. A new algorithm for reconstructing signals with sparse spectrum from noisy compressive measurements is also introduced. Such model-based algorithm takes the signal structure into account for estimating the unknown parameters which are the frequencies and the amplitudes of linearly combined sinusoidal signals. A high-resolution spectral estimation method is used to recover the frequencies of the signal elements, while the amplitudes of the signal components are estimated by minimizing the squared norm of the compressed estimation error using the least squares technique. The Cramer-Rao bound for the given system model is also derived. It is shown that the proposed algorithm approaches the bound at high signal to noise ratios.

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arXiv2013

Finite-Length and Asymptotic Analysis of Correlogram for Undersampled Data

This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into a number of segments and estimates the average power within each spectral segment. This method is able to estimate the power spectrum density of a signal from undersampled data without essentially requiring the signal to be sparse. We derive the bias and the variance of the spectrum estimator, and show that there is a tradeoff between the accuracy of the estimation, the frequency resolution, and the complexity of the estimator. A closed-form approximation of the estimation variance is also derived, which clearly shows how the variance is related to different parameters. The asymptotic behavior of the estimator is also investigated, and it is proved that this spectrum estimator is consistent. Moreover, the estimation made for different spectral segments becomes uncorrelated as the signal length tends to infinity. Finally, numerical examples and simulation results are provided, which approve the theoretical conclusions.

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arXiv2013

Permutation Meets Parallel Compressed Sensing: How to Relax Restricted Isometry Property for 2D Sparse Signals

Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational complexity significantly. To solve this problem, we propose to reshape the multidimensional signal into a 2D signal and sample the 2D signal using compressed sensing column by column with the same sensing matrix. It is referred to as parallel compressed sensing, and it has much lower storage and computational complexity. For a given reconstruction performance of parallel compressed sensing, if a so-called acceptable permutation is applied to the 2D signal, we show that the corresponding sensing matrix has a smaller required order of restricted isometry property condition, and thus, storage and computation requirements are further lowered. A zigzag-scan-based permutation, which is shown to be particularly useful for signals satisfying a layer model, is introduced and investigated. As an application of the parallel compressed sensing with the zigzag-scan-based permutation, a video compression scheme is presented. It is shown that the zigzag-scan-based permutation increases the peak signal-to-noise ratio of reconstructed images and video frames.

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arXiv2013

Efficient Transmit Beamspace Design for Search-free Based DOA Estimation in MIMO Radar

In this paper, we address the problem of transmit beamspace design for multiple-input multiple-output (MIMO) radar with colocated antennas in application to direction-of-arrival (DOA) estimation. A new method for designing the transmit beamspace matrix that enables the use of search-free DOA estimation techniques at the receiver is introduced. The essence of the proposed method is to design the transmit beamspace matrix based on minimizing the difference between a desired transmit beampattern and the actual one under the constraint of uniform power distribution across the transmit array elements. The desired transmit beampattern can be of arbitrary shape and is allowed to consist of one or more spatial sectors. The number of transmit waveforms is even but otherwise arbitrary. To allow for simple search-free DOA estimation algorithms at the receive array, the rotational invariance property is established at the transmit array by imposing a specific structure on the beamspace matrix. Semi-definite relaxation is used to transform the proposed formulation into a convex problem that can be solved efficiently. We also propose a spatial-division based design (SDD) by dividing the spatial domain into several subsectors and assigning a subset of the transmit beams to each subsector. The transmit beams associated with each subsector are designed separately. Simulation results demonstrate the improvement in the DOA estimation performance offered by using the proposed joint and SDD transmit beamspace design methods as compared to the traditional MIMO radar technique.

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arXiv2013

Sum-Rate Maximization with Minimum Power Consumption for MIMO DF Two-Way Relaying: Part I - Relay Optimization

The problem of power allocation is studied for a multiple-input multiple-output (MIMO) decode-and-forward (DF) two-way relaying system consisting of two source nodes and one relay. It is shown that achieving maximum sum-rate in such a system does not necessarily demand the consumption of all available power at the relay. Instead, the maximum sum-rate can be achieved through efficient power allocation with minimum power consumption. Deriving such power allocation, however, is nontrivial due to the fact that it generally leads to a nonconvex problem. In Part I of this two-part paper, a sum-rate maximizing power allocation with minimum power consumption is found for MIMO DF two-way relaying, in which the relay optimizes its own power allocation strategy given the power allocation strategies of the source nodes. An algorithm is proposed for efficiently finding the optimal power allocation of the relay based on the proposed idea of relative water-levels. The considered scenario features low complexity due to the fact that the relay optimizes its power allocation without coordinating the source nodes. As a trade-off for the low complexity, it is shown that there can be waste of power at the source nodes because of no coordination between the relay and the source nodes. Simulation results demonstrate the performance of the proposed algorithm and the effect of asymmetry on the considered system.

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