Covariance Shaping Research Articles

Desensitized Optimal Control

Desensitized optimal control (DOC) enables the formulation of optimal control problems that incorporate the optimal reference solution’s sensitivities to state perturbations into the optimization process. Mathematically, this is achieved through the introduction of Lagrange multiplierlike quantities that act as additional state variables and capture the desired sensitivity information. By penalizing user-specified sensitivities, the reference solution becomes easier to control under feedback. Thus, the DOC method can be viewed as a method to improve nonlinear robustness. By converting fixed parameters appearing in the problem formulation to state variables with trivial dynamics, the DOC approach can be used to improve robustness to parameter uncertainties. The paper also analyzes the relationship between sensitivities and the covariance matrix and compares the benefits and limitations of covariance shaping versus DOC. A simple Zermelo-type boat path optimization problem with uncertainties in the water current is analyzed to demonstrate the DOC approach.

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Ergodic Capacity Analysis of Downlink Communication Systems under Covariance Shaping Equalizers

Advances in higher-end spectrum utilization has enabled user equipment to dock multiple antenna elements, and hence make use of selectivity via equalization in new generation of mobile networks. The equalization can exploit channel statistics to shape covariance matrices, and hence improve network performance at the physical layer of these networks by projecting segregated signals to non-overlapping subspaces. We propose to establish the promise of covariance shaping method by incorporating the equalizers in the modelling of a downlink multi-user multiple-input multiple-output (MU-MIMO) systems and thereby characterizing a key performance indicator, namely, the sum ergodic capacity. This is achieved by utilizing a residue theory approach which can account for indefinite eigenvalues. The system modelling is generic in a sense that it requires the base station (BS) to only have second order statistics of the channel rather than instantaneous knowledge. Furthermore, the BS incorporates a transmit beamformer design to enhance the ergodic capacity and feedforward the information of covariance shaping equalizers. Search method for transmit beamforming is also proposed which shows a promising three fold increase in sum ergodic capacity at signal-to-noise ratio of 10 dB for the considered MU-MIMO system. Proposed characterization of the system is authenticated using simulation means, and a comparative analysis of transmit beamformer designs on the sum ergodic rate is showcased.

Enforcing Statistical Orthogonality in Massive MIMO Systems via Covariance Shaping

This paper tackles the problem of downlink data transmission in massive multiple-input multiple-output (MIMO) systems where user equipments (UEs) exhibit high spatial correlation and channel estimation is limited by strong pilot contamination. Signal subspace separation among UEs is, in fact, rarely realized in practice and is generally beyond the control of the network designer (as it is dictated by the physical scattering environment). In this context, we propose a novel statistical beamforming technique, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIMO covariance shaping</i> , that exploits multiple antennas at the UEs and leverages the realistic non-Kronecker structure of massive MIMO channels to target a suitable shaping of the channel statistics performed at the UE-side. To optimize the covariance shaping strategies, we propose a low-complexity block coordinate descent algorithm that is proved to converge to a limit point of the original nonconvex problem. For the two-UE case, this is shown to converge to a stationary point of the original problem. Numerical results illustrate the sum-rate performance gains of the proposed method with respect to spatial multiplexing in scenarios where the spatial selectivity of the base station is not sufficient to separate closely spaced UEs.

User Coordination for Fast Beam Training in FDD Multi-User Massive MIMO

Massive multiple-input multiple-output (mMIMO) communications are one of the enabling technologies of 5G and beyond networks. While prior work indicates that mMIMO networks employing time division duplexing have a significant capacity growth potential, deploying mMIMO in frequency division duplexing (FDD) networks remains problematic. The two main difficulties in FDD networks are the scalability of the downlink reference signals and the overhead associated with the required uplink feedback for channel state information (CSI) acquisition. To address these difficulties, most existing methods utilize assumptions on the radio environment such as channel sparsity or angular reciprocity. In this work, we propose a novel cooperative method for a scalable and low-overhead approach to FDD mMIMO under the so-called grid-of-beams architecture. The key idea behind our scheme lies in the exploitation of the near-common signal propagation paths that are often found across several mobile users located in nearby regions, through a coordination mechanism. In doing so, we leverage the recently specified device-to-device communications capability in 5G networks. Specifically, we design beam selection algorithms capable of striking a balance between CSI acquisition overhead and multi-user interference mitigation. The selection exploits statistical information, through so-called covariance shaping. Simulation results demonstrate the effectiveness of the proposed algorithms, which prove particularly well-suited to rapidly-varying channels with short coherence time.

Performance Analysis and Joint Statistical Beamformer Design for Multi-User MIMO Systems

In this letter, we propose techniques for joint transmit and receive beamforming in downlink multi-user MIMO systems under Rayleigh fading channels using knowledge of the second-order statistics. The contribution of our work is twofold. First, we derive a closed-form expression for the outage probability for a general channel model using a recent covariance shaping method and for the conventional Kronecker structured model. Second, we present an outage minimization technique obtained by designing the transmit and receive beamformers. The transmit beamformers maximize the statistics of the signal-to-leakage-plus-noise ratio, while the receive beamformers minimize the cross-covariance of all users. Our techniques are “blind” in the sense that they do not require the transmission of pilot symbols, nor the estimation of the instantaneous state of the channel, making them bandwidth efficient. The derived theoretical results are validated via Monte Carlo simulations and show significant reduction in the outage probability by employing the proposed statistical beamforming techniques.

A covariance shaping filtering method for tightly-coupled MIMU/GNSS of UAV

Purpose Regarding the important roles of accuracy and robustness of tightly-coupled micro inertial measurement unit (MIMU)/global navigation satellite system (GNSS) for unmanned aerial vehicle (UAV). This study aims to explore the efficient method to improve the real-time performance of the sensors. Design/methodology/approach A covariance shaping adaptive Kalman filtering method is developed. For optimal performance of multiple gyros and accelerometers, a distribution coefficient of precision is defined and the data fusion least square method is applied with fault detection and identification using the singular value decomposition. A dual channel parallel filter scheme with a covariance shaping adaptive filter is proposed. Findings Hardware-in-the-loop numerical simulation was adopted, the results indicate that the gain of the covariance shaping adaptive filter is self-tuning by changing covariance weighting factor, which is calculated by minimizing the cost function of Frobenius norm. With the improved method, the positioning accuracy with tightly-coupled MIMU/GNSS of the adaptive Kalman filter is increased obviously. Practical implications The method of covariance shaping adaptive Kalman filtering is efficient to improve the accuracy and robustness of tightly-coupled MIMU/GNSS for UAV in complex and dynamic environments and has great value for engineering applications. Originality/value A covariance shaping adaptive Kalman filtering method is presented and a novel dual channel parallel filter scheme with a covariance shaping adaptive filter is proposed, to improve the real-time performance in complex and dynamic environments.

A Framework for Transceiver Designs for Multi-Hop Communications With Covariance Shaping Constraints

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.

Efficient estimation algorithm for ARMA, exponential and other trigonometric model with quantum constraints

A new estimation algorithm has been developed here, which refers to covariance shaping least square estimation (CSLS) based on the quantum mechanical concepts and constraints. The algorithm has been applied to ARMA, complex exponential, sine, cosine and sinc models with various parameter values. The same models can be applied with white Gaussian noise, which estimates the bias in the parameter and the validity of the uncertainty can be analysed. For optimal quantum measurement design, the performance of the CSLS estimator is developed, discussed and compared with LS, Shrunken and Ridge estimators for different applications. The results suggest that the CSLS estimator can outperform from others at low-to-moderate signal-to-noise ratio.

Mobile Location Using Improved Covariance Shaping Least-Squares Estimation in Cellular Systems

This Letter deals with the problem of non-line-of-sight (NLOS) in cellular systems devoted to location purposes. In conjugation with a variable loading technique, we present an efficient technique to make covariance shaping least squares estimator has robust capabilities against the NLOS effects. Compared with other methods, the proposed improved estimator has high accuracy under white Gaussian measurement noises and NLOS effects.

Covariance Shaping Least-Squares Location Estimation Using TOA Measurements

Localization of mobile terminals has received considerable attention in wireless communications. In this letter, we present a covariance shaping least squares (CSLS) estimator using time-of-arrival measurements of the signal from the mobile station received at three or more base stations. It is shown that the CSLS estimator yields better performance than the other LS estimators at low signal-to-noise ratio conditions.

A Covariance Shaping Framework for Linear Multiuser Detection

A new class of linear multiuser receivers, referred to as the covariance shaping multiuser (CSMU) receiver, is proposed, for suppression of interference in multiuser wireless communication systems. This class of receivers is based on the recently proposed covariance shaping least-squares estimator, and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal, subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix, so that we control the dynamic range and spectral shape of the output noise. Some of the well-known linear multiuser receivers are shown to be special cases of the CSMU receiver. This allows us to interpret these receivers as the receivers that minimize the total error variance in the observations, among all linear receivers with the same output noise covariance, and to analyze their performance in a unified way. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio in the large system limit. We also characterize the spectral efficiency versus energy-per-information bit of the CSMU receiver in the wideband regime. Finally, we consider a special case of the CSMU receiver, equivalent to a mismatched minimum mean-squared error (MMSE) receiver, in which the channel signal-to-noise ratio (SNR) is not known precisely. Using our general performance analysis results, we characterize the performance of the mismatched MMSE receiver. We then treat the case in which the SNR is known to lie in a given uncertainty range, and develop a robust mismatched MMSE receiver whose performance is very close to that of the MMSE receiver over the entire uncertainty range.

Comments on "Covariance shaping least-squares estimation"

A routine linear algebra-based derivation is provided for the optimal estimate in a parametric estimation problem, which is a little more general than that discussed in the above paper. Compared with the procedure adopted by Eldar and Oppenheim, it is more direct and simple and, therefore, easier to be understood. Moreover, the optimal estimate is expressed in a more computationally attractive form, and the results of Eldar and Oppenheim can be regarded as a special case.

Rebuttal to “Comments on Covariance Shaping Least-Squares Estimation”

The author presents a reply to the paper by Zhou (IEEE Trans. Signal Processing, vol.52, no.10, p.2938-9, 2004) which commented on the original paper by Eldar and Oppenheim (IEEE Trans. Signal Processing, vol. 51, p.686-97, 2003 March).

Covariance shaping least-squares estimation

A new linear estimator is proposed, which we refer to as the covariance shaping least-squares (CSLS) estimator, for estimating a set of unknown deterministic parameters, x, observed through a known linear transformation H and corrupted by additive noise. The CSLS estimator is a biased estimator directed at improving the performance of the traditional least-squares (LS) estimator by choosing the estimate of x to minimize the (weighted) total error variance in the observations subject to a constraint on the covariance of the estimation error so that we control the dynamic range and spectral shape of the covariance of the estimation error. The presented CSLS estimator is shown to achieve the Cramer-Rao lower bound for biased estimators. Furthermore, analysis of the mean-squared error (MSE) of both the CSLS estimator and the LS estimator demonstrates that the covariance of the estimation error can be chosen such that there is a threshold SNR below which the CSLS estimator yields a lower MSE than the LS estimator for all values of x. As we show, some of the well-known modifications of the LS estimator can be formulated as CSLS estimators. This allows us to interpret these estimators as the estimators that minimize the total error variance in the observations, among all linear estimators with the same covariance.

Quantum signal processing

In this article we present a signal processing framework that we refer to as quantum signal processing (QSP) (Eldar 2001) that is aimed at developing new or modifying existing signal processing algorithms by borrowing from the principles of quantum mechanics and some of its interesting axioms and constraints. However, in contrast to such fields as quantum computing and quantum information theory, it does not inherently depend on the physics associated with quantum mechanics. Consequently, in developing the QSP framework we are free to impose quantum mechanical constraints that we find useful and to avoid those that are not. This framework provides a unifying conceptual structure for a variety of traditional processing techniques and a precise mathematical setting for developing generalizations and extensions of algorithms, leading to a potentially useful paradigm for signal processing with applications in areas including frame theory, quantization and sampling methods, detection, parameter estimation, covariance shaping, and multiuser wireless communication systems. We present a general overview of the key elements in quantum physics that provide the basis for the QSP framework and an indication of the key results that have so far been developed within this framework. In the remainder of the article, we elaborate on the various elements in this figure.