Multivariate Nonnegative Quadratic Mappings

In this paper we study several issues related to the characterization of speci c classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity de ned by a pre-speci ed conic order.In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semide nite matrix cone, and study when it can be represented by linear matrix inequalities.We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models.In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semide nite program.optimization;linear programming;models

Dissipative Resilient Observer

Cybersecurity is a major concern for designers of control systems that can be directed against any of their components. Observers are an integral part of control systems that require state feedback. This paper considers an observer subject to errors in implementation or subject to cyberattacks. The errors and cyberattacks result in perturbations in the gain and in a finite-energy but unknown disturbance input. We obtain conditions for Q-S-R dissipativity and stability of the observer in the presence of the gain errors and disturbances in the form of linear matrix inequalities (LMIs). Three examples are presented to show how the LMIs can yield resilient observer designs

MIMO Linear Precoder Design with Non-Ideal Transmitters

We investigate the linear precoder design problem for multiple-input multiple-output (MIMO) channels under non-ideal transmitter hardware. We consider two different non-ideal hardware models: i) an additive noise model in which the level of the noise at an antenna is proportional to the signal power at that antenna, ii) an additive precoder error model. We focus on the problem of minimizing mean-square error at the receiver under transmit power constraints at the transmitter. For the first hardware impairment model, this scenario leads to a non-convex formulation for which we propose a block-coordinate descent technique. The proposed method has a convergence guarantee and provides rank-constrained solutions. For the second model, analytical expressions for the optimum designs are provided. We compare the performance of our hardware impairment aware designs with that of designs developed with ideal hardware assumptions. Our results suggest that significant gains can be obtained by the proposed designs for sufficiently high signal-to-noise ratio values

Spatially Selective Artificial-Noise Aided Transmit Optimization for MISO Multi-Eves Secrecy Rate Maximization

Consider an MISO channel overheard by multiple eavesdroppers. Our goal is to design an artificial noise (AN)-aided transmit strategy, such that the achievable secrecy rate is maximized subject to the sum power constraint. AN-aided secure transmission has recently been found to be a promising approach for blocking eavesdropping attempts. In many existing studies, the confidential information transmit covariance and the AN covariance are not simultaneously optimized. In particular, for design convenience, it is common to prefix the AN covariance as a specific kind of spatially isotropic covariance. This paper considers joint optimization of the transmit and AN covariances for secrecy rate maximization (SRM), with a design flexibility that the AN can take any spatial pattern. Hence, the proposed design has potential in jamming the eavesdroppers more effectively, based upon the channel state information (CSI). We derive an optimization approach to the SRM problem through both analysis and convex conic optimization machinery. We show that the SRM problem can be recast as a single-variable optimization problem, and that resultant problem can be efficiently handled by solving a sequence of semidefinite programs. Our framework deals with a general setup of multiple multi-antenna eavesdroppers, and can cater for additional constraints arising from specific application scenarios, such as interference temperature constraints in interference networks. We also generalize the framework to an imperfect CSI case where a worst-case robust SRM formulation is considered. A suboptimal but safe solution to the outage-constrained robust SRM design is also investigated. Simulation results show that the proposed AN-aided SRM design yields significant secrecy rate gains over an optimal no-AN design and the isotropic AN design, especially when there are more eavesdroppers.Comment: To appear in IEEE Trans. Signal Process., 201