Adaptive time-frequency detection and filtering for imaging in heavy clutter

Abstract. We introduce an adaptive approach for the detection of a reflector in a strongly scattering medium using a timefrequency representation of the array response matrix followed by a Singular Value Decomposition (SVD). We use the Local Cosine Transform (LCT) for the time-frequency representation and introduce a detection criterion that identifies anomalies in the top singular values, across frequencies and in different time windows, that are due to the reflector. The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width is identified by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [3]. While the detection and filtering algorithm presented here works well in general clutter it has been analyzed theoretically only for the case of randomly layered media [1]

Lyapunov exponents for products of complex Gaussian random matrices

The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.Comment: 15 page

Energy-efficient power control in impulse radio UWB wireless networks

Abstract In this paper, a game-theoretic model for studying power control for wireless data networks in frequency-selective multipath environments is analyzed. The uplink of an impulse-radio ultrawideband system is considered. The effects of self-interference and multiple-access interference on the performance of generic Rake receivers are investigated for synchronous systems. Focusing on energy efficiency, a noncooperative game is proposed in which users in the network are allowed to choose their transmit powers to maximize their own utilities, and the Nash equilibrium for the proposed game is derived. It is shown that, due to the frequency selective multipath, the noncooperative solution is achieved at different signal-to-interference-plus-noise ratios, depending on the channel realization and the type of Rake receiver employed. A large-system analysis is performed to derive explicit expressions for the achieved utilities. The Pareto-optimal (cooperative) solution is also discussed and compared with the noncooperative approach

Asymptotic learning requirements for stealth attacks on linearized state estimation

Information-theoretic stealth attacks are data injection attacks that minimize the amount of information acquired by the operator about the state variables, while simultaneously limiting the Kullback-Leibler divergence between the distribution of the measurements under attack and the distribution under normal operation with the aim of controling the probability of attack detection. For Gaussian distributed state variables, attack construction requires knowledge of the second order statistics of the state variables, which is estimated from a finite number of past realizations using a sample covariance matrix. Within this framework, the attack performance is studied for the attack construction with the sample covariance matrix. This results in an analysis of the amount of data required to learn the covariance matrix of the state variables used on the attack construction. The ergodic attack performance is characterized using asymptotic random matrix theory tools, and the variance of the attack performance is bounded. The ergodic performance and the variance bounds are assessed with simulations on IEEE test systems