Yao Xie

On Probing Signal Design for MIMO Radar

A multiple-input multiple-output (MIMO) radar system, unlike a standard phased-array radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern, and also to minimize the cross-correlation of the signals reflected back to the radar by the targets of interest. In this paper, we show how the above desirable features can be achieved by designing the covariance matrix of the probing signal vector transmitted by the radar. Moreover, in a numerical study, we show that the proper choice of the probing signals can significantly improve the performance of adaptive MIMO radar techniques. Additionally, we demonstrate the advantages of several MIMO transmit beampattern designs, including a beampattern matching design and a minimum sidelobe beampattern design, over their phased-array counterparts.

Multistatic Adaptive Microwave Imaging for Early Breast Cancer Detection

We propose a new multistatic adaptive microwave imaging (MAMI) method for early breast cancer detection. MAMI is a two-stage robust Capon beamforming (RCB) based image formation algorithm. MAMI exhibits higher resolution, lower sidelobes, and better noise and interference rejection capabilities than the existing approaches. The effectiveness of using MAMI for breast cancer detection is demonstrated via a simulated 3-D breast model and several numerical examples

MIMO Transmit Beamforming Under Uniform Elemental Power Constraint

We consider multi-input multi-output (MIMO) transmit beamforming under the uniform elemental power constraint. This is a nonconvex optimization problem, and it is usually difficult to find the optimal transmit beamformer. First, we show that for the multi-input single-output (MISO) case, the optimal solution has a closed-form expression. Then we propose a cyclic algorithm for the MIMO case which uses the closed-form MISO optimal solution iteratively. The cyclic algorithm has a low computational complexity and is locally convergent under mild conditions. Moreover, we consider finite-rate feedback methods needed for transmit beamforming. We propose a simple scalar quantization method, as well as a novel vector quantization method. For the latter method, the codebook is constructed under the uniform elemental power constraint and the method is referred as VQ-UEP. We analyze VQ-UEP performance for the MISO case. Specifically, we obtain an approximate expression for the average degradation of the receive signal-to-noise ratio (SNR) caused by VQ-UEP. Numerical examples are provided to demonstrate the effectiveness of our proposed transmit beamformer designs and the finite-rate feedback techniques.

Multi-Static Adaptive Microwave Imaging for Early Breast Cancer Detection

We propose a new multi-static adaptive microwave imaging (MAMI) method for early breast cancer detection. MAMI is a two-stage robust Capon beamforming (RCB) based image formation algorithm. MAMI exhibits higher resolution, lower sidelobes, and better noise and interference rejection capabilities than the existing approaches. The effectiveness of using MAMI for breast cancer detection is demonstrated via a simulated 3-D breast model and several numerical examples

Change-Point Detection for High-Dimensional Time Series With Missing Data

This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the true change-point before it can be reliably detected. Furthermore, missing components in the observed data handicap conventional approaches. The proposed method addresses these challenges by modeling the dynamic distribution underlying the data as lying close to a time-varying low-dimensional submanifold embedded within the ambient observation space. Specifically, streaming data is used to track a submanifold approximation, measure deviations from this approximation, and calculate a series of statistics of the deviations for detecting when the underlying manifold has changed in a sharp or unexpected manner. The approach described in this paper leverages several recent results in the field of high-dimensional data analysis, including subspace tracking with missing data, multiscale analysis techniques for point clouds, online optimization, and change-point detection performance analysis. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Novel multistatic adaptive microwave imaging methods for early breast cancer detection

Multistatic adaptive microwave imaging (MAMI) methods are presented and compared for early breast cancer detection. Due to the significant contrast between the dielectric properties of normal and malignant breast tissues, developing microwave imaging techniques for early breast cancer detection has attracted much interest lately. MAMI is one of the microwave imaging modalities and employs multiple antennas that take turns to transmit ultra-wideband (UWB) pulses while all antennas are used to receive the reflected signals. MAMI can be considered as a special case of the multi-input multi-output (MIMO) radar with the multiple transmitted waveforms being either UWB pulses or zeros. Since the UWB pulses transmitted by different antennas are displaced in time, the multiple transmitted waveforms are orthogonal to each other. The challenge to microwave imaging is to improve resolution and suppress strong interferences caused by the breast skin, nipple, and so forth. The MAMI methods we investigate herein utilize the data-adaptive robust Capon beamformer (RCB) to achieve high resolution and interference suppression. We will demonstrate the effectiveness of our proposed methods for breast cancer detection via numerical examples with data simulated using the finite-difference time-domain method based on a 3D realistic breast model.

Dynamic Spectrum Management With the Competitive Market Model

Ye [¿Competitive Communication Spectrum Economy and Equilibrium,¿ 2008, working paper] and Lin [¿Budget Allocation in a Competitive Communication Spectrum Economy,¿ EURASIP J. Adv. Signal Process., Article ID: 963717, vol. 2009, p. 12, Sep. 2009] have shown that dynamic spectrum management (DSM) using the market competitive equilibrium (CE), which sets a price for transmission power on each channel, leads to better system performance in terms of the total data transmission rate (by reducing cross talk), than using the Nash equilibrium (NE). But how to achieve such a CE is an open problem. We show that the CE is the solution of a linear complementarity problem (LCP) and can be computed efficiently. We propose a decentralized tatonnement process for adjusting the prices to achieve a CE. We show that under reasonable conditions, any tatonnement process converges to the CE. The conditions are that users of a channel experience the same noise levels and that the crosstalk effects between users are low-rank and weak.

Beampattern Synthesis via a Matrix Approach for Signal Power Estimation

We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight matrices at the array output, which leads to matrix approaches (MA). We consider several versions of MA, including a (data) adaptive MA (AMA), as well as several data-independent MA designs. For all of these MA designs, globally optimal solutions can be determined efficiently due to the convex optimization formulations obtained by SDR. Numerical examples as well as theoretical evidence are presented to show that the optimal weight matrix obtained via SDR has few dominant eigenvalues, and often only one. When the number of dominant eigenvalues of the optimal weight matrix is equal to one, MA reduces to VA, and the main advantage offered by SDR in this case is to determine the globally optimal solution efficiently. Moreover, we show that the AMA allows for strict control of main-beam shape and peak sidelobe level while retaining the capability of adaptively nulling strong interferences and jammers. Numerical examples are also used to demonstrate that better beampattern designs can be achieved via the data-independent MA than via its VA counterpart.

Adaptive and Robust Methods of Reconstruction (ARMOR) for Thermoacoustic Tomography

In this paper, we present new adaptive and robust methods of reconstruction (ARMOR) for thermoacoustic tomography (TAT), and study their performances for breast cancer detection. TAT is an emerging medical imaging technique that combines the merits of high contrast due to electromagnetic or laser stimulation and high resolution offered by thermal acoustic imaging. The current image reconstruction methods used for TAT, such as the delay-and-sum (DAS) approach, are data-independent and suffer from low-resolution, high sidelobe levels, and poor interference rejection capabilities. The data-adaptive ARMOR can have much better resolution and much better interference rejection capabilities than their data-independent counterparts. By allowing certain uncertainties, ARMOR can be used to mitigate the amplitude and phase distortion problems encountered in TAT. The excellent performance of ARMOR is demonstrated using both simulated and experimentally measured data.

Poisson Matrix Recovery and Completion

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix M of size d1-by-d2, and establish theoretical upper and lower bounds on the recovery error. Our bounds for matrix completion are nearly optimal up to a factor on the order of O(log(d1d2)). These bounds are obtained by combining techniques for recovering sparse vectors with compressed measurements in Poisson noise, those for analyzing low-rank matrices, as well as those for one-bit matrix completion [Davenport , “1-bit Matrix Completion, Information and Inference,” Information and Inference, vol. 3, no. 3, pp. 189-223, Sep. 2014] (although these two problems are different in nature). The adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of the Poisson case compared to the prior work including having to impose a minimum signal-to-noise requirement on each observed entry and a gap in the upper and lower bounds. We also develop a set of efficient iterative algorithms and demonstrate their good performance on synthetic examples and real data.