Luzhou Xu

On Parameter Identifiability of MIMO Radar

A multi-input multi-output (MIMO) radar system, unlike a standard phased-array radar, can transmit multiple linearly independent probing signals via its antennas. We show herein that this waveform diversity enables the MIMO radar to significantly improve its parameter identifiability. Specifically, we show that the maximum number of targets that can be uniquely identified by the MIMO radar is up to Mt times that of its phased-array counterpart, where Mt is the number of transmit antennas.

Target detection and parameter estimation for MIMO radar systems

We investigate several target detection and parameter estimation techniques for a multiple-input multiple-output (MIMO) radar system. By transmitting independent waveforms via different antennas, the echoes due to targets at different locations are linearly independent of each other, which allows the direct application of many data-dependent beamforming techniques to achieve high resolution and excellent interference rejection capability. In the absence of array steering vector errors, we discuss the application of several existing data-dependent beamforming algorithms including Capon, APES (amplitude and phase estimation) and CAPES (combined Capon and APES), and then propose an alternative estimation procedure, referred to as the combined Capon and approximate maximum likelihood (CAML) method. Via several numerical examples, we show that the proposed CAML method can provide excellent estimation accuracy of both target locations and target amplitudes. In the presence of array steering vector errors, we apply the robust Capon beamformer (RCB) and doubly constrained robust Capon beamformer (DCRCB) approaches to the MIMO radar system to achieve accurate parameter estimation and superior interference and jamming suppression performance.

Range Compression and Waveform Optimization for MIMO Radar: A CramÉr–Rao Bound Based Study

A multi-input multi-output (MIMO) radar system, unlike standard phased-array radar, can transmit via its antennas multiple probing signals that may be correlated or uncorrelated with each other. This waveform diversity offered by MIMO radar enables superior capabilities compared with a standard phased-array radar. One of the common practices in radar has been range compression. We first address the question of ldquoto compress or not to compressrdquo by considering both the Cramer-Rao bound (CRB) and the sufficient statistic for parameter estimation. Next, we consider MIMO radar waveform optimization for parameter estimation for the general case of multiple targets in the presence of spatially colored interference and noise. We optimize the probing signal vector of a MIMO radar system by considering several design criteria, including minimizing the trace, determinant, and the largest eigenvalue of the CRB matrix. We also consider waveform optimization by minimizing the CRB of one of the target angles only or one of the target amplitudes only. Numerical examples are provided to demonstrate the effectiveness of the approaches we consider herein.

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

Iterative Generalized-Likelihood Ratio Test for MIMO Radar

We consider a multiple-input multiple-output (MIMO) radar system where both the transmitter and receiver have multiple well-separated subarrays with each subarray containing closely spaced antennas. Because of this general antenna configuration, both the coherent processing gain and the spatial diversity gain can be simultaneously achieved. We compare several spatial spectral estimators, including Capon and APES, for target detection and parameter estimation. We introduce a generalized-likelihood ratio test (GLRT) and a conditional generalized-likelihood ratio test (cGLRT) for the general antenna configuration. Based on GLRT and cGLRT, we then propose an iterative GLRT (iGLRT) procedure for target detection and parameter estimation. Via several numerical examples, we show that iGLRT can provide excellent detection and estimation performance at a low computational cost

Signal Waveform's Optimal-under-Restriction Design for Active Sensing

We consider Signal Waveforms Optimal-under-Restriction Design (SWORD) for active sensing. In the presence of colored interference and noise with known statistical properties, waveform optimization for active sensors such as radar can significantly increase the signal-to-interference-plus-noise ratio needed for much improved target detection. However, the so-obtained optimal waveforms can result in significant modulus variation, poor range resolution, and/or high peak sidelobe levels. To mitigate these problems, we can constrain the waveform optimization problem by restricting the sought-after waveform to be similar to a desired waveform, which is known to have, for example, constant modulus as well as reasonable range resolution and peak sidelobe level. One example of the desired waveform is the widely used linear frequency modulated waveform or chirp. We will provide a detailed solution to the constrained optimization problem and explain how it is related with the existing waveform optimization methods

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

ASEO: A Method for the Simultaneous Estimation of Single-Trial Event-Related Potentials and Ongoing Brain Activities

Cognitive functions are often studied by recording electric potentials from the brain over repeated presentations of a sensory stimulus or repeated performance of a motor action. Each repetition is called a trial. Recent work has demonstrated that contrary to the traditional view, the event-related potential (ERP) can vary from trial to trial and the background ongoing activity often contains rich information about the cognitive state of the brain. Based on such a variable signal plus ongoing activity model, an iterative parameter estimation method is proposed in which both the single-trial parameters of the ERP and the autoregressive representation of the ongoing activity are obtained simultaneously. This technique, referred to as the analysis of single-trial ERP and ongoing activities method, is first tested on simulation examples, and then applied to the local field potential recordings from monkeys performing a visuomotor task.

Ground Moving Target Indication via Multichannel Airborne SAR

We consider moving target detection and velocity estimation for multichannel synthetic-aperture-radar (SAR)-based ground moving target indication (GMTI). Via forming velocity versus cross-range images, we show that small moving targets can be detected even in the presence of strong stationary ground clutter. Furthermore, the velocities of the moving targets can be estimated, and the misplaced moving targets can be placed back to their original locations based on the estimated velocities. An iterative adaptive approach, which is robust and user parameter free, is used to form velocity versus cross-range images for each range bin of interest. Moreover, we discuss calibration techniques to estimate the relative antenna distances and antenna gains in practical systems. Furthermore, we present a simple algorithm for stationary clutter cancelation. We conclude by demonstrating the effectiveness of our approaches by using the Air Force Research Laboratory publicly released Gotcha airborne SAR-based GMTI data set.

Nonparametric Missing Sample Spectral Analysis and Its Applications to Interrupted SAR

We consider nonparametric adaptive spectral analysis of complex-valued data sequences with missing samples occurring in arbitrary patterns. We first present two high-resolution missing-data spectral estimation algorithms: the Iterative Adaptive Approach (IAA) and the Sparse Learning via Iterative Minimization (SLIM) method. Both algorithms can significantly improve the spectral estimation performance, including enhanced resolution and reduced sidelobe levels. Moreover, we consider fast implementations of these algorithms using the Conjugate Gradient (CG) technique and the Gohberg-Semencul-type (GS) formula. Our proposed implementations fully exploit the structure of the steering matrices and maximize the usage of the fast Fourier transform (FFT), resulting in much lower computational complexities as well as much reduced memory requirements. The effectiveness of the adaptive spectral estimation algorithms is demonstrated via several numerical examples including both 1-D spectral estimation and 2-D interrupted synthetic aperture radar (SAR) imaging examples.