Yujie Gu

Source Estimation Using Coprime Array: A Sparse Reconstruction Perspective

Direction-of-arrival (DOA), power, and achievable degrees-of-freedom (DOFs) are fundamental parameters for source estimation. In this paper, we propose a novel sparse reconstruction-based source estimation algorithm by using a coprime array. Specifically, a difference coarray is derived from a coprime array as the foundation for increasing the number of DOFs, and a virtual uniform linear subarray covariance matrix sparse reconstruction-based optimization problem is formulated for DOA estimation. Meanwhile, a modified sliding window scheme is devised to remove the spurious peaks from the reconstructed sparse spatial spectrum, and the power estimation is enhanced through a least squares problem. Simulation results demonstrate the effectiveness of the proposed algorithm in terms of DOA estimation and power estimation as well as the achievable DOFs.

Radar Target Profiling and Recognition Based on TSI-Optimized Compressive Sensing Kernel

The design of wideband radar systems is often limited by existing analog-to-digital (A/D) converter technology. State-of-the-art A/D rates and high effective number of bits result in rapidly increasing cost and power consumption for the radar system. Therefore, it is useful to consider compressive sensing methods that enable reduced sampling rate, and in many applications, prior knowledge of signals of interest can be learned from training data and used to design better compressive measurement kernels. In this paper, we use a task-specific information-based approach to optimizing sensing kernels for high-resolution radar range profiling of man-made targets. We employ a Gaussian mixture (GM) model for the targets and use a Taylor series expansion of the logarithm of the GM probability distribution to enable a closed-form gradient of information with respect to the sensing kernel. The GM model admits nuisance parameters such as target pose angle and range translation. The gradient is then used in a gradient-based approach to search for the optimal sensing kernel. In numerical simulations, we compare the performance of the proposed sensing kernel design to random projections and to lower-bandwidth waveforms that can be sampled at the Nyquist rate. Simulation results demonstrate that the proposed technique for sensing kernel design can significantly improve performance.

Doa estimation by covariance matrix sparse reconstruction of coprime array

In this paper, we propose a direction-of-arrival estimation method by covariance matrix sparse reconstruction of coprime array. Specifically, source locations are estimated by solving a newly formulated convex optimization problem, where the difference between the spatially smoothed covariance matrix and the sparsely reconstructed one is minimized. Then, a sliding window scheme is designed for source enumeration. Finally, the power of each source is re-estimated as a least squares problem. Compared with existing methods, the proposed method achieves more accurate source localization and power estimation performance with full utilization of increased degrees of freedom provided by coprime array.

Information-Theoretic Compressive Sensing Kernel Optimization and Bayesian Cramér–Rao Bound for Time Delay Estimation

With the adoption of arbitrary and increasingly wideband signals, the design of modern radar systems continues to be limited by analog-to-digital converter technology and data throughput bottlenecks. Meanwhile, compressive sensing (CS) promises to reduce sampling rates below the Nyquist rate for some applications by constraining the set of possible signals. In many practical applications, detailed prior knowledge on the signals of interest can be learned from training data, existing track information, and/or other sources, which can be used to design better compressive measurement kernels. In this paper, we use an information-theoretic approach to optimize CS kernels for time delay estimation. The measurements are modeled via a Gaussian mixture model by discretizing the a priori probability distribution of the time delay. The optimal CS kernel that approximately maximizes the Shannon mutual information between the measurements and the time delay is then found by a gradient-based search. Furthermore, we also derive the Bayesian Cramér–Rao bound (CRB) for time delay estimation as a function of the CS kernel. In numerical simulations, we compare the performance of the proposed optimal sensing kernels to random projections and the Bayesian CRB. Simulation results demonstrate that the proposed technique for sensing kernel optimization can significantly improve performance, which is consistent with the Bayesian CRB versus signal-to-noise ratio (SNR). Finally, we use the Bayesian CRB expressions and simulation results to make conclusions about the usefulness of CS in radar applications. Specifically, we discuss CS SNR loss versus resolution improvement in SNR- and resolution-limited scenarios.

Compressed sensing kernel design for radar range profiling

Compressive sensing (CS) is a technique for accurate signal reconstruction using lower sampling rates than prescribed by Nyquist/Shannon sampling theory under conditions where the signal has a sparse representation in some basis. However, the random projections usually adopted by CS do not exploit priori knowledge of the sensing task or signal structure (other than sparsity). In this paper, we use a task-specific information-based approach to optimizing sensing kernels for radar range profiling of man-made targets. We assume a MoG prior model for the targets and a Taylor series expansion that enables a closed-form gradient of information with respect to the matrix representation of the sensing kernel. We compare the performance of this optimized sensing matrix to random measurements and to optimum Nyquist performance. Simulation results demonstrate that the proposed technique for sensing kernel design outperforms random projections.

Compressive sensing kernel optimization for time delay estimation

The random projections usually adopted in compressive sensing applications do not exploit a priori knowledge of the sensing task or expected signal structure (other than the fundamental assumption of sparsity). In this paper, we use a task-specific information-based approach to optimizing the compressive sensing kernels for the time delay estimation of radar targets. The measurements are modeled according to a Gaussian mixture model by approximately discretizing the a priori distribution of the time delay. The sensing kernel that maximizes the Shannon mutual information between the measurements and the time delay is then approximated via a gradient-based approach. In addition, we also derive the Bayesian Cramér-Rao bound (CRB) on the time delay estimate as a function of the compressive sensing measurement kernels. Simulation results demonstrate that the proposed optimal sensing kernel outperforms random projections and the performance is consistent with the Bayesian CRB versus signal-to-noise ratio. We conclude that compressive sensing has potential utility in providing measurements with improved resolution for radar target parameter estimation problems.

Time domain CS kernel design for mitigation of wall reflections in urban radar

In this paper, we use the task-specific information (TSI) metric to optimize a compressive sensing kernel for target detection behind a wall. When the target is close to the wall, strong reflections from the wall can obscure the target. Even if wall reflections are estimated and subtracted from the measurement, the dynamic range between wall and target reflections may saturate the analog-to-digital converter (ADC). Furthermore, resolving the target from the wall requires high bandwidth. In this paper, we consider the potential for using custom-designed compressive measurement kernels to mitigate these resolution and dynamic range problems. We treat wall reflections as colored noise in our Gaussian Mixture-based kernel optimization procedure, which results in custom-generated kernels that can reject the dominant wall reflections. Although this places more burden on a receivers analog components, in some scenarios it can significantly improve the situation at the ADC.