Subspace-based methods suffer from the rank loss of the noise free data covariance matrix in the context of direction of arrival (DOA) estimation of coherent sources. The well-known spatial smoothing techniques are then widely employed to create a rank restored data covariance matrix. However, conventional spatial smoothing techniques, such as the spatial smoothing pre-processing (SSP), modified spatial smoothing pre-processing (MSSP), and improved spatial smoothing (ISS), do not make full use of the available information in the data covariance matrix. In this paper, an enhanced spatial smoothing (ESS) technique is proposed to exploit both the covariance matrices of individual subarrays and the cross-covariance matrices of different subarrays. Besides, the proposed method can work directly on the signal subspace (ESS-SS), since the signal subspace contains all the information of the DOAs of incoming signals. After de-correlation, the subspace method ESPRIT is adopted to estimate the DOAs. Compared with conventional approaches, the proposed method is more powerful to de-correlate the correlation between signals, and also more robust to the noise impact. The proposed method is tested on numerical data in coherent scenarios, and compared with conventional approaches. Simulation results show that the proposed method has an enhanced resolving capability and a lower signal-to-noise ratio threshold.

Ground-penetrating radar (GPR) is a common technique for evaluating the structure and quality of civil engineering materials. The ever-increasing demand for higher GPR time resolution and better interpretation of GPR data has motivated the use of advanced signal processing methods for GPR applications. In this article, we review the major advances in signal processing techniques employed in civil engineering for different tasks, such as estimation of thickness, permittivity, and roughness. Their performance is tested and compared through numerical testing and using experimental data from laboratory measurements.

Ground-penetrating radars (GPR) are widely used in media parameters' estimation and targets' localization. This paper focuses on time-delay estimation (TDE) using the GPR signal, which contains important information about the probed media structure. However, TDE tends to be a challenging task in GPR applications, in the scenarios of overlapping, coherent signals and limited snapshots. Forward-backward linear prediction (FBLP) is a high time-resolution method, which is able to directly deal with coherent signals. Support vector regression (SVR) is robust with small samples. Therefore, we propose to combine the theory of FBLP and SVR together to enhance the robustness of TDE in the case of coherent, overlapping signals as well as limited snapshots. The proposed method is tested with both numerical and experimental data. Both the results demonstrate the effectiveness of the proposed method.

In coherent direction of arrival (DOA) estimation, subspace-based methods suffer from performance deterioration because of the rank loss of the signal covariance matrix. A variety of spatial smoothing preprocessing techniques have been proposed for decorrelation, among which the enhanced spatial smoothing preprocessing (ESS) technique shows outstanding performance by exploiting the signal subspace. However, ESS is applied by squaring the matrix whose columns span the signal subspace (called signal matrix), which involves unnecessary computational loads. Besides, the smoothed covariance matrix after ESS is a linear combination of the sub-matrices of signal matrix, where the coefficients of the combination may undermine the decorrelation performance. In this context, a simplified spatial smoothing (SSS) technique is proposed for decorrelation by averaging the sub-matrices of the signal matrix directly, and avoids redundant operations in squared signal matrix. The proposed method is tested numerically in terms of the signalto-noise ratio (SNR), the number of snapshots, angle separation, and the execution time. Simulation results show the improvement of the decorrelation performance, efficiency, and robustness with the proposed method in coherent scenarios, compared with the other spatial smoothing preprocessing based methods.

Coprime array possesses a larger array aperture and element spacing compared with the conventional uniform linear array (ULA) for the equivalent number of sensors, attracting considerable scholarly attention. However, the direction of arrival (DOA) estimation of coherent signals has been a major challenge for the practical application of the coprime array. In this paper, based upon the perspective of signal subspace reconstruction, we propose two effective approaches to resolve the DOA of completely correlated signals with a coprime array. For the first method, we exploit two selection matrices to separate the signal subspace into two parts and rearrange the elements within them to construct two Hankel matrices. By applying the MUSIC method to these Hankel matrices and finding common solutions, we can determine the DOA of coherent signals. In the second method, we first convert the signal subspace of the coprime array into the signal subspace of ULA using a mapping matrix and the total least squares method. We then construct a Hankel matrix and restore its rank by solving a rank minimization problem. Finally, by applying the MUSIC method to the rank-restored Hankel matrix, we can obtain the angles of the coherent signals. Finally, simulation results are presented to demonstrate the efficiency and superiority of our proposed methods.

With its increased aperture and enlarged minimum spacing among sensors, coprime array with displaced subarrays (CADiS) receives a great deal of attention among sparse arrays. However, the holes in the difference co-array of CADiS extremely degrade the achievable number of uniform degrees of freedom (uDOFs). In recent years, increasing researches of direction of arrival (DOA) estimation with moving sparse arrays have brought new insights into the releasing the holes problem. In this paper, we first explore the structure of difference co-array generated from array motion, and propose a hole-free motion strategy that can fill all the holes in difference co-array of coprime arrays, and resulting increased number of uDOFs as well as array aperture. Secondly, based on the analysis of hole positions, we propose another motion strategy that needs only one step motion of CADiS to generate a difference co-array with no holes in the central part. We find all the qualified steps length of the one-step motion method and provide the closed-form expression of the corresponding achievable number of uDOFs. Finally, the number of uDOF and DOA estimation accuracy of the proposed motion strategies are compared with several state-of-the-art motion methods. Numerical results show the superiority of the proposed methods.