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A theoretical analysis of a spherical focusing transducer for broadband acoustic microscopy is proposed. The originality of the present contribution is the particular attention we have paid to describe, as rigorously as possible, the diffraction phenomena. Our analysis starts in the harmonic domain with the well-known angular spectrum method, and then gets into the time domain. A new formulation of the angular spectrum in the focal plane has been obtained and compared to other expressions previously reported. This article is deliberately limited to isotropic semi-infinite plane reflectors in order to carry out the inverse Fourier transform in an analytical way. The analytical approach is helpful for the physical interpretation of particular interesting phenomena observed in the transient analysis. A new kind of contribution to the echographic response has been identified and named “geometrical edge waves.” The weight and the arrival time of each discontinuity of the impulse response is analytically evaluated and the physical meaning of each of them is clearly established with the help of a ray model. In the last part of this article, a broadband polyvinylidene fluoride transducer excited by short pulses is used for the experimental validation of the model. The excellent quantitative agreement observed on the time waveforms confirms the efficiency of our approach both in the time domain and in the harmonic one. The comparison between theory and experiment is limited here to some typical examples, but similar results have been obtained on a wide range of defocus and for a large variety of materials. Applications for the characterization of materials will be discussed in future publications.

A novel signal subspace reconstruction method for multiple-input multiple-output (MIMO) radar is proposed. The developed method realises signal subspace resconstruction by the eigendecomposition of two low dimension matrixes. It provides lower computational complexity and fewer training samples compared to the full DOF method. Simulation results are given to demonstrate the effectiveness of the method.Introduction: Multiple-input multiple-output (MIMO) radar systems can transmit orthogonal waveforms to enhance resolution [1] and parameter identifiability [2] and detection performance [3] by greatly increasing the degrees of freedom (DOF) of the system. It was shown in [4] that paramaters estimation with the full DOF of the MIMO radar can achieve the highest resolution capability. However, the DOF of MIMO radar is often proportional to the product of M (the number of transmitters) and N (the number of receivers) and it can be very large. Thus the estimation of the covariance matrix and its eigendecomposition require a great number of training samples and very high computational cost. In this Letter, we propose a signal subspace reconstruction method for MIMO radar which can significantly reduce computational cost and the number of training samples.

A novel method employing an ESPRIT and Kalman filter is proposed for the one-dimensional direction finding problem of MIMO radar. The rotational invariance among the multiple equivalent virtual subarrays of MIMO radar is exploited to derive multiple estimates of the direction of each target through ESPRIT. The multiple estimates of each target are fused through a Kalman filter to refine the accuracy of estimation. Numerical examples demonstrate the effectiveness of the proposed method.Introduction: By transmitting multiple orthogonal signals via multiple sensors and separating their echoes through matched filter banks, MIMO radar can extend the array aperture by virtual sensors [1], from which the accuracy of direction finding would benefit. The computationally efficient ESPRIT algorithm has been applied to the one-dimensional direction finding problem of bistatic MIMO radar in [2] and the reference therein, which is also applicable to the one-dimensional direction finding problem of monostatic MIMO radar concerned in this Letter. However, the estimation and eigen-decomposition of the covariance matrix of the huge virtual sensor array as required by the method in [2] are still computational complex. In this Letter, the virtual sensor array of monostatic MIMO radar is decomposed into multiple identical virtual subarrays [3]. The rotational invariance among these virtual subarrays is exploited to derive multiple estimates of the one-dimensional direction of each target through a modified ESPRIT algorithm. Then, the multiple estimates are fused through a Kalman filter to refine the estimation accuracy. Moreover, the sample multiplexing based on the symmetric data structure of MIMO radar further improves the estimation accuracy. The proposed method is more computationally efficient and accurate than the method presented in [2].

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