Coprime Array Signal Processing

Array signal processing has been widely applied in a variety of practical applications,includ-ing radar,sonar,seismic,speech recognition,radio astronomy,and wireless communications.As compared to the commonly used uniform linear array(ULA)satisfying the spatial Nyquist sampling theorem,the recently proposed coprime array configurations belong to a special kind of sparse array with a systematic design,which combine the advantages of sparse sensing and the distinguishing properties of prime numbers.With a coprime array,an enlarged array aperture and an increased number of degrees-of-freedom(DOFs)can be achieved by using the same number of sensors as the ULA.In other words,under the same performance requirements,the utilization of coprime ar-ray makes it possible to reduce the number of physical sensors and the associated hardware costs.Based on the literature review of the most recent advances on coprime array signal processing techniques,this thesis focuses on the problem of direction-of-arrival(DOA)estimation and beam-forming,where a series of efficient and robust signal processing algorithms are proposed in the framework of coprime array.The main content of this thesis can be summarized as follows:1.A virtual array covariance matrix sparse reconstruction-based coprime array DOA estima-tion algorithm is proposed.By exploiting the sparse nature of the incident sources that is relative to the entire spatial domain.the second-order signal statistics corresponding to an augmented virtual array are represented by a given overcomplete basis.Based on the principle of covariance matrix sparse reconstruction,an optimization problem is devised by minimizing the virtual array covari-ance matrix fitting error under the sparsity constraints,where the optimized spatial power spectrum is formulated.The proposed algorithm is capable of simultaneously estimating the DO As,power,and source number with an increased number of DOFs.2.A compressive sensing-based coprime array DOA estimation algorithm is proposed.To achieve a high efficiency algorithm design,a compressive sensing kernel is incorporated to com-press the coprime array received signals by random projection,where the contained key information is not destroyed in the sketch of the original coprime array received signals.With the compressed lower-dimensional measurements,the DOA estimation algorithm designs with high-resolution and increased number of DOFs are sequentially realized via spatial power spectrum calculation and virtual signal sparse reconstruction.The proposed algorithm greatly reduces the computational complexity while maintains the distinguishing advantages of coprime array signal processing.3.A virtual array interpolation-based coprime array DOA estimation algorithm is proposed via covariance matrix gridless reconstruction.Considering the problem of information loss caused by the derived non-uniform virtual array,the idea of array interpolation is incorporated to the virtual domain for constructing a virtual ULA.Meanwhile,the atomic norm is implemented to represent the multiple virtual measurements,where the contained directional information are continuously parameterized,and the inherent estimation bias caused by the predefined spatial sampling grids is effectively avoided.By investigating the properties of the defined virtual domain atomic norm,an atomic norm minimization-based optimization problem is formulated to reconstruct the interpolated virtual array covariance matrix in a gridless manner.The proposed algorithm can make full use of all the signal information contained in the non-uniform virtual array,and accurately estimate the off-grid targets.4.The framework of beamforming exploiting coprime array is established,and a coprime array adaptive beamforming based on the reconstruction of covariance matrix and steering vector is proposed.Considering the efficiency and robustness requirements,the operation mechanism of adaptive beamformer is analyzed,based on which the essential difference between the adap-tive beamforming and DOA estimation in the framework of coprime array signal processing is re-vealed.A novel coprime array adaptive beamforming algorithm is proposed by reconstructing the interference-plus-noise covariance matrix and the desired signal steering vector,where the key pa-rameters for reconstruction are obtained from the designed decomposed coprime sparse subarrays-based DOA estimation method and covariance matrices joint optimization-based power estimation method.On one hand,the utilization of coprime feature enables an efficient and accurate parame-ter estimation.On the other hand,the incorporation of reconstruction principle effectively avoids the signal self-nulling phenomenon and the signal model mismatch problem.Simulation results demonstrate the effectiveness of the proposed algorithm in terms of both efficiency and robustness.