适用于压缩感知估计角度的测量矩阵研究

针对接收数据压缩投影后导致到达角 (Direction-Of-Arrival, DOA)估计精度不高的问题，提出一种高精度的全局信息压缩投影到达角估计算法。该算法首先提出更适应角度估计的空域稀疏化范德蒙矩阵作为测量矩阵，然后对由其组成的Gram矩阵的非对角元素进行压缩处理得到目标矩阵，接着利用步长符合沃尔夫条件的梯度下降法优化Gram矩阵，得到当Gram矩阵与目标矩阵最接近时所对应的可以保留更多全局信息的测量矩阵，最后利用此矩阵压缩接收数据，将接收数据投影到测量矩阵空间，进行稀疏重构得到角度估计结果。仿真实验表明，所提算法角度估计精度远优于同等条件下辐射源信号直接重构的角度估计结果，且在信噪比大于-6dB时数据压缩投影后角度估计的成功率达到100%，性能优越。 

Research on the Measurement Matrix Apply to Estimate the Angle Using Compressed Sensing

A DOA estimation algorithm based on global information’s compression projection is proposed to solve the problem that the estimated accuracy of the DOA is low after compressing the received data. Firstly, the vandermonde matrix which is sparse in the space has been proposed and it is used to get the Gram matrix of the model, and then the non-diagonal elements of the Gram matrix are compressed to obtain the target matrix. In order to optimize the Gram matrix, Gradient descent method with Wolfson condition is used to reduce the difference between the target matrix and the Gram matrix. The measurement matrix corresponds to the resulting Gram matrix can retain more global information. Finally, the received data is compressed by this matrix, and projected into the space of the measurement matrix. The angle estimation result is obtained by sparse reconstruction. Simulation results show that the accuracy of the proposed algorithm is higher than the direct reconstruction results of the source signal under the same conditions, when the signal-to-noise ratio is greater than -6dB, the estimated success rate of the data compression projection is 100%, and the performance is superior.