A Study On Robust Compressed Sensing Method With Non Ideal Model

Compressive sensing theory points out that a sparse signal under a certain base can be sampled through a lower sampling rate,and then we can reconstruct the original signal by sparse reconstruction algorithm.Compressive sensing theory breaks through the limitation of the traditional Nyquist sampling theorem.Therefore,applying compressed sensing to radar signal processing can not only reduce the data acquisition and hardware burden of radar,but also achieve high detection accuracy.But in the actual data processing,there are array gain and phase errors,system error,off-grid error in the radar system.These errors will cause the calculation bias of actual observation matrix,resulting in the non idealization of the compressed sensing model,which seriously affects the detection performance of the radar.Therefore,it is of theoretical significance and practical value to study the robust compressed sensing method under the non ideal model.In view of the above problems,this thesis mainly studies the robust reconstruction algorithm under the condition of array gain and phase errors and off-grid errors.The main work is summed up in the following two aspects:When there are array gain and phase errors,the calculation of the observation matrix is inaccurate,which affects the accuracy of the sparse recovery.Consider a bistatic MIMO radar system with array gain and phase errors in the transmit and receive arrays,this thesis proposes a new signal model,we unified the array gain and phase errors into a random perturbation matrix added to the observation matrix,on the basis of this,this thesis proposes a robust sparse reconstruction algorithm.We regard the observation matrix as an unknown quantity and constrain it,and then use the alternate iterative method to solve the optimization problem.When the sparse signal is known,we use Lagrange multiplier method to solve the closed solution of the observation matrix,then we use the estimated observation matrix to recover the sparse signal.After several alternating iteration operations,the algorithm converges to an ideal solution.Simulation results show that the algorithm is more accurate than the direct compressive sensing algorithm and the existing robust algorithm[52] under small sample data,and the algorithm is more robust when the array gain and phase errors change.In most radar imaging systems,it is necessary to divide the target scene into the grid point,and this discretization will cause the off-grid error.Based on the bistatic MIMO radar system,it is assumed that the actual target does not fall on the grid that we have partitioned.At the same time,the echo data and the ideal observation matrix do not match,so the real location of the target can not be recovered exactly.In view of this situation,we first established a non ideal signal model,and then the real position of the target is represented by the first order Taylor expansion at the nearest grid,through some derivation,the relationship between the observation matrix with the grid error and the ideal observation matrix is obtained.We extend the observation matrix,and then merge the first order coefficients of Taylor approximation into the sparse signals to be solved,and then the robust algorithm is used to recover the sparse signal.Finally,the first order Taylor approximation solution of the grid error is obtained.The simulation results show that this method can obtain more accurate results of the off-grid error estimation.