Optimized Sensing Matrix Design Of Compressed Sensing Radar

Recently, an emerging theory of Compressed Sensing Radar (CSR) has been proposed. Takingadvantage of the sparsity of the target scene, which restricts the number of targets, CSR can recoverthe target scene from far fewer samples of measurements than traditional methods. Obviouscharacteristics of CSR system can be summarized as follows:1) reducing the required receiveranalog-to-digital (A/D) conversion sampling rate, it can operate only at the low ‘information rate’rather than at the Nyquist rate;2) eliminating the need for the pulse compression matched filter at thereceiver;3) providing the potential to achieve higher range resolution as well as higher Dopplerresolution between targets than traditional radars which is limited by uncertainty principle.The sparse scene recovery performance of CSR relies on the reconstruction quality and stabilityof the recovery algorithm. It has shown that the performance of recovery algorithm requires that thecorrelation between the atoms of sensing matrix should be as small as possible. Low coherence of thesensing matrix leads to higher reconstruction accuracy and stronger noise immunity. So optimizingthe transmit waveform and measurement matrix separately or simultaneously with the hope ofreducing the coherence of sensing matrix can improve the system performance. Based on this thought,a notion of CSR optimal sensing matrix design system is proposed. The methods for optimizing thetransmit waveform and measurement matrix separately and simultaneously are presented to decreasethe cross correlations between atoms of the sensing matrix. The content of this paper can besummarized as follows:Based on CSR theory, the relationship between CSR sparse scene reconstruction performanceand incoherence of sensing matrix is analyzed. Then the CSR optimal sensing matrix design model isestablished.Three algorithms are proposed to optimize the transmit waveform.1) To minimize the mutualcoherence parameter of sensing matrix, the Simulated Annealing (SA) algorithm is employed todesign polyphase coded signal.2) To minimize the average normalized cross correlation coefficientbetween atoms of the sensing matrix, an iterative algorithm base on matrix eigenvalue decompositionis presented to design complex waveform.3) To find the complex waveform such that thecorresponding Gramm matrix is as close to the identity as possible, an iterative algorithm based onsingular value decomposition (SVD) is presented.In order to meet the needs of real-time data processing in radar system, we adopt filter structure as a paradigm for compressed signal acquisition. Based on this structure, genetic algorithm (GA) isemployed to design filter whose taps are {±1}’ s, and an iterative algorithm based on SVD ispresented to design filter whose taps are complex numbers.At the end of this paper, we introduce a framework for the joint design and optimization oftransmit waveform and measurement matrix which implement the CSR optimal sensing matrix designmodel. Two joint optimization algorithms in this framework are proposed to achieve a sensing matrixwith smaller coherence.Simulation results demonstrate the algorithms can improve CSR target scene reconstructionaccuracy, enhance noise immunity and increase the maximum permissible sparsity of CSR, and thatthe joint optimization outperforms both the use of transmit waveform or measurement matrixoptimized separately.