Quadrature compressive sampling（QuadCS） can directly obtain the in-phase and quadrature components of radio signals at sub-Nyquist rates and is one of efficient analog-to-information systems sampling wideband/ultra-wideband signals. This paper studies the QuadCS system properties from the time-domain point of view. Firstly, the sensing matrix describing QuadCS system is derived in time-domain, and it is further decomposed into three components. Then with the decomposition structure, the QuadCS reconstructability is simply built in virtue of the theory of unit-norm tight frame.Finally, the signal power and the noise variance in the QuadCS output are analyzed, the signal-to-noise ratios before and after the QuadCS system are proved to keeps intact, and the SNR loss after reconstruction is given. The work of this paper further improves the theory of QuadCS.

亚奈奎斯特采样雷达是利用回波信号的稀疏性,基于模信转换系统发展起来的欠采样雷达系统.本文研究亚奈奎斯特采样雷达的运动目标回波信号的快速重构问题.与单脉冲回波重构不同,运动目标在脉冲积累时间内可能产生跨距离单元现象,使得回波信号表示系数呈现稀疏时变性.本文采用概率分布模型描述稀疏位置的变化,首先将多脉冲回波信号重构转化为加权稀疏重构问题;然后根据分段滑动重构思想,提出一种基于正交投影的加权稀疏分段滑动重构方法来实现快速重构.该方法利用前一个脉冲稀疏位置估计信息,构造分段产生干扰的正交补空间,将子段压缩测量投影到构造的正交补空间,有效地抑制了相邻段引入的干扰.数值仿真验证了方法的有效性.

It has been shown that analog-to-information conversion(AIC) is an efficient scheme to perform sub-Nyquist sampling of pulsed radar echoes. However, it is often impractical, if not infeasible, to reconstruct full-range Nyquist samples because of huge storage and computational load requirements. Based on the analyses of AIC measurement system, this paper develops a novel segment-sliding reconstruction(Seg SR) scheme to effectively reconstruct the Nyquist samples. The Seg SR performs segment-by-segment reconstruction in a sliding mode and can be implemented in real time. An important characteristic that distinguishes the proposed Seg SR from existing methods is that the measurement matrix in each segment satisfies the restricted isometry property(RIP) condition. Partial support in the previous segment can be incorporated into the estimation of the Nyquist samples in the current segment. The effect of interference introduced from adjacent segments is theoretically analyzed, and it is revealed that the interference consists of two interference levels with different impacts to the signal reconstruction performance. With these observations, a two-step orthogonal matching pursuit(OMP)procedure is proposed for segment reconstruction, which takes into account different interference levels and partially known support of the previous segment. The proposed Seg SR scheme achieves near-optimal reconstruction performance with a significant reduction of computational loads and storage requirements. Theoretical analyses and simulations verify its effectiveness.