压缩感知非凸优化超宽带信道估计方法研究

超宽带信号由于传输路径较复杂且功率谱密度较低，准确的信道估计十分重要．但是由于其带宽较宽，难以直接采样．压缩感知理论提供了一种可行的低速采样方法．目前的压缩感知超宽带信道估计方法一般采用l1范数约束的凸优化形式或无稀疏性的l2范数约束形式，对目标向量的稀疏性约束不强，而拥有最强稀疏性的l0范数又缺少有效的重构算法．针对上述问题，本文设计一种基于非凸优化算法的压缩感知超宽带信道估计方法．首先将目标函数设置成l，范数约束的非凸优化形式，然后利用凸函数较易求得极值的性质，将原非凸函数组合成为凸函数形式的目标函数，并通过每步迭代凸函数对非凸函数的逼近来求解目标函数，进而估计出原信道．由于lp范数更接近于l0范数，所以对目标向量稀疏性的约束更强．实验结果表明，所提方法相对于现有的压缩感知超宽带信道估计方法能够有效降低重构误差．

UWB channel estimation based on non-convex optimization of compressed sensing

Considering the complicated transfer propagation and low power spectrum density of ultra-wideband （UWB） signal, accurate estimation of UWB channel is crucial. However, it is difficult to sample UWB signal directly for its band width is ultra wide. Compressed sensing （CS） provides a feasible method for low speed sampling. Existing CS-based UWB channel estimation method generally adopts convex optimization form using l1 norm restriction, or non-sparse form using l2-norm restriction. These methods have a weak restriction on sparseness of objective vector, and l0-norm which is the sparsest lacks of effective reconstruction algorithm. To solve these problems, a CS-based UWB channel estimation method based on non-convex optimization is devised in this paper. Firstly, objective function is set as non-convex optimization form using lp-norm restriction; original non-convex function is then combined as convex function form, using the property that convex function obtains extremum easily. Convex function is used to approximate non-convex function at each iteration, for objective vector reconstruction and original channel estimation. Since lp-norm is closer to l0-norm, it has stronger restric- tion on sparseness of objective vector. Experimental results show that proposed method can effectively lower reconstruction error compared to existing CS-based UWB channel estimation method.