基于自适应投影矩阵的压缩感知超宽带信道估计  

UWB channel estimation through compressed sensing based on adaptive projection matrix

作　　者：王蔚东[1,2] 杨俊安[1,2] 

机构地区：[1]电子工程学院,安徽合肥230037 [2]安徽省电子制约技术重点实验室,安徽合肥230037

出　　处：《电路与系统学报》2013年第1期310-317,331,共9页Journal of Circuits and Systems

摘　　要：超宽带信号由于功率谱密度较低和传输多径复杂,准确的信道估计十分重要。考虑其过高带宽带来的采样难度较高的问题,压缩感知理论提供了一种可行的低速采样方法。而目前常用的随机投影矩阵与超宽带信道稀疏变换矩阵相关度较高,算法必须在降维比较高时才能达到重构要求,采样速率依然较高。针对上述问题,提出使用贝叶斯压缩感知理论中的自适应投影矩阵设计方法进行超宽带信道估计。贝叶斯压缩感知理论给信道向量中的每个值设置受超参数控制的后验概率密度,计算信道向量的统计特性,并根据协方差矩阵计算新的投影向量,该投影向量可以使重构解的微分熵下降最快。通过这种自适应的投影矩阵设计方法,可以利用较少的采样值进一步地提高重构解的可信度,达到进一步降低采样速率的目的。实验结果表明该方法相对于现有的压缩感知重构算法可以在较低的降维比条件下达到较好的重构效果,显著降低了采样速率。Due to the low power spectrum density and complicated transfer multi-path of Ultra-Wideband（UWB） signal,it is important to do channel estimation accurately.But it’s difficult to sample it directly as its wider band width.However,compressed sensing（CS） provides a feasible way with lower sampling speed.Common random projection matrix remains high coherence with UWB channel sparse transform matrix and this leads the algorithm achieve reconstruction requirement only at high compressing ratio,which means that it still needs a high sampling speed.To solve these problems,an UWB channel estimation method based on an adaptive projection matrix using bayesian compressed sensing（BCS） is proposed in this paper.BCS sets posterior probability density function which is controlled by hyperparameters to each value in the channel vector and computes its statistical characteristics.Using covariance matrix to reckon new projection vector which can lower the differential entropy of reconstruction value steepest.This method enhances the certainty of reconstruction value and lowers the sampling speed using fewer samples.The experimental results show that this method can achieve a better reconstruction performance compared to the existing CS reconstruction algorithm at low compressing ratio and decrease the sampling speed notably.

关 键 词：超宽带 信道估计 贝叶斯压缩感知 投影向量 微分熵 

分 类 号：TN911.5[电子电信—通信与信息系统]