压缩感知(Compressed Sensing, CS)理论可以从较少的观测样本中恢复稀疏信号。针对超宽带(Ultra- WideBand, UWB)信道的稀疏特性，将压缩感知理论应用于UWB系统的信道估计中，能够有效地降低系统的采样速率。该文针对UWB信道的特点对过完备字典库和观测矩阵进行设计，提出了一种滤波矩阵估计算法。然后,分别利用丹茨格选择器(Dantzig Selector, DS)，基追踪降噪(Basis Pursuit De-Noising, BPDN)算法和正交匹配跟踪(Orthogonal Matching Pursuit, OMP)算法实现信号检测，进一步给出UWB信道估计中CS重建算法的选择建议。基于IEEE 802.15.4a信道模型的仿真结果表明，该算法同随机观测算法的检测结果相比，能够在较低的采样速率下获得更好的误码率性能。
The theory of compressed sensing can be used to reconstruct sparse signals from fewer observations. According to the sparsity of UWB channels, a reduced sampling rate can be obtained at the detector based on compressed sensing frame. In this paper, a filter matrix estimation algorithm is proposed by designing the over-completed dictionary and observation matrix. Then, the Orthogonal Matching Pursuit (OMP), the Basis Pursuit De-noising (BPDN) and the Dantzig Selector (DS) are used to detect original signal to give the opinions for choosing suitable reconstruction algorithms. The simulation results in the IEEE 802.15.4a channel model show that the coherence detection based on the new channel estimation method outperforms the one based on random observation method for better bit error rate performances with a reduced sampling rate.