基于稀疏小波变换的超宽带低信噪比信号检测算法

Detection algorithm for low SNR signal in UWB systembased on sparse wavelet transform

脉冲超宽带信号是时域瞬态脉冲,功率谱密度极低,在远距离通信时,信号淹没在噪声中较难检测,对前端采样率要求较高。针对脉冲超宽带低信噪比检测问题,提出了一种在脉冲波形先验信息已知条件下,基于稀疏小波变换的低信噪比检测方法。针对超宽带信号在小波域具有稀疏分布这一特征,依据压缩传感理论,分析并仿真了稀疏基矩阵选择时域采样矩阵和小波矩阵时,信噪比对于性能的影响,提供了重构算法中迭代终止门限的选择方法。仿真实验表明,相对于稀疏基矩阵为时域采样矩阵,采用小波变换矩阵可以在较低信噪比条件下实现超宽带信号的降噪重构。

The ultra wideband impulse radio （IR-UWB） signal is time domain transient pulse with low power spectral density. In long-distance communication, the signal is submerged in noise and is difficult to be detected ; therefore high front end sampling rate is required, which is a formidable challenge. Aiming at the problem of IR-UWB signal detection in low SNR, in case that the waveform of the UWB pulse signal is known, a sparse wavelet transform based detection method is proposed in low SNR condition. According to the characteristic that UWB signal has sparse distri- bution in wavelet domain and based on compressed sensing theory, time domain sampling matrix and wavelet matrix are selected as the sparse basis matrix, the influence of SNR on BER is analyzed and simulated, and the selection method for iteration stopping threshold in the reconstruction algorithm is given. Simulation experiment shows that compared with the time domain sampling matrix method, the wavelet matrix based detection method can achieve the noise reduction and reconstruction of UWB signal in lower SNR condition.