基于欠奈奎斯特采样的超宽带信号总体最小二乘重建算法

该文针对超宽带无线通信中需要设计高速模数转换器的问题，提出了一种欠奈奎斯特采样方法，该方法所要求的采样率仅与信号新息率相关，低于奈奎斯特率1个数量级。基于欠采样得到的离散时间超宽带信号，从理论上推导出信号的傅里叶频谱表达式，由此给出了一种总体最小二乘参数估计算法，能够准确地估计出冲激串信号的幅度和时移；通过将估计出的冲激串信号与高斯单脉冲波形卷积，完成超宽带信号的波形重建。仿真和实验结果表明，该文算法能够准确地重建原始超宽带信号，且算法性能优于现有的零化滤波重建算法。

A Total Least Squares Reconstruction Algorithm of UWB Signals Based on Sub-Nyquist Sampling

A sub-Nyquist sampling method is presented to reduce the ADC sampling rate in UWB wireless communications. Sampling rate of the proposed method is related to the signal innovation rate, which is about one tenth of the Nyquist rate in conventional Shannon sampling theorem. Fourier transform coefficients of the UWB signals are derived from theoretical analysis based on sub-Nyquist sampling. Then Total Least Squares (TLS) algorithm is proposed to estimate the parameters of the amplitudes and time shifts of impulse signals. The waveform of UWB signals can be reconstructed by convolving the estimated impulse signals with Gaussian monocycle. Simulation and experiment results show that the UWB signals can be accurately reconstructed, and the proposed methods outperform annihilating filter method in the presence of noise.