基于压缩感知的信号频谱测量方法研究
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摘要
压缩感知理论利用信号稀疏性直接采样压缩后的信号,具有信号采样速率低、数据存储压力小等优点,在模拟信号采集、雷达和通信系统频谱测量、多输入多输出系统设计以及变换域采样系统设计等领域具有广泛的应用前景。将压缩感知理论应用于频谱测量过程中,不但可以降低采样速率、提高频谱测量精确度,而且能够简化采样器结构,利于实际应用。本论文对压缩感知频谱测量中的信号建模、频谱测量算法设计以及采样硬件实现等问题进行了系统研究,取得的研究结果如下：
针对多谐波稀疏信号模型开展了频谱感知方法研究。构造了信号重排函数和平坦滤波函数,使用这两种函数将多谐波稀疏信号转化为多频带稀疏信号,采用降采样压缩感知方法配合两点测频法重构原始频谱,构造了基于信号重排滤波的频谱感知方法PFSCS。与其他频谱感知方法相比,该方法既可以减少采样数量,又能够降低频谱感知计算复杂度,适合应用于窄带信号频谱测量过程中。
针对多频带稀疏信号模型开展了频谱感知方法研究。采用小波边缘检测函数检测活动频带位置,构造了自适应离散椭球序列变换基进行原始频谱重构,建立了两级自适应多频带稀疏信号频谱感知方法TAMS2。实验结果表明,该方法不但降低了频谱感知计算复杂度,而且具有更好的抗噪声鲁棒性,适合应用于高噪声环境下的多频带信号频谱测量过程中。
研究了压缩感知采样值的量化问题,分析了压缩感知量化原理及动态范围。针对1-bit CS框架,设计了标志位压缩感知重构算法SCSR-L2以及快速精确的两级信号重构算法FATS,分别具有信号重构精确度高以及信号重构速度快的特点。研究了“测量压缩”和“量化压缩”两种量化体制,分别针对低噪声环境和高噪声环境可以获得最佳的信号重构效果。
研究了压缩感知理论的硬件实现方法。基于随机解调架构,设计并搭建了电路级和系统级的AIC采样方案。相比于传统ADC,该硬件具有采样速率低、抗噪声鲁棒性高、信号重构精确度高的特点,为目前频谱测量硬件设计所面临的来自可靠性和低采样率方面的压力,提供了有效的解决方案。
By directly sampling compressed signals that are sparse in an appropriate basis, Com-pressive Sensing (CS) could tremendously reduce the sampling rate and data storage. Just for its superiority, CS has worked its way into a wide application foreground, including signal acquisition in analog domain, spectrum measurement in radar and communication systems, sampling system design in transform domain, multiple input and output system design, and so on. Applying CS to the spectral measurement process can not only reduce sampled rate, increase spectrum measurement accuracy, but also simplify the sampling structure. This the-sis presents in detail the application of CS theory in spectrum measurement, the algorithm design of spectrum measurement and the realization of sampling hardware. Main research works are as follows:
The spectrum measurement method of multi-tone sparse signal is researched. I propose a new algorithm called permuted&filtered spectrum compressive sensing (PFSCS). It firstly turns multi-tone sparse signals into multi-band sparse signals by the signal permute function and the flat filter function, then the original spectrum is reconstructed using the sub-sampling CS method and the two samples recovery method. This algorithm not only reduces the sampling rate but also improves the efficiency of spectrum measurement, make it suitable for the spectrum measurement in narrow band signals.
I probe into the spectrum measurement of multi-band sparse signals. I propose a new algorithm named two-stage adaptive multi-band spectrum sensing (TAMS2). It firstly detects the position of active bands using wavelet edge detection function, then reconstructs the original spectrum using adaptive discrete prolate spheroidal sequences(ADPSS) basis. This scheme has several advantages over the classical approaches. First, this algorithm enable us to reduce the computational complexity. Second, it takes advantage of the ADPSS properties to improve the noise robustness. Experimental results show that it has high performance for multi-band signal spectrum measurement with high noise.
The quantization method of compressive sensing measurements is researched. I ana- lyze the quantization principle and dynamic range in detail at the beginning. Based on1-bit framework, i develop two efficient signal reconstruction algorithms, respectively named sign compressive sensing reconstruction algorithm (SCSR-l2) and fast&accurate two-stage algorithm (FATS). The superiorities of these schemes are high detection accuracy and fast reconstruction speed respectively. In addition, i analyze two distinct compressive sensing quantization regimes called' Measurement Compression (MC) regime' and 'Quantization Compression (QC) regime'. Experimental results show that i can obtain perfect reconstruc-tion accuracy by using MC for low noise signal detection and using QC for high noise signal detection.
On the basis of the above philosophy, i extend further to the hardware design of CS. I design the analog-to-information converter (AIC) at circuit level and system level based on random demodulation. Compared with the traditional ADC, this AIC is a new sampling system with unprecedented low sampling rate, high noise robustness and high signal recon-struction accuracy. This scheme provides an effective solution for easing the pressure to design a reliability and low sampling rate hardware design in the spectrum measurement.
针对多谐波稀疏信号模型开展了频谱感知方法研究。构造了信号重排函数和平坦滤波函数,使用这两种函数将多谐波稀疏信号转化为多频带稀疏信号,采用降采样压缩感知方法配合两点测频法重构原始频谱,构造了基于信号重排滤波的频谱感知方法PFSCS。与其他频谱感知方法相比,该方法既可以减少采样数量,又能够降低频谱感知计算复杂度,适合应用于窄带信号频谱测量过程中。
针对多频带稀疏信号模型开展了频谱感知方法研究。采用小波边缘检测函数检测活动频带位置,构造了自适应离散椭球序列变换基进行原始频谱重构,建立了两级自适应多频带稀疏信号频谱感知方法TAMS2。实验结果表明,该方法不但降低了频谱感知计算复杂度,而且具有更好的抗噪声鲁棒性,适合应用于高噪声环境下的多频带信号频谱测量过程中。
研究了压缩感知采样值的量化问题,分析了压缩感知量化原理及动态范围。针对1-bit CS框架,设计了标志位压缩感知重构算法SCSR-L2以及快速精确的两级信号重构算法FATS,分别具有信号重构精确度高以及信号重构速度快的特点。研究了“测量压缩”和“量化压缩”两种量化体制,分别针对低噪声环境和高噪声环境可以获得最佳的信号重构效果。
研究了压缩感知理论的硬件实现方法。基于随机解调架构,设计并搭建了电路级和系统级的AIC采样方案。相比于传统ADC,该硬件具有采样速率低、抗噪声鲁棒性高、信号重构精确度高的特点,为目前频谱测量硬件设计所面临的来自可靠性和低采样率方面的压力,提供了有效的解决方案。
By directly sampling compressed signals that are sparse in an appropriate basis, Com-pressive Sensing (CS) could tremendously reduce the sampling rate and data storage. Just for its superiority, CS has worked its way into a wide application foreground, including signal acquisition in analog domain, spectrum measurement in radar and communication systems, sampling system design in transform domain, multiple input and output system design, and so on. Applying CS to the spectral measurement process can not only reduce sampled rate, increase spectrum measurement accuracy, but also simplify the sampling structure. This the-sis presents in detail the application of CS theory in spectrum measurement, the algorithm design of spectrum measurement and the realization of sampling hardware. Main research works are as follows:
The spectrum measurement method of multi-tone sparse signal is researched. I propose a new algorithm called permuted&filtered spectrum compressive sensing (PFSCS). It firstly turns multi-tone sparse signals into multi-band sparse signals by the signal permute function and the flat filter function, then the original spectrum is reconstructed using the sub-sampling CS method and the two samples recovery method. This algorithm not only reduces the sampling rate but also improves the efficiency of spectrum measurement, make it suitable for the spectrum measurement in narrow band signals.
I probe into the spectrum measurement of multi-band sparse signals. I propose a new algorithm named two-stage adaptive multi-band spectrum sensing (TAMS2). It firstly detects the position of active bands using wavelet edge detection function, then reconstructs the original spectrum using adaptive discrete prolate spheroidal sequences(ADPSS) basis. This scheme has several advantages over the classical approaches. First, this algorithm enable us to reduce the computational complexity. Second, it takes advantage of the ADPSS properties to improve the noise robustness. Experimental results show that it has high performance for multi-band signal spectrum measurement with high noise.
The quantization method of compressive sensing measurements is researched. I ana- lyze the quantization principle and dynamic range in detail at the beginning. Based on1-bit framework, i develop two efficient signal reconstruction algorithms, respectively named sign compressive sensing reconstruction algorithm (SCSR-l2) and fast&accurate two-stage algorithm (FATS). The superiorities of these schemes are high detection accuracy and fast reconstruction speed respectively. In addition, i analyze two distinct compressive sensing quantization regimes called' Measurement Compression (MC) regime' and 'Quantization Compression (QC) regime'. Experimental results show that i can obtain perfect reconstruc-tion accuracy by using MC for low noise signal detection and using QC for high noise signal detection.
On the basis of the above philosophy, i extend further to the hardware design of CS. I design the analog-to-information converter (AIC) at circuit level and system level based on random demodulation. Compared with the traditional ADC, this AIC is a new sampling system with unprecedented low sampling rate, high noise robustness and high signal recon-struction accuracy. This scheme provides an effective solution for easing the pressure to design a reliability and low sampling rate hardware design in the spectrum measurement.
引文
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