Research Of Signal Spectrum Measurement Based On Compressive Sensing

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.