Research On Spectrum Sensing Of Wideband Signals Based On Sub-Nyquist Sampling

With the development of electronic and communication technology,the bandwidth of signal has increased drastically,and the wideband signal generally has sparsity characteristics.It is a trend to process the wideband signal in the digital domain,and the Nyquist sampling theorem establishes a bridge between analog signal processing and digital signal processing.The theorem states that the required sampling rate must be higher than twice the highest frequency of the wideband signal.The current available Analog-to-Digital Converter(ADC)can hardly satisfy this sampling rate requirement,even with such a high sampling rate ADC,it is usually very high in terms of power consumption and price.However,the Nyquist sampling theorem is just a sufficient condition for alias-free sampling rather than a necessary condition.The sub-Nyquist sampling technique,such as Multi-Coset Sampling(MCS),Random Demodulator(RD)and Modulated Wideband Converter(MWC),utilize the sparsity or statistical property of signal,and combined with compressive sensing to acquire and reconstruct signal at a rate which is much lower than the Nyquist sampling rate.This technology has greatly influenced the development of spectrum test for wideband signal.This dissertation aims at solving the following problems: 1.the mismatch among sub-ADCs in parallel MCS;2.the high computational complexity of power spectrum reconstruction using sub-Nyquist samples;3.the 1-bit compressive sensing is only applicable to mathematical vector model.Meanwhile,this dissertation considers the following three aspects of wideband signal spectrum test: 1.the spectrum test of frequency-domain multi-band signal;2.the power spectrum test of Wide-Sense Stationary(WSS)signal;3.the normalized spectrum test of signal with line spectrum.The content of this dissertation mainly includes the following four parts:1.Aiming at the mismatch problem among sub-ADCs(Sub-Analog-to-Digital Converter)in traditional parallel MCS,a single-channel MCS method suitable for the spectrum(including magnitude spectrum and phase spectrum)test of multi-band signal is studied.First,a single-channel MCS method using single periodic non-uniform sampling clock,single Sample-and-Hold(S/H)and single ADC is proposed.The periodic non-uniform sampling clock can be generated by a pseudo-random binary sequence generator,the S/H is used to improve the analog bandwidth of single-channel MCS.Moreover,the method of estimating the number of active sub-bands using the model-order-selection theory is introduced,and the method of spectrum reconstruction using the sub-Nyquist samples is discussed.A universal sampling pattern design method suitable for spectrum reconstruction is proposed.Simulation and experiment uses different signal to test the proposed method,and the result shows that the single-channel MCS proposed by this dissertation has better spectrum reconstruction performance compared with the traditional parallel MCS.2.Aiming at the mismatch problem among sub-ADCs in traditional parallel MCS,a single-channel MCS method suitable for finite resolution power spectrum reconstruction of WSS signal is studied.The finite resolution power spectrum is defined as: the entire frequency range is evenly divided into sub-bands,and the finite resolution power spectrum is the average power spectrum within these sub-bands.Firstly,a single-channel MCS method suitable for finite resolution power spectrum reconstruction is proposed.Clocks of S/H and ADC are provided by two different periodic non-uniform sampling clocks,and the cooperation between these two different periodic non-uniform sampling clocks shifts the high sampling rate requirement from the ADC to the S/H.Secondly,the finite resolution power spectrum reconstruction method using the sub-Nyquist samples is introduced,and a five-step spectrum sensing method is proposed.A universal sampling pattern design method for finite resolution power spectrum reconstruction is proposed as well.Simulation and experiment show that when the number of samples per coset is greater than 1400,single-channel MCS has excellent performance to detect both spectrum holes and primary users for signals with Signal-to-Noise Ratio(SNR)higher than-3d B.3.Aiming at the high computational complexity problem of power spectrum reconstruction which is based on MCS,efficient spectrum sensing methods based on frequency-smoothed power spectrum and Fast Fourier Transform(FFT)are studied.Firstly,a method of reconstructing power spectrum using MCS samples is introduced,and an efficient spectrum sensing algorithm is proposed.By utilizing the frequency-smoothing characteristics,the efficient spectrum sensing algorithm proposed in this dissertation only needs to estimate the power spectrum of partial frequency bins for spectrum sensing,which would save a lot of computational cost.Secondly,in order to further reduce the computational complexity of frequency-smoothing power spectrum reconstruction,an FFT-based algorithm is proposed to replace the traditional least square algorithm.Since the system matrix of power spectrum estimation has a special structure(its row vectors are all selected from the row vectors of the Discrete Fourier Transform Matrix(DFT)),this dissertation uses this special structure combined with FFT to reduce the computational complexity of power spectrum reconstruction.Simulation and experiment use the Quadrature Phase Shift Keying(QPSK)as the test signal.The result shows that both methods exhibit excellent spectrum sensing performance,in addition to approximately 90% reduction of computing resource.4.Aiming at the 1-bit compressive sensing is based on mathematical vector model,it cannot be applicable to acquire and reconstruct the analog signal directly,an 1-bit RD suitable for analog signal sampling studied.Firstly,an 1-bit RD is proposed by combining the advantage of the input bandwidth of RD and 1-bit compressive sensing.The relationship between the 1-bit compressive observation and the input signal is analyzed,and then establishes the 1-bit compressive sensing matrix.Secondly,an adaptive Binary Iterative Hard Threshold(BIHT)algorithm is designed in order to adapt to signal with different sparsity level.By comparison,the residual is used to establish the stopping condition,which ensured that signal with different sparsity can be recovered by using the minimum number of iterations.Simulation uses the line spectrum signal as the test signal,and the result shows that the proposed method can accurately reconstruct the normalized spectrum.