Compressive Sampling And Reconstruction Of Frequency-Hopping Signals

The broadening of frequency band of frequency-hopping(FH)signal brings about the problem of high sampling rate.The theory of compressed sensing points out that when the signal itself is sparse or the signal is sparse in the transform domain,the signal can be compressed and sampled at a rate far lower than Nyquist's sampling rate without loss of signal information,and the signal can be accurately reconstructed using reconstruction algorithm based on the sampling value.FH signals have natural sparse characteristics in the frequency domain.Therefore,it is of great practical significance to use compression sampling technology to solve the problem of high sampling rate of FH signals.Since the further processing of FH signal still needs the original signal,the research on the reconstruction algorithm of FH signal after compression and sampling has great application value.This paper mainly studies the compression sampling and reconstruction algorithms of FH signals.The work of this paper mainly includes the following aspects:(1)Aiming at the compression sampling of FH signal,this paper studies the compression sampling of FH signal by two compression sampling structures: random demodulation structure and modulation wideband converter,and realizes the self-adaptive of random demodulation structure and modulation wideband converter compression sampling rate,which reduces the compression sampling rate while ensuring the reconstruction accuracy.The compression sampling of the FH signal by random demodulation structure is realized,and the influences of the compression sampling rate,the signal-to-noise ratio,the cut-off frequency of low-pass filter and the type of low-pass filter on the performance of the compression sampling are analyzed.Furthermore,the sequential compression sensing method based on the feedback mechanism is applied to the random demodulation structure to realize the self-adaptive compression sampling rate of FH signal and the compression sampling rate is reduced while ensuring the reconstruction accuracy.The compression sampling of the FH signal by the modulation wideband converter is realized,and the influences of the compression sampling rate,the signal-to-noise ratio,and the type of low-pass filter on the performance of the compression sampling are analyzed.Furthermore,the sequential compression sensing method based on feedback mechanism is applied to the modulation wideband converter to realize the self-adaptive compression sampling rate of FH signal and the compression sampling rate is reduced while ensuring the reconstruction accuracy.(2)Aiming at the reconstruction algorithm of FH signals,the fast block sparse Bayesian learning algorithm is studied deeply and it is used to realize the reconstruction of FH signal.Aiming at the problem that fast block sparse Bayesian learning algorithm needs to know the noise energy,a fast block sparse Bayesian learning algorithm with adaptive noise is proposed,which further improves the reconstruction performance of frequency hopping signal.In the reconstruction process,the fast block sparse Bayesian learning algorithm needs to know the noise energy,and the noise energy is generally unknown during the receiving process of FH signal.In order to solve this problem,this paper proposes a noise estimation method.This method uses the product of the FH signal observation vector and its conjugate transpose matrix to obtain autocorrelation matrix.The eigenvalues in the autocorrelation matrix are used to represent the signal energy and noise energy respectively.A method to estimating the noise energy of FH signals is given,and a fast block sparse Bayesian learning algorithm with adaptive noise is obtained,which further improves the reconstruction accuracy,especially in the case of ow and medium SNR.