Research On Cumulants Of Communication Signals Based On Compressed Sensing

With the rapid development of wireless communication services,electromagnetic spectrum resources are becoming more and more limited,so how to deal with the complex communicatio n signals with broadband,multi-signal and multi-modulation modes has become the focus of research.Since the traditional compressed sensing method has many disadvantages,such as high computational complexity,which makes the processing of compressed signals a research hotspot,that is,how to combine signal processing tasks with compressed sensing theory organically to achieve the signal processing tasks quickly and efficiently.Because of the encoding,modulating and other operations,the digital signal generally has cyclostationarity,that is,their statistical characteristics are related to time,and these statistical characteristics are periodic,and their frequency spectrum is sparse.Therefore,the parameters of a received signal can be estimated by using the cyclostationarity of the digital signal in the blind signal processing.Based on compressed sensing theory,this dissertation focuses on how to directly reconstruct the cyclic cumulant by using t he compressed sampling values of the time-domain aliased signal.Then the parameters of the signal are estimated by utilizing the relationship between the cyclic frequency and the parameters.The main research contents include:1.The signal sparse representation,observation matrix design,and signal reconstruction algorithms for compressive sensing theory are studied.A sampling frame suitable for analog domain and a compressed sampling frame suitable for cyclic cumulant reconstruction are proposed.In addition,the related reconstruction algorithms are simulated and analyzed.2.Theories related to higher-order statistics,including higher moments,higher-order cumulants,time-varying moments,time-varying cumulants,cyclic moments,and cyclic cumulants,were studied.The properties and estimation methods of these statistics were studied.Finally,the cyclostationarity of the digital signal,the sparsity of the cyclic cumulant,the selectivity of cyclic cumulant with the aliasing signal,and the good noise immunity are discussed in detail.3.A reconstruction algorithm about directly reconstructing the cyclic cumulant of the signal using the compressed sampling values is proposed.Specifically,a zero-based high-order cyclic cumulant reconstruction algorithm is included.But the zero-based reconstruction algorithm is not suitable for an actual segmented sampling model.This paper proposes a cyclic cumulant reconstruction algorithm based on compressed sensing to establish the matrix linear relationship between the compressed sample value and the cyclic cumulant.The cyclic cumulant is reconstructed using the compressed sensing algorithm.In addition,an improved algorithm based on zero-padding is proposed,which mainly uses the compressed sensing method to optimize the zero-based reconstruction algorithm.Finally,the simulation of cyclic cumulant reconstruction is performed for the single-signal and multi-signal cases,and the performance of the reconstruction algorithm is studied through simulation.4.The classical carrier and code rate estimation algorithms are briefly studied.Since the classical algorithm is only applicable to the single-signal case,a cyclic cumulant-based parameter estimation algorithm is proposed for multi-signal aliasing.The simulation of the parameter estimation performance of the commonly used MPSK\MQAM signal is performed.