Study On Cyclostationary Signal Processing Methods In Alpha-stable Distributed Noise

Cyclostationary(CS)signal processing,an important branch of signal processing,is the main theoretical methodology to process cyclostationary signals.After more than sixty years of development,cyclostationary signal processing has been widely used in radio supervision,communication,and detection,and has received extensive attention from worldwide scholars.The existing cyclostationary signal processing methods can effectively suppress additive Gaus-sian noise,but the performance of these methods is significantly degraded under the influence of alpha-stable distributed noise.Therefore,this dissertation deeply studies the cyclostationary signal processing methods in alpha-stable distributed noise.In this dissertation,based upon processing methods for alpha-stable distributed noise and cyclostationary theory,two novel cyclostationary signal processing methods in alpha-stable dis-tributed noise are first studied.Second,according to compressive sensing(CS~*)theory,the implementation ways and detailed procedures of cyclostationary signal processing methods in alpha-stable distributed noise with sub-Nyquist sampling are further investigated.Finally,this dissertation goes deep into sparse reconstruction in compressive sensing and proposes a semi-greedy algorithm based upon tree search.The main innovative works of this dissertation are as follows:(1)To address the problem that the performance of classic cyclostationary signal process-ing methods is degraded in alpha-stable distributed noise,cyclic correntropy is introduced and its theory is studied in this dissertation.First,the definitions of correntropy for the multidimen-sional random variables,multidimensional deterministic signals,and multidimensional random processes are provided.Second,the analytical expression for correntropy of alpha-stable random variables is derived.Gaussian kernel function in correntropy is analyzed in-depth and a corre-sponding mapping function from one dimension to infinite dimension is derived.The relation-ship between the time-varying correntropy and the time-varying correlation function is analyzed.Finally,the properties of cyclic correntropy and cyclic correntropy spectrum are derived.(2)To address the problem that cyclic correntropy does not have phase information and the kernel size of Gaussian kernel function is not easily set,hyperbolic tangent cyclic correlation(HTCC)is proposed and its theory is studied in this dissertation.First,based upon hyperbolic tangent function,phased hyperbolic tangent transform(PHTT)is proposed,leading to the defini-tion of hyperbolic tangent correlation(HTC).Second,the relationship between the time-varying hyperbolic tangent correlation and the time-varying correlation function is analyzed in the real and complex domains.The properties of hyperbolic tangent cyclic correlation and hyperbolic tangent cyclic correlation spectrum are derived.Finally,hyperbolic tangent cyclic ambiguity function(HT-CAF)and its application methods are proposed.(3)According to the characteristics of sparseness and symmetry of cyclic spectrum in the frequency domain and cyclic frequency domain,two implementation ways and detailed proce-dures of cyclostationary signal processing methods in alpha-stable distributed noise through sub-Nyquist sampling are studied in this dissertation.The first way is processed in the real domain.The original signal is completely acquired,and compressive sensing is applied to the sparse two-dimensional projection from the cyclic spectrum.Finally,the two-dimensional cyclic spectrum projection is rebuilt by sparse reconstruction using a greedy algorithm.The second way is pro-cessed in the complex domain,and compressive sensing is applied to the non-sparse original signal at sub-Nyquist rates.According to the relationship between fractional lower-order cor-relation,fractional lower-order cyclic correlation,and fractional lower-order cyclic correlation spectrum,an objective function of the three-dimensional fractional lower-order cyclic correlation spectrum is designed.Finally,the three-dimensional fractional lower-order cyclic correlation spectrum is rebuilt by sparse reconstruction using convex optimization.(4)To address the problem that the preset parameters in the heuristic function of A~*or-thogonal matching pursuit are not easily set,nonlinear regression A~*orthogonal matching pur-suit(NR-A~*OMP)is proposed in this dissertation.First,based upon A~*search(A~*algorithm)from the shortest path search in graph theory and greedy algorithms in compressive sensing,the heuristic function of A~*orthogonal matching pursuit is evaluated and the trend of the squares of the l2 norms of the residues in greedy algorithms is analyzed.Second,following the design rule of the heuristic function of A~*search,a novel heuristic function without preset parameters is constructed.Finally,based upon the restricted isometry property(RIP)and related lemmas,the sufficient condition for the success of NR-A~*OMP to complete sparse reconstruction is derived by mathematical induction.