Research On Atomic Norm-based Broadband Compressive Spectrum Sensing

To achieve direct observation of wide-band spectrum and detect all active signals,broadband spectrum sensing technology requires a very high sampling rate and processes a large amount of data.Compressive sensing theory provides a theoretical basis for low-rate sampling.Therefore,wideband compressive spectrum sensing technology has become an important research directio.However,the traditional compressive sensing model discretizes in frequency domain and,as a result,generates base mismatch problems,which reduces the accuracy of frequency estimation.Besides,the schedules of the primary users are unknown to cognitive users and change dynamically and randomly with time,which results in the mutative sparse structure of broadband spectrum,making it difficult to track.In addition,since wireless signal is easily affected multipath effects,cognitive users may receive a signal with relatively low energy,resulting in a decrease of sensing performance.Accrding to the research status of broadband compressive spectrum sensing technology,this paper summarizes the existing difficulties into four points: accuracy,speediness,dynamic and fading.The research content is also centered on these points.Firstly,in the light of atomic norm and gridless compressive sensing theory,a broadband compressive spectrum sensing model based on atomic norm is established for static Gaussian channel.Then combined with the Kalman filter theory,a dynamic wideband compressive spectrum sensing model was formulated to achieve wideband compressive spectrum sensing in dynamic situation.Finally,using the joint spectrum sensing technique,a MMV broadband compressive spectrum sensing model is analyzed to realize spectrum sensing under the fading channel.The detailed research content and achievements are as follows:Firstl of all,this paper describes the causes of the base mismatch problem and its impact on broadband spectrum sensing.In order to intrinsically solve the problem of base mismatch,the atomic norm and gridless compressive sensing theory are used to formulate an atomic norm-based broadband compressed spectrum sensing model.Under this model,from signal sparse representation to compressive sampling and to signal reconstruction,all the procedures avoid discretization of frequency domain,which is essentially different from traditional compressive sensing theory,and thus has better frequency estimation accuracy.In this paper,the broadband spectrum sensing problem is divided into two sub-problems: line spectral estimation and modulated signal recovery,of which the former is the basis of the latter.In these problems,signal reconstruction is formulated as a convex optimization problem of atomic norm minimization.And it can be equivalently converted to a semidefinite programming problem and sovled by some softwares.We also provide a fast algorithm for solving such problems.Numerical simulations show that the atomic norm-based wideband compression spectrum sensing model has better performance than traditional compressed sensing,and can achieve more accurate frequency estimation without significantly increasing the complexity of the algorithm.Secondly,this paper discusses the characteristics of mutation in broadband spectrum,which can be concluded as slowness and randomness,with strong temporal correlation.According to the analysis,we propose a signal model that formulates the dynamic feature of the broadband spectrum,namely the Gaussian random walk model.This signal model can generate a wideband signal with sparse structure varying stochastically over time.Because the Kalman filter theory has good performance with time-correlation signals,we proposes a Kalman filter-based dynamic wideband compressive spectrum sensing algorithm.The proposed algorithm first utilizes the frequency support set at the previous time to accomplish signal reconstruction,and then calculates the residuals of recovered signals of the current time and the previous time.According to the idea of differential,the frequency estimation of all signals at current moment is converted into that of the differential signal,resulting in obvious advantages when the number of primary user signals is large.Numerical simulations demonstrate that the dynamic algorithm based on Kalman filter has better performance than the common one,and has obvious advantages in terms of mean square error,detection probability and success rate.Finally,this paper analyzes the multipath transmission of signals.According to the assumptions of the primary user signal and the broadband spectrum,the fading channel is selected as a frequency non-selective slow fading channel.As an effective anti-fading technique,the joint spectrum sensing method can fuse the sensing information of multiple cognitive users and achieve spatial diversity.In this paper,we abstract the joint spectrum sensing as an atomic MMV model,and proposes an atomic MMV based broadband spectrum sensing algorithm.The algorithm first preprocesses the sampled data of all cognitive users,obtaining the corresponding sparse description matrix,then converts the sparse matrix to sparse vectors through random projections and forms an atomic MMV model.The frequency of the signal can be estimated by solving the atomic MMV problem.Numerical simulations illustrate that the joint spectrum sensing method has obvious advantages over the single user spectrum sensing method in fading channel.