Research On The Application Of Sparsity And Incoherence In Electromagnetic Environment Field Reconstruction

Acquiring knowledge of the distribution within a spatial region of geographical environment is highly desirable in many civil and industrial applications.For instance,it is a key process in assessing whether the electromagnetic(EM)radiation,and the pollution generated by a base station lying within the mandatory limits imposed by the regulatory organizations.Moreover,a reliable field strength evaluation can indicate suitable guidelines for an effective and large-scale deployment and optimization of current and next-generation wireless networks.On the other hand,it is worth pointing out that accurate EM measurements in a large-scale area respect to the wavelength is quite time-consuming whether from simulation or realistic dosimeters.Therefore,efficient and reliable field reconstruction strategies,which exploit a limited set of measurement positions,but without any information on the EM radiating source are usually necessary and certainly very profitable.To solve the problem of field reconstruction(electric field magnitude reconstruction),the characteristics of the EM distribution in different geographical environment is investigated firstly.On that basis,the sparsity and incoherence in Compressive Sensing(CS)are applied for the reconstruction of the distribution of the EM field,a series of research work are done.The details are summarized as follows:(1)The characteristics and laws of the field distribution in different are discussed,including free space,half space,vegetation,and rough ground,which lays a foundation for the cognition and reconstruction of EM information in geographical environment.(2)Adaptive sampling method for EM environment is proposed.Based on the distribution characteristics of EM,that is the EM field distribution radiated by one or multiple sources in wide environments is generally smooth except close to the complex boundary and the source,which nees more concerntrated measurements because of the rapidly changing trends.A sequential experimental design strategy LOLA-Voronoi is introduced to adaptive sampling.The outcome is a representative set of data samples that is more concentrated within those regions in which larger deviations from a local linear approximation have been observed while guaranteeing a uniform coverage of the whole measured area without any a-priori knowledge on the radiating source.(3)The concept of sparsity and incoherence in CS is proposed to solve the field strength reconstruction problem,and a clear technical route of CS field strength reconstruction has been pointed out.Three sparsity basis: discrete Fourier transform(DFT),discrete cosine transform(DCT),and discrete wavelet transform(DWT)are used and compared;for the sampling strategy,besides random and uniform sampling,a hybrid sequential experimental design using LOLA-Voronoi is also considered;differnet CS recovery algorithms such as Orthogonal Matching Pursuit(OMP),L1 norm minimization and BCS are used under different sparsity basis and different sampling strategy for the recovery.Representative numerical results are discussed to assess,also comparatively with respect to the state-of-art prediction strategy,the potentialities and features of the proposed method.(4)A total-variation CS(TV-CS)algorithm as applied to field reconstruction is introduced.For the problem that traditional CS methods need to code the unknown FS distribution in a one-dimensional(1D)stacked vector,thus loosing the spatial correlation relationships existing among adjacent or spatially-contiguous locations.Moreover,they typically suffer of slow convergence especially when dealing with large domains.In this work,the inverse problem at hand is recast to the minimization of the augmented Lagrangian function,then it is efficiently solved by means of a TV-CS algorithm.Moreover,to remarkably reduce the computational cost of the inversion,an accelerated version of the TV-CS(ATV-CS)is introduced,for the first time to the authors' best knowledge,by making more efficient the costly matrixvector multiplications involved in the TV minimization.Representative numerical results are then commented and compared with the traditional CS technique both in terms of prediction accuracy and computational efficiency.(5)Adaptive Total-Variation CS(LV-ATV-CS)technique is arised.Despite its success when the number of affordable measurements is sufficiently large by ATV-CS,however,in many practical scenarios the level of sparsity of a real signal is unpredictable and it is not easy to a-priori determine how many measurements will be necessary to guarantee the best trade-off between accuracy and efficiency.Based on the integration of the ATV-CS solver with a LOLA Voronoi adaptive sampling technique for iteratively generating the ATV-CS observation matrix,an innovative LV-ATV-CS methodology for field strength prediction is presented in this thesis.LV-ATV-CS algorithm takes advantage of the trait that the sensing matrix of ATV-CS does not need to be constrained by CS incoherence condition and the same optimization object that is the field gradient.Mathematical theory and representative numerical results are shown to verify the effectiveness of the method.