Analysis And Design Of The Measurement Matrix In Frequency-hopping Using Compressive Sampling

When dealing with the wideband signals such as frequency hopping (FH) signal, the traditionalsignal processing methods always produce large amounts of sampling data and consume storagespace seriously. Compressive sampling has opened up a new signal processing mode, which doesthe signal sampling and data compression simultaneously. Using only a small number ofmeasurements it can restore the signal with high probability, so its application prospect is verybroad. Measurement matrix, which directly affects the signal data acquisition in the front-end andsignal reconstruction in the back-end, is of vital importance in compressive sampling. Therefore,designing good performance measurement matrix has very important theoretical and practicalsignificance. Based on the analysis of the measurement matrix in compressive sampling, this papermainly studies on the optimal design of measurement matrix and specifically carries out thefollowing works:Firstly, we introduced the constraints that the measurement matrix need to meet and therelationship of measurement matrix, signals’ sparsity, sampling numbers and reconstruction effect incompressive sampling in order to analysis the importance of the measurement matrix. Then wedescribed the structure and properties of common used measurement matrix so as to research theconstruction methods to measurement matrix. And we analyzed the performance and characteristicsof the existing measurement matrix optimization methods in order to learn techniques of theoptimization measurement matrix.Secondly, according to the characteristics of wideband FH signals, we analyzed thecharacteristics of measurement matrix in depth from the view of subsequent detection andparameter estimation. We researched the requirements of measurement matrix from the propertiesthat the compressed samples should be independent, that the Signal to Noise Ratio (SNR) lossbefore and after compression should be minimized, and that the background noise should be whiteafter compression. Combined with the Restricted Isometry Property(RIP) of measurement matrix,we pointed out that the ETF is a best choice from the perspective of either the maximizecompression ratio or the optimal performance of the reconstruction.Thirdly, on the purpose of reducing the mutual coherence between different columns of therecovery matrix, we proposed the projection construction of measurement matrix based onGrassmannian frames. We analyzed the construction methods to Grassmanian frames andintroduced the projection optimization method to gram matrix. At last, we proposed the projectionconstruction of measurement matrix based on optimal Grassmannian frames and implemented the concrete algorithm. The simulation results showed that this method can effectively reduce themutual coherence between different columns of the recovery matrix and improved the effect ofsignals construction; thereby this construction method can improve the performance ofmeasurement matrix.Finally, according to the idea of joint optimization of measurement matrix and sparse dictionary,we proposed the optimization method based on the KSVD-ETF. We analyzed the sparse dictionariesand its optimization in compressive sampling. Afterwards, we expounded the K Singular ValueDecomposition (KSVD) training method of sparse dictionaries and the Equiangular Tight Frame(ETF) optimization method of measurement matrix. In the end, we introduced the KSVD-ETF jointoptimization method that the measurement matrix is ETF optimized and the dictionary is KSVDupdated at the same time. The simulation results showed that joint optimization method canincrease the successful recovery rate and SNR of reconstructed signals, therefore this method canimprove the overall performance of compressive sampling...