Research On Compressed Sensing And The Application In Wireless Channel Estimation

Compressed sensing theory is one of current research focuses in the field of signal processing. Traditional signal processing is based on the Nyquist sampling theorem, in which the signal is usually sampled firstly and then compressed, and the signal sampling and processing rate must be higher than the Nyquist frequency. If the signal is sparse or compressiblem, the signal can be sampled and processed at the same time with the rate far below the Nyquist frequency, which is compressed sensing. In the theory of compressed sensing,information sampling (ie, the data of observation or perception)is instead of the signal sampling(the signal reconstructionthe traditional decoding at the receiving end ),and therefore it can not subject to the Nyquist sampling rate. This advantage makes the compressed sensing theory has a great prospect in many aspects of communications and information processing.This paper proposes an improved convex optimization compressed sensing reconstruction algorithm based on study in the compressed sensing theory framework and the simulation of the algorithm confirmes the reconstruction performance of improved one is better obviously. Based on compressed sensing theory research, this paper also discusses a new ultra-wideband channel estimation scheme based on compressed sensing. In this scheme, the PN encoder is introduced into the framework of compressed sensing so that the quasi-Toeplitz Matrice produced by the PN encoder is instead of completely random Gaussian matrix.The encoder can store the measurement operators and solve the difficult problems in a large amount of data compression for its storage function, and the encoder is easy to implement in the hardware and software. In addition, the transmitter bears a part of the complex algorithm computation to save the reconstruction time of receiving end. The model moves the down-sampling process in traditional channel estimation model to the emission side according to the time reversal theory so that to reduce the complexity of the receiving end and speed up data processing speed.This article consists of the following four parts:The research significance of compressed sensing theory and ultra wideband technology developmentCompressed sensing theory frameworkIntroduction of UWB wireless communication system Ultra-bandwidth channel estimation method based on compressed sensing technologyThe study results of this paper can be as reference for further research in compressed sensing and its application in ultra-wideband wireless communication system.