Research On Compressed Sensing And The Application Of Channel Estimation

With the rapid development of signal processing technology, the signal we need to deal with bring much of sampling data. In 2006, the scholars raise the compressed sensing theory, witch can break the Nyquist sampling theorem. By using of this theorem, we can reduce the number of sampling data. It offers a new way for the signal processing technology and attracts a lot of scholars to study on it, witch promote the rapid development of this theory.This paper first introduces the background and study significance of the compressed sensing theory, including the current research status and the application of this theory. Then this paper introduces the compressed sensing theory briefly, including the sparse decomposition, the design of the measurement matrix and the reconstruction algorithm of the theory. In this paper, the major work includes the reconstruction algorithm of the compressed sensing and the application of the theory in channel estimation of wireless channel.Then this paper analysis the matching pursuit and orthogonal matching pursuit algorithm, including the mathematical principle of the algorithm, the algorithm process, and the performance of the two algorithms in compressed sensing system. But the matching pursuit algorithm exists mismatch phenomenon, and the orthogonal matching pursuit algorithm needs too much computation time, this paper then analysis the regular orthogonal matching pursuit algorithm and compressed sampling matching pursuit algorithm. On the basis of these algorithms, this paper proposes a regular orthogonal matching pursuit algorithm with the thought of feedback. This algorithm can improve the accuracy of signal reconstruction result, and computational complexity is acceptable. Then we make the simulation to analyze the performance of these algorithms.Finally, this paper applies the compressed sensing theory to the channel estimation of the wireless communication system. Compared to traditional channel estimation method, compressed sensing theory can take full use of the sparse characteristics of the channel and provide a new idea for channel estimation. This section can be divided into three main elements. First, we establish the broadband wireless communication mathematical system model and prove the feasibility of the compressed sensing in the application of channel estimation. Second, we prove that most of the radio channel has a sparse feature. Finally, according to the wireless system model, we make simulation experiments to compare the accuracy of the estimation by using of different channel estimation algorithm, including the least squares method, the compressed sensing channel estimation method and the algorithm proposed in this paper. That is compressed sensing method with the feedback adjustment of frequency domain. We can see the advantages and great value of compressed sensing method in wireless channel estimation.