Research On Compressed Sensing And The Application In UWB Channel Estimation

Nyquist sampling theorem is the theoretical guidance of traditional signal sampling and processing. It proves that the signal sampling rate is not less than twice the signal bandwidth for precise signal reconstruction. However, with the development of information technology, the demand for information requirements and the ability to process information is also increasing, which brings great challenges to traditional signal processing framework based on the Nyquist theorem on sampling rate and processing speed. At the same time, it also leads to a heavy burden to the subsequent processing and transmission because of excessive sampling points. Recently, a new signal acquisition and processing method - compressed sensing theory is expected to solve these problems. It points out that as long as the signal is compressible or sparse in a transform domain, a measurement matrix which is not related to transform domain can be used to transform the high-dimensional signal to the low-dimensional space, and then reconstruct the original signal with appropriate algorithm. The theory has a great prospect in many ways; channel estimation in ultra-wideband wireless communication systems is one of research focuses. The main work of this paper is as follows:I) The research of CS reconstruction algorithms based on l0 norm minimization: Signal reconstruction is one of the researches in the theory of compressed sensing. The smooth l0 norm algorithm based on approximate norm minimization is one of the convex optimization algorithms which are easy to calculate and the reconstruction quality is satisfied, but the rate of reconstruction and the noisy signal reconstruction is not very satisfactory. On this basis, an improved algorithm is proposed and the performance analysis is made in noise-free case and in noisy case. The results show that, compared with the original algorithm in the noiseless case, the running time is shorter, and with the signal length increases, this superiority is even more prominent and therefore more applicable to the large-scale signal reconstruction; in noisy situation, the improved is better due to adding a noise reduction technology and it still obtain good estimation effect even at low input SNR, which extends the scope of application of the smoothing norm algorithm.II) The research of compressed sensing in UWB Channel estimation: To achieve the difficult problem that the sampling rate requirement is too high in the UWB communication system, an improved ultra-wideband estimation model based on CS is proposed in the paper by utilizing the channel inherent sparse features. Access to the channel gain distribution from the received pilot signal, and by this to construct the adaptive observation matrix, then combined with the distributed compressed sensing technology to build multi-channel joint estimation model, finally the correlation algorithm is used to estimate the channel. Simulation results show that compared with traditional compressed sensing channel estimation method, the pilot transmission power of the modified algorithm is lower and the estimation performance is better at low SNR.