Research on compressed sensing and its applications in wireless communications

Compressed Sensing (CS) suggests that it is possible to enable sub-Nyquist sampling, by merging sampling and compression into one single step. Hence, CS will lead to a revolution in the sampling area. Moreover, CS will have great impacts on information theory, coding and wireless communications. In this thesis, we will study the basic sampling problem of analog sparse signals and investigate the applications of CS into Cognitive Radio Networks (CRNs) and Wireless Sensor Networks (WSNs). The main contributions of this thesis are summarized as follows. (1) Application of discrete CS into WSNs. Based on discrete CS and network coding, we significantly improve the energy efficiency of WSN by simultaneously reducing the number of required transmissions and receptions. (2) Research on analog CS. Based on the non-modulated Slepian basis, we simultaneously improve the recovery performance and reduce the recovery computation complexity of analog CS. Based on the structure of the random cyclic orthogonal matrix, we reduce the hardware complexity of analog CS by utilizing the cyclic shifts of the Zadoff-Chu sequence. (3) Application of analog CS into CRNs. By introducing analog CS and multiantenna technology, we improve the detection performance of wideband spectrum sensing (WSS) in CRNs at the sub-Nyquist sampling rate. (4) Research on denoising CS recovery algorithm. To improve the CS recovery performance in noisy environments, we propose a regularized subspace pursuit (RSP) denoising CS recovery algorithm, which has the highest recovery performance in comparison with existing CS recovery algorithms. So far, the application of CS in channel estimation for LTE-A systems has been discussed by 3GPP. It is believed that, in the future, more and more new problems faced by wireless communications will be resolved with the help of CS.