Compressive sensing (CS) can efficiently recover sparse signals, i.e., signals that are sparse in some domains. There are many sparse signals in wireless communication and their sparsities may be exploited to reduce the use of sampling resources. However, traditional CS does not provide guidelines on how much sampling resource could be practically reduced. Further, some sparsities cannot be modeled by a simple linear measurement form as in the traditional CS model. In this thesis, we explore novel ways of modeling and exploiting some sparsities in wireless communication to stably recover the signal while saving the sampling resources. To find the minimum required sampling resources for the recovery of sparse signals, we propose a closed-loop control algorithm to autonomously ada...[ Read more ]

Compressive sensing (CS) can efficiently recover sparse signals, i.e., signals that are sparse in some domains. There are many sparse signals in wireless communication and their sparsities may be exploited to reduce the use of sampling resources. However, traditional CS does not provide guidelines on how much sampling resource could be practically reduced. Further, some sparsities cannot be modeled by a simple linear measurement form as in the traditional CS model. In this thesis, we explore novel ways of modeling and exploiting some sparsities in wireless communication to stably recover the signal while saving the sampling resources. To find the minimum required sampling resources for the recovery of sparse signals, we propose a closed-loop control algorithm to autonomously adapt to the minimum sampling resource to maintain a certain quality of service. Then we model the joint sparsity of multi-user channel in the problem of multi-user channel estimation in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems and apply this algorithm. To recover a sparse signal when it is non-linearly and compressively sampled, we propose a polynomial gradient pursuit algorithm and apply it to the problem of data recovery with a sub-Nyquist and non-linear receiver in massive carrier aggregation systems. To recover a sparse transmitted signal based on the compressively received signal, we propose a sparse maximum likelihood estimation framework to jointly recover the channel and the transmitted signal. To find the accurate location of a user in millimeter wave systems with sparse channels, we propose a sparse channel model that incorporates adjustable grids of spatial paths’ angles and multipath delays. Then we formulate a sparse Bayesian learning problem to estimate the channel and the location. For each of the proposed algorithm, we provide theorems to guarantee the performance, and extensive simulation results to verify the advantages over baselines.