Cloud radio access network (C-RAN) is an evolved network architecture for future mobile communication systems. It aims to provide higher spectral efficiency, lower energy consumption and reduced cost of operations and maintenance for the network, which will enable the operators to not only satisfy growing user demands, but provide new services and applications. However, the huge load on the fronthaul network which connects the baseband unit (BBU) and a large number of remote radio heads (RRHs) is a significant challenge. To improve the fronthaul performance, a data compression and recovery scheme based on compressive sensing is proposed in this thesis. First, the theory of compressive sensing is studied, including the essential principles, standard compressive sensing model, potential measurement matrices, etc. Several popular recovery algorithms in compressive sensing are demonstrated in detail. Secondly, a compression and recovery scheme is proposed for the uplink of a cell-free C-RAN system. In the proposed scheme, compressive sensing is applied by exploiting the sparsity of user data. In particular, the multi-access fading in this system is incorporated into the formulation of the compressive sensing model. The aggregated measurement matrix which contains both the channel matrix and the fronthaul compression matrix is shown to satisfy the restricted isometry property (RIP) condition. Furthermore, two different recovery algorithms, basis pursuit denoising (BPDN) and sparsity adaptive matching pursuit (SAMP), are used respectively for estimating the sparse signals. The major advantage is that they do not require the sparsity of user data as a prior information during the process of signal recovery. It allows easy applications in many practical scenarios where the number of non-zero elements of the signals is not available. The simulation results show that the proposed scheme can efficiently alleviate the heavy burden on the fronthaul network, and meanwhile provide stable signal recovery for this system
