Rate splitting multiple access (RSMA) and reconfigurable intelligent surface (RIS) are two prospective technologies for improving the spectral and energy efficiency in future wireless communication systems. In this work, we investigate a rate splitting (RS) technique for an RIS-aided system in the presence of only statistical channel knowledge. We propose an algorithm with a quasi closed-form solution based only on the second-order channel statistics, which reduces the design complexity of the system as it does not require estimation of the channel state information (CSI) and optimisation of the precoding filters and phase shifts of the RIS in every channel coherence interval.

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.