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This thesis introduces a new algorithmic solution to the massive unsourced random access (mURA) problem. The proposed uncoupled compressed sensing (UCS)-based scheme relies on slotted transmissions and takes advantage of the inherent coupling provided by the users’ spatial signatures in the form of channel correlations across slots to completely eliminate the need for concatenated coding. As opposed to all existing methods, the proposed solution combines the steps of activity detection, channel estimation, and data decoding into a unified mURA framework. It capitalizes on the bilinear generalized vector approximate message passing (BiG-VAMP) algorithm, tailored to fit the inherent constraints of mURA. To account for the quantization effects, we incorporate an output denoising module into the algorithm. Furthermore, this work presents a novel approach for handling a coarse quantized massive MIMO system by integrating activity detection, channel estimation, and data decoding within a unified framework. The proposed quantized mURA algorithm is evaluated using low-precision analog-to-digital converters (ADCs). Additionally, a state evolution algorithm is developed to validate the performance of both the proposed unquantized and quantized algorithms, demonstrating their consistency in the asymptotic regime. Furthermore, exhaustive computer simulations reveal that the proposed scheme shows promising results even in challenging scenarios.