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We consider the problem of unsourced random access (U-RA), a grant-free uncoordinated form of random access, in a wireless channel with a massive MIMO base station equipped with a large number M of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the M-dimensional channel vector of each user remains constant over a coherence block containing L signal dimensions in time-frequency. In the considered setting, the number of potential users K _tot is much larger than L but at each time slot only K _a ≪ K _tot of them are active. Previous results, based on compressed sensing, require that K _a ≤ L, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and U-RA. In the context of activity detection it is known that such a limitation can be overcome when the number of base station antennas M is sufficiently large …