With the reuse of identical training sequences by users in different cells, massive MIMO is severely affected by pilot contamination due to residual error in channel estimation. In this paper, we consider the traditional structure of the training phase, where orthogonal pilot sequences are reused, and analyze a recently proposed group- blind detector in the uplink of an interference- limited network. We derive the asymptotic SINR gain achievable by the group-blind detector compared to conventional schemes, and find that it depends on the number of cells and channel gains only. We show that group-blind detection can significantly improve the asymptotic achievable rate. We propose a simple scheme, that we call method of silences, to estimate the aggregate instantaneous out-of-cell channel covariance that is required to implement the group-blind detector. Numerical results confirm our analysis in scenarios of practical interest, and show cases where a scheme as simple as the method of silences allows to achieve a large fraction of the promised SINR gain.