  Massive MIMO has been regarded as a key enabling technique for 5G and beyond
networks. Nevertheless, its performance is limited by the large overhead needed
to obtain the high-dimensional channel information. To reduce the huge training
overhead associated with conventional pilot-aided designs, we propose a novel
blind data detection method by leveraging the channel sparsity and data
concentration properties. Specifically, we propose a novel $\ell_3$-norm-based
formulation to recover the data without channel estimation. We prove that the
global optimal solution to the proposed formulation can be made arbitrarily
close to the transmitted data up to a phase-permutation ambiguity. We then
propose an efficient parameter-free algorithm to solve the $\ell_3$-norm
problem and resolve the phase permutation ambiguity. We also derive the
convergence rate in terms of key system parameters such as the number of
transmitters and receivers, the channel noise power, and the channel sparsity
level. Numerical experiments will show that the proposed scheme has superior
performance with low computational complexity.
