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.
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