Massive multiple-input multiple-output (MIMO) is a promising technology that provides high system capacity, and with excellent performance in energy efficiency and system robustness. However, pilot contamination restricts the system performance due to the limited length of orthogonal training sequences. In this paper, we propose optimization of non-orthogonal pilots for uplink training. The Grassmannian line packing method is applied in the design of pilots that leads to maximum chordal distances between training sequences which reduces pilot contamination. The analytical expression of the user equipments (UEs) signal-to-intereference-plus-noise ratio (SINR) in multi-cell massive MIMO system and the analytical SINR of UEs in Grassmannian manifold are presented. Simulation results show shown that non-orthogonal pilot sequences with the Grassmainn line packing method yield significant improvements of the system capacity.
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