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In time division duplex (TDD) massive multiple-input multiple-output (MIMO) systems, pilot contamination seriously limits the improvement of spectral efficiency (SE). In order to provide good communication quality for every user, this paper devotes to enhance minimum spectral efficiency of the system. Firstly, a multi-cell multi-user system model is established to derive the objective function of Max-Min spectral efficiency. Through analysis of the mathematical expressions, we found that it is not a convex optimization problem for joint pilot allocation and power control, but a non-deterministic polynomial (NP) problem that is difficult to deal with. In order to solve the problem, a new algorithm is proposed to decompose the problem into two easy-to-handle sub-problems. We employ weight graph coloring (WGC) algorithm to deal with the sub-problem of pilot allocation, where uplink transmission power is fixed. The geometric programming (GP) approach is utilized to solve the sub-problem of power control, in which the large-scale fading factor is fixed. Then the computational complexity of the proposed algorithm is analyzed. Compared with the ideal optimal solution algorithm that requires exhaustive search, our algorithm has much less computational complexity. Finally, the simulation results demonstrate that the proposed algorithm significantly improves the minimum spectral efficiency, which is close to the ideal optimal solution.

Joint Pilot Allocation and Power Control to Enhance Max-Min Spectral Efficiency in TDD Massive MIMO Systems