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This paper optimizes the pilot assignment and pilot transmit powers tomitigate pilot contamination in Massive MIMO (multiple-input multiple-output)systems. While prior works have treated pilot assignment as a combinatorialproblem, we achieve a more tractable problem formulation by directly optimizingthe pilot sequences. To this end, we compute a lower bound on the uplink (UL)spectral efficiency (SE), for Rayleigh fading channels with maximum ratio (MR)detection and arbitrary pilot sequences. We optimize the max-min SE withrespect to the pilot sequences and pilot powers, under power budgetconstraints. This becomes an NP-hard signomial problem, but we propose anefficient algorithm to obtain a local optimum with polynomial complexity.Numerical results manifest the near optimality of the proposed algorithm andshow significant gains over existing suboptimal algorithms.

Joint Pilot Sequence Design and Power Control for Max-Min Fairness in Uplink Massive MIMO