User capacity of pilot-contaminated TDD massive MIMO systems

Pilot contamination has been regarded as a main limiting factor of time division duplexing (TDD) massive multiple-input-multiple-output (Massive MIMO) systems, as it will make the signal-to-interference-plus-noise ratio (SINR) saturated. However, how pilot contamination will limit the user capacity of downlink Massive MIMO, i.e., the maximum number of admissible users, has not been addressed. This paper provides an explicit expression of the Massive MIMO user capacity in the pilot-contaminated regime where the number of users is larger than the pilot sequence length. Furthermore, the scheme for achieving the user capacity, i.e., the uplink pilot training sequence and downlink power allocation, has been identified. By using this capacity-achieving scheme, the SINR requirement of each user can be satisfied and energy-efficient transmission is feasible in the large-antenna-size (LAS) regime. Comparison with two non-capacity-achieving schemes highlights the superiority of our proposed scheme in terms of achieving higher user capacity.