Downlink User Capacity of Massive MIMO Under Pilot Contamination

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 users whose SINR targets can be achieved, 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. This capacity expression characterizes a region within which a set of SINR requirements can be jointly satisfied. The size of this region is fundamentally limited by the pilot sequence length. Furthermore, the scheme for achieving the user capacity, i.e., the uplink pilot training sequences and downlink power allocation, has been identified. Specifically, the generalized Welch bound equality sequences are exploited and it is shown that the power allocated to each user should be proportional to its SINR target. With this capacity-achieving scheme, the SINR requirement of each user can be satisfied and energy-efficient transmission is achieved in the large-antenna-size (LAS) regime. The comparison with two non-capacity-achieving schemes highlights the superiority of our proposed scheme in terms of achieving higher user capacity. Furthermore, for the practical scenario with a finite number of antennas, the actual antenna size required to achieve a significant percentage of the asymptotic performance has been analytically quantified.