  We propose a novel pilot sequence design to mitigate pilot contamination in
multi-cell multiuser massive multiple-input multiple-output networks. Our
proposed design generates pilot sequences in the multi-cell network and devises
power allocation at base stations (BSs) for downlink transmission. The pilot
sequences together with the power allocation ensure that the user capacity of
the network is achieved and the pre-defined signal-to-interference-plus-noise
ratio (SINR) requirements of all users are met. To realize our design, we first
derive new closed-form expressions for the user capacity and the user capacity
region. Built upon these expressions, we then develop a new algorithm to obtain
the required pilot sequences and power allocation. We further determine the
minimum number of antennas required at BSs to achieve certain SINR requirements
of all users. Numerical results are presented to corroborate our analysis and
to examine the impact of key parameters, such as the pilot sequence length and
the total number of users, on the network performance. A pivotal conclusion is
reached that our design achieves a larger user capacity region than the
existing designs and needs less antennas at the BS to fulfill the pre-defined
SINR requirements of all users in the network than the existing designs.
