  We propose a novel algorithm to design user load-achieving pilot sequences
that mitigate pilot contamination in multi-cell massive multiple-input
multiple-output (MIMO) networks. To this end, we first derive expressions for
the user load and the load region of the network considering both small-scale
and large-scale propagation effects. We then develop the pilot sequence
algorithm for multi-cell massive MIMO networks as per the rules of generalized
Welch bound equality design. Notably, we find that our algorithm and the
corresponding downlink power allocation ensure that the user load is achieved
when the signal-to-interference-plus-noise ratio (SINR) requirements for the
users lie within the load region. Furthermore, we demonstrate the performance
advantage of our proposed design relative to the existing designs, in terms of
a larger load region and a higher maximum permitted SINR. Finally, we show that
our proposed design can satisfy the pre-defined SINR requirements for users
with a finite number of antennas at the base station (BS), while the existing
designs cannot satisfy the same requirements even with an infinite number of
antennas at the BS.
