  We address the design of pilot sequences for channel estimation in the
context of multiple-user Massive MIMO; considering the presence of channel
correlation, and assuming that the statistics are known, we seek to exploit the
spatial correlation of the channels to minimize the length of the pilot
sequences, and specifically the fact that the users can be separated either
through their spatial signature (low-rank channel covariance matrices), or
through the use of different training sequences. We introduce an algorithm to
design short training sequences for a given set of user covariance matrices.
The obtained pilot sequences are in general non-orthogonal, however they ensure
that the channel estimation error variance is uniformly upper-bounded by a
chosen constant over all channel dimensions. We show through simulations using
a realistic scenario based on the one-ring channel model that the proposed
technique can yield pilot sequences of length significantly smaller than the
number of users in the system.
