  In this paper, the pilot signal design for massive MIMO systems to maximize
the training-based received signal-to-noise ratio (SNR) is considered under two
channel models: block Gauss-Markov and block independent and identically
distributed (i.i.d.) channel models. First, it is shown that under the block
Gauss-Markov channel model, the optimal pilot design problem reduces to a
semi-definite programming (SDP) problem, which can be solved numerically by a
standard convex optimization tool. Second, under the block i.i.d. channel
model, an optimal solution is obtained in closed form. Numerical results show
that the proposed method yields noticeably better performance than other
existing pilot design methods in terms of received SNR.
