  The use of large-scale antenna systems in future commercial wireless
communications is an emerging technology that uses an excess of transmit
antennas to realize high spectral efficiency. Achieving potential gains with
large-scale antenna arrays in practice hinges on sufficient channel estimation
accuracy. Much prior work focuses on TDD based networks, relying on reciprocity
between the uplink and downlink channels. However, most currently deployed
commercial wireless systems are FDD based, making it difficult to exploit
channel reciprocity. In massive MIMO FDD systems, the problem of channel
estimation becomes even more challenging due to the attendant substantial
training resources and feedback requirements which scale with the number of
antennas. In this paper, we consider the problem of training sequence design
that employs a set of training signals and its mapping to the training periods.
We focus on reduced-dimension training sequence designs, along with transmit
precoder designs, aimed at reducing both hardware complexity and power
consumption. The resulting designs are extended to hybrid analog-digital
beamforming systems, which employ a limited number of active RF chains for
transmit precoding, by applying the Toeplitz distribution theorem to
large-scale linear antenna systems. A practical guideline for training sequence
parameter selection is presented along with performance analysis.
