  This paper considers a multi-cell multiple antenna system with precoding used
at the base stations for downlink transmission. For precoding at the base
stations, channel state information (CSI) is essential at the base stations. A
popular technique for obtaining this CSI in time division duplex (TDD) systems
is uplink training by utilizing the reciprocity of the wireless medium. This
paper mathematically characterizes the impact that uplink training has on the
performance of such multi-cell multiple antenna systems. When non-orthogonal
training sequences are used for uplink training, the paper shows that the
precoding matrix used by the base station in one cell becomes corrupted by the
channel between that base station and the users in other cells in an
undesirable manner. This paper analyzes this fundamental problem of pilot
contamination in multi-cell systems. Furthermore, it develops a new multi-cell
MMSE-based precoding method that mitigate this problem. In addition to being a
linear precoding method, this precoding method has a simple closed-form
expression that results from an intuitive optimization problem formulation.
Numerical results show significant performance gains compared to certain
popular single-cell precoding methods.
