  We consider a multi-cell multiple-input multiple-output (MIMO) coordinated
downlink transmission, also known as network MIMO, under per-antenna power
constraints. We investigate a simple multiuser zero-forcing (ZF) linear
precoding technique known as block diagonalization (BD) for network MIMO. The
optimal form of BD with per-antenna power constraints is proposed. It involves
a novel approach of optimizing the precoding matrices over the entire null
space of other users' transmissions.
  An iterative gradient descent method is derived by solving the dual of the
throughput maximization problem, which finds the optimal precoding matrices
globally and efficiently. The comprehensive simulations illustrate several
network MIMO coordination advantages when the optimal BD scheme is used. Its
achievable throughput is compared with the capacity region obtained through the
recently established duality concept under per-antenna power constraints.
