  We propose a downlink beamforming scheme that combines spatial division and
orthogonal space-time block coding (OSTBC) in multi-user massive MIMO systems.
The beamformer is divided into two parts: a pre-beamforming matrix to separate
the users into different beams with no interference between each other, which
is designed based on the low rank covariance matrix of the downlink channel,
and a linear precoding matrix using partial or even no channel state
information (CSI) concatenated by an OSTBC. To construct the pre-beamforming
matrix, a simple method that selects columns from DFT matrix is presented. To
design the linear precoding matrix with partial CSI of the effective channel
after the pre-beamforming, we solve an optimization problem to minimize the
pairwise error probability (PEP) of the users under an individual power or sum
power constraint, respectively. For the individual power constraint, a
semi-definite relaxing (SDR) method with a sufficient condition achieving the
globally optimal solution is proposed to provide a performance benchmark. In
addition, an efficient iterative successive convex approximation (SCA) method
is provided to achieve a suboptimal solution. Furthermore, closed form
solutions are derived under some special cases. For the sum power constraint,
we consider two different designs, i.e., minimizing the average PEP and
minimizing the maximum PEP of all users. We find that both non-convex problems
have a similar structure, and proposed a unified SCA-Alternating Direction
Method of Multipliers (ADMM) algorithm to handle them. The SCA-ADMM method can
be implemented in a parallel manner, and thus is with great efficiency.
Simulation results show the efficiency of our proposed JSDD scheme and the
optimization method.
