  Asynchronous distributed hybrid beamformers (ADBF) are conceived for
minimizing the total transmit power subject to
signal-to-interference-plus-noise ratio (SINR) constraints at the users. Our
design requires only limited information exchange between the base stations
(BSs) of the mmWave multi-cell coordinated (MCC) networks considered. To begin
with, a semidefinite relaxation (SDR)-based fully-digital (FD) beamformer is
designed for a centralized MCC system. Subsequently, a Bayesian learning (BL)
technique is harnessed for decomposing the FD beamformer into its analog and
baseband components and construct a hybrid transmit precoder (TPC). However,
the centralized TPC design requires global channel state information (CSI),
hence it results in a high signaling overhead. An alternating direction based
method of multipliers (ADMM) technique is developed for a synchronous
distributed beamformer (SDBF) design, which relies only on limited information
exchange among the BSs, thus reducing the signaling overheads required by the
centralized TPC design procedure.
  However, the SDBF design is challenging, since it requires the updates from
the BSs to be strictly synchronized. As a remedy, an ADBF framework is
developed that mitigates the inter-cell interference (ICI) and also control the
asynchrony in the system.
  Furthermore, the above ADBF framework is also extended to the robust ADBF
(R-ADBF) algorithm that incorporates the CSI uncertainty into the design
procedure for minimizing the the worst-case transmit power. Our simulation
results illustrate both the enhanced performance and the improved convergence
properties of the ADMM-based ADBF and R-ADBF schemes.
