  We investigate the coordinated multi-point noncoherent joint transmission
(JT) in dense small cell networks. The goal is to design beamforming vectors
for macro cell and small cell base stations (BSs) such that the weighted sum
rate of the system is maximized, subject to a total transmit power at
individual BSs. The optimization problem is inherently nonconvex and
intractable, making it difficult to explore the full potential performance of
the scheme. To this end, we first propose an algorithm to find a globally
optimal solution based on the generic monotonic branch reduce and bound
optimization framework. Then, for a more computationally efficient method, we
adopt the inner approximation (InAp) technique to efficiently derive a locally
optimal solution, which is numerically shown to achieve near-optimal
performance. In addition, for decentralized networks such as those comprising
of multi-access edge computing servers, we develop an algorithm based on the
alternating direction method of multipliers, which distributively implements
the InAp-based solution. Our main conclusion is that the noncoherent JT is a
promising transmission scheme for dense small cell networks, since it can
exploit the densitification gain, outperforms the coordinated beamforming, and
is amenable to distributed implementation.
