Abstract—Multiple-InputMultiple-Output (MIMO) full-duplex
relaying (FDR) has been considered as an efficient technique
to provide coverage to users where their direct links from the
base station (BS) are too weak for reliable signal reception.
However, when multiple MIMO full-duplex relays are deployed
in a network, the signal reception quality relies on the effective
suppression of multiple types of interference. In this paper,
the distributed beamforming is studied for the MIMO FDR
network, by formulating a power minimization problem with
a non-strict convex objective function (total transmit power of
both the BS and all the relays in the network) under individual user rate constraints. We come up with two iterative distributed
beamforming algorithms, Algorithm 1 for relays equipped with
single receive antenna and Algorithm 2 with multiple receive
antennas. The former can yield a global optimal solution of the
power minimization problem, while the latter can only yield
a local optimal solution due to conservative successive convex
approximations performed at each iteration, and a rigorous
analysis on the upper bounds of step sizes is also proposed
to guarantee their convergence. The proposed two algorithms
only require local information exchange between relays, and
hence are scalable for different network sizes and topologies.
An “early termination” strategy in the operation of the proposed
two algorithms is also presented to acquire an acceptable transmit
power solution with less computation time consumption, and thus
suitable for realistic applications. Finally, some simulation results
are provided to demonstrate that the proposed two algorithms
perform well and significantly better than the existing state-ofthe-art scheme reported in [22].