  This paper investigates relaying schemes in an amplify-and-forward
multiple-input multiple-output relay network, where an energy-constrained relay
harvests wireless power from the source information flow and can be further
aided by an energy flow (EF) in the form of a wireless power transfer at the
destination. However, the joint optimization of the relay matrix and the source
precoder for the energy-flow-assisted (EFA) and the non-EFA (NEFA) schemes is
intractable. The original rate maximization problem is transformed into an
equivalent weighted mean square error minimization problem and optimized
iteratively, where the global optimum of the nonconvex source precoder
subproblem is achieved by semidefinite relaxation and rank reduction. The
iterative algorithm finally converges. Then, the simplified EFA and NEFA
schemes are proposed based on channel diagonalization, such that the matrices
optimizations can be simplified to power optimizations. Closed-form solutions
can be achieved. Simulation results reveal that the EFA schemes can outperform
the NEFA schemes. Additionally, deploying more antennas at the relay increases
the dimension of the signal space at the relay. Exploiting the additional
dimension, the EF leakage in the information detecting block can be nearly
separated from the information signal, such that the EF leakage can be
amplified with a small coefficient.
