  In Part II of this two-part paper, a sum-rate-maximizing power allocation
with minimum power consumption is found for multiple-input multiple-output
(MIMO) decode-and-forward (DF) two-way relaying (TWR) in a network optimization
scenario. In this scenario, the relay and the source nodes jointly optimize
their power allocation strategies to achieve network optimality. Unlike the
relay optimization scenario considered in part I which features low complexity
but does not achieve network optimality, the network-level optimal power
allocation can be achieved in the network optimization scenario at the cost of
higher complexity. The network optimization problem is considered in two cases
each with several subcases. It is shown that the considered problem, which is
originally nonconvex, can be transferred into different convex problems for all
but two subcases. For the remaining two subcases, one for each case, it is
proved that the optimal strategies for the source nodes and the relay must
satisfy certain properties. Based on these properties, an algorithm is proposed
for finding the optimal solution. The effect of asymmetry in the number of
antennas, power limits, and channel statistics is also considered. Such
asymmetry is shown to have a negative effect on both the achievable sum-rate
and the power allocation efficiency in MIMO DF TWR. Simulation results
demonstrate the performance of the proposed algorithm and the effect of
asymmetry in the system.
