|We consider two-way amplify-and-forward relaying in a multichannel system with two
end nodes and a single relay, using a two-slot multi-access broadcast (MABC) as well as
time-division broadcast (TDBC) relaying strategies. We investigate the problem of joint
subchannel pairing and power allocation to maximize the achievable sum-rate in the network,
under an individual power budget at each node. To solve this challenging joint optimization
problem, an iterative approach is proposed to decompose the problem into pairing
optimization and joint power allocation optimization, and solve them iteratively.
For given power allocation, we first consider the problem of subchannel pairing at the
relay to maximize the achievable sum rate in TDBC-based network. Unlike in the one-way
relaying case, our result shows that there exists no explicit SNR-based subchannel pairing
strategy that is optimal for sum-rate maximization for two-way relaying.
Nonetheless, for TDBC-based two way relaying, we formulate the pairing optimization
as an axial 3-D assignment problem which is NP-hard, and propose an iterative optimization
method to solve it with complexity O(N3). Based on SNR over each subchannel, we
also propose sorting-based algorithms for scenarios with and without direct link, with a low
complexity of O(N logN).
For the joint power allocation at the relay and the two end nodes, we propose another
iterative optimization procedure to optimize the power at the two end nodes and at the relay
iteratively. By using different forms of optimization parameters, the sum-rate maximization
problem turns out to be convex and the optimal solutions can be obtained for each
The simulation first demonstrates the proposed sorting-based pairing algorithm offers
the performance very close to the iterative optimization method. Then, shows the gain of
joint optimization approach over other pairing-only or power-allocation-only optimization