Filter-and-Forward Distributed Beamforming for Two-Way Relay Networks With Frequency Selective Channels

In filter-and-forward (FF) based two-way relay networks, each transmission for data exchange between two transceivers consists of only two time slots (or phases). In the first time slot, both transceivers transmit their data simultaneously to the relays. The received signal of each relay is filtered using a finite impulse response (FIR) filter to compensate for the frequency selectivity of the channels, and then, the output of the filter is forwarded to both transceivers in the second time-slot. In this paper, new approaches to distributed cooperative beamforming for such two-way relay networks with frequency selective channels are proposed. The first two distributed beamforming approaches assume that the transmitted powers of the transceivers are given and fixed. The first beamformer is based on minimizing the total transmitted power of the relays subject to two constraints on the signal-to-inter-symbol-interference-plus-noise ratio (SINR) at both transceivers. The second beamformer is designed through maximization of the lowest SINR of the two transceivers while keeping the relay transmitted power under certain levels. We show that these two problems can be cast as second-order convex cone programming problems. The other two distributed beamforming methods aim to calculate the transmitted powers of the transceivers as well as the coefficients of the relay filters using two different beamforming techniques. The first technique is based on the minimization of the total transmitted power of the transceivers and the relays subject to the SINR requirements for both transceivers, and the second method maximizes the lowest SINR of the two transceivers subject to a constraint on the total transmitted power. Simulation results demonstrate that using an FF relaying strategy can significantly improve the underlying performance measure as compared to the traditional amplify-and-forward relaying approach.