Beamforming Design for Full-Duplex Two-Way Amplify-and-Forward MIMO Relay

Abstract

We consider the full-duplex (FD) two-way amplify-and-forward relay system with imperfect cancelation of loopback self-interference (SI) and investigate joint design of relay and receive beamforming for minimizing the mean square error under a relay transmit power constraint. Due to loopback channel estimation error and limitation of analog-to-digital converter, the loopback SI cannot be completely canceled. Multiple antennas at the relay can help loopback SI suppression but beamforming is required to balance between the residual SI suppression and the desired signal transmission. Moreover, the relay beamforming matrix should be updated every time slot because the residual SI in the previous time slot is amplified by the current beamforming matrix and added to the received signals from the two sources in the current time slot. We derive the optimally balanced relay beamforming and receive beamforming matrices in closed form based on minimum mean square error, taking into account the propagation of the residual loopback SI from the first to the current time slot. We also propose beamforming design using only the channels of the m latest time slots, not from the first time slot. Based on our numerical results, we also identify when FD is beneficial and propose selection between FD and half-duplex according to signal-to-noise ratio and interference-to-noise ratio.

Joint Source-Relay Optimization for MIMO Full-Duplex Bidirectional Wireless Sensor Networks with SWIPT

“…Due to this characteristic, half of the spectrum resources are theoretically wasted. Recent advances suggest that the FD mode enables the concurrent transmission and reception of user signals over the same frequency band for which it can provide nearly double the improvement in spectral efficiency than HD [24]. Therefore, much interest has been turned to incorporating the networks into the FD [25,26,27,28,29,30,31,32].…”

Rate Balancing in Full-Duplex MIMO Two-Way Relay Networks

“…In this appendix, details of finding the upper and lower bounds of j is discussed. As mentioned earlier, j is defined by (10). The numerators of the fractional terms of (10) are power values; thus, they are non-negative values.…”

Low complexity robust recursive beamforming for two‐way full duplex relay network

“…Not only does the beamforming method suppresses residual interference, but it is also required to balance between desired signal enhancement and residual interference mitigation at FD relay networks. The TWFD AF relay system with the imperfect cancellation of loopback SI was considered in [22] and joint design of relay and receive beamforming for minimising the mean square error (MSE) under the relay transmit power constraint was investigated. The optimal beamforming matrix was analytically investigated, which was updated in each time slot as a function of all channel matrices from the first time slot to the current time slot [22].…”

“…The TWFD AF relay system with the imperfect cancellation of loopback SI was considered in [22] and joint design of relay and receive beamforming for minimising the mean square error (MSE) under the relay transmit power constraint was investigated. The optimal beamforming matrix was analytically investigated, which was updated in each time slot as a function of all channel matrices from the first time slot to the current time slot [22]. Thus, the CSI or the channel matrices of all previous time slots are required for computing the current time slot beamforming matrices.…”

“…This requires an infinite memory size so the computational complexity and memory usage grow to infinity as time lapses. In [22], a simplified method that requires just the m latest time slot channel matrices was proposed. However, using just the m latest time slots declines the performance of the system.…”