Optimal Beamforming for Two-Way Multi-Antenna Relay Channel with Analogue Network Coding (0808.0075v4)

Abstract: This paper studies the wireless two-way relay channel (TWRC), where two source nodes, S1 and S2, exchange information through an assisting relay node, R. It is assumed that R receives the sum signal from S1 and S2 in one time-slot, and then amplifies and forwards the received signal to both S1 and S2 in the next time-slot. By applying the principle of analogue network (ANC), each of S1 and S2 cancels the so-called "self-interference" in the received signal from R and then decodes the desired message. Assuming that S1 and S2 are each equipped with a single antenna and R with multi-antennas, this paper analyzes the capacity region of an ANC-based TWRC with linear processing (beamforming) at R. The capacity region contains all the achievable bidirectional rate-pairs of S1 and S2 under the given transmit power constraints at S1, S2, and R. We present the optimal relay beamforming structure as well as an efficient algorithm to compute the optimal beamforming matrix based on convex optimization techniques. Low-complexity suboptimal relay beamforming schemes are also presented, and their achievable rates are compared against the capacity with the optimal scheme.

• The paper introduces an optimal relay beamforming strategy that converts capacity characterization into a relay power minimization problem using convex optimization techniques.
• The study shows that the maximal-ratio reception and transmission (MRR-MRT) scheme nearly achieves capacity bounds, maintaining a negligible rate gap across varying SNRs and channel conditions.
• Analogue network coding is employed to enable efficient bidirectional communication, significantly reducing the required time slots for data exchange between the source nodes.

Optimal Beamforming for Two-Way Multi-Antenna Relay Channel with Analogue Network Coding

This paper examines a two-way relay channel (TWRC) model in wireless networks, focusing on the application of analogue network coding (ANC) combined with optimal beamforming at a multi-antenna relay. The paper addresses a scenario involving two source nodes, S1 and S2, each equipped with a single antenna, and a relay node, R, equipped with multiple antennas. The ANC protocol allows for efficient bidirectional communication, enhancing the overall throughput by reducing the necessary time slots for data exchange.

The key contribution of this research is the derivation of the capacity region of the ANC-based TWRC, which is characterized by bidirectional rate pairs achievable under specific transmit power constraints. The authors introduce an optimal relay beamforming strategy, demonstrating a significant reduction in the complexity of designing the beamforming matrix, from M squared to 4 complex values when M exceeds two. This is achieved using convex optimization techniques, converting the capacity characterization challenge into a relay power minimization problem with certain SNR constraints.

Numerical Results and Strong Claims

Through rigorous simulations, the paper yields results that underscore the effectiveness of the proposed beamforming structure. Notably, when channel coefficients exhibit low correlation, the maximal-ratio reception and transmission (MRR-MRT) scheme closely approaches optimal performance, with minimal rate loss observed across different signal-to-noise ratios (SNRs). The zero-forcing reception and transmission (ZFR-ZFT) scheme, although advantageous in scenarios of minimal channel correlation, shows performance degradation as correlation increases, where ANC's self-interference cancellation proves beneficial.

The MRR-MRT scheme stands out for achieving rates close to the capacity bounds under various SNRs and channel conditions, suggesting its practical viability. Theoretical analyses confirm that the asymptotic behavior of these schemes aligns with the capacity limits, with MRR-MRT maintaining a small constant rate gap at high SNRs compared to optimal solutions.

Practical and Theoretical Implications

Practically, this research contributes to the design of efficient relay systems in future wireless communication networks, where spectrum scarcity drives the need for advanced coding and signal processing techniques. The adoption of ANC and beamforming can significantly improve spectral efficiency, particularly in decentralized networks and multihop scenarios.

Theoretically, the results extend the understanding of relay network capacity, particularly in contexts where simultaneous bidirectional transmission is necessary. It offers insights into power allocation and processing techniques required to optimize network throughput.

Future Developments and Speculation

Future work could involve extending these findings to multi-antenna sources or multiple relay nodes, exploring the integration of ANC within larger network topologies. Additionally, a comparative analysis involving decode-and-forward (DF) strategies against ANC applications would provide a comprehensive view of the trade-offs involved. As AI continues to evolve, intelligent network systems may leverage such frameworks to adaptively optimize relay operations and improve communication reliability and efficiency.

Overall, this research offers a robust framework for exploring advanced relay strategies, with profound implications for both academic research and practical applications in next-generation wireless networks.