MIMO Two-Way Relaying: A Comparison of Beamforming and Antenna Selection

We propose and analyze two MIMO protocols with analog network coding (ANC) in two-way amplify-and-forward (AF) relaying where multi-antenna nodes communicate via a single antenna relay. Specifically, we present a new framework for the comparative analysis of beamforming and antenna selection in two-way relaying with non-identical Rayleigh fading between the hops. To facilitate the comparison, we derive new closed-form expressions for the exact and asymptotic sum symbol error rate (SSER). We show that beamforming and antenna selection offer the same diversity order of min{NA, NB}, where NA and NB are the number of antennas at the two nodes. We proceed to characterize the fundamental difference between the two protocols in terms of their array gains. A pivotal conclusion is reached that when either of the two nodes is equipped with a single antenna, antenna selection provides identical performance to beamforming at medium and high signal-to-noise ratios without the added hardware and signaling overhead.