MULTI-GROUP MULTICAST BEAMFORMING FOR MULTI-USER TWO-WAY RELAYING Aditya Umbu Tana Amah 1 , Anja Klein 1 , Yuri C. B. Silva 2 , Andreas Fernekeß 1 1 Communications Engineering Lab, Technische Universit¨ at Darmstadt, Darmstadt, Germany {a.amah, a.klein, a.fernekess}@nt.tu-darmstadt.de 2 Wireless Telecommunications Research Group - GTEL, Federal University of Cear´ a, Fortaleza, Brazil yuri@gtel.ufc.br ABSTRACT In this work, we consider a multi-user two-way relaying pro- tocol. A multi-antenna relay station (RS) serves 2K nodes where K pairs of nodes would like to perform bidirectional communication. In the first phase, the 2K nodes transmit si- multaneously and the RS spatially separates and decodes all the 2K bit sequences. In the second phase, after perform- ing bit-wise XOR network coding for each bidirectional pair, which results in only K bit sequences, the RS sends all the K XOR-ed bit sequences simultaneously. At each node, hav- ing received its intended XOR-ed bit sequence, it cancels the self-interference by XOR-ing its received bit sequence with its transmitted one to obtain the bit sequence sent by its part- ner. Considering the second phase, as each node in a spe- cific pair expects the same XOR-ed bit sequence from the RS, while seeing other pairs’ XOR-ed bit sequences as in- terference, the RS has to separate the different pairs’ XOR- ed bit sequences spatially. Thus, in the second phase, multi- group multicast beamforming can be applied with the node pairs being the multicast group. With this new perspective on the second phase, we propose to apply multi-group mul- ticast beamforming algorithms which provide fairness to all pairs and have low computational complexity. We investi- gate several multi-group multicast beamforming algorithms, namely Zero Forcing (ZF), Multicast Aware ZF (MAZF) and SINR Balancing with Bisection Search (SINRB-Bisec), for the second phase transmission of the multi-user two-way re- laying. We consider also two different XOR network coding approaches, namely with and without zero padding (ZP). The overall two-phase sum rate analysis is given which shows that both MAZF and SINRB-Bisec have similar performance and outperform ZF. Nevertheless, MAZF has lower computational complexity compared to SINRB-Bisec. The work of Aditya U. T. Amah is supported by the ’Excellence Initia- tive’ of the German Federal and State Governments and the Graduate School of Computational Engineering, Technische Universit¨ at Darmstadt 1. INTRODUCTION In two-hop communication, a relay station (RS) assists the communication between a source node and a destination node. Due to the half-duplex constraint, two orthogonal resources are needed, one resource for the transmission from the source node to the RS and another one for the transmission from the RS to the destination node. This leads to a loss in capacity by a factor of 2 compared to single-hop communication [1, 2]. One way to mitigate this capacity loss is by allowing the RS to assist bidirectional communication between two nodes with the so-called two-way relaying protocol [2]. The com- munication in two-way relaying is performed in two phases [2]. In the first phase, the multiple access (MAC) phase, both nodes transmit at the same time to the RS. In the second phase, the broadcast (BC) phase, the RS forwards the super- imposed signal to both nodes. Since each node a priori knows its own transmitted signal, it can subtract it from the received signal to obtain the signal from the other node. At the RS, different types of signal processing can be per- formed. In Amplify and Forward (AF), the RS forwards the received signal after amplifying it [2–5]. In Decode and For- ward (DF), the RS decodes the information of both nodes and forwards the re-encoded information [2, 6, 7]. Two-way relaying with two multi-antenna nodes and a multi-antenna RS has been treated in [8, 9] for AF and in [10] for DF. DF two-way relaying has the advantage that the noise at the RS is not propagated to the receive nodes. Its perfor- mance depends on the coding which is used to re-encode the information in the second phase. In [10,11], for the DF multi- antenna two-way relaying case, it has been shown that for the re-encoding of the decoded information of both nodes, bit- wise XOR coding outperforms superposition coding. The aforementioned contributions considered a scenario where an RS assists two nodes (single pair) to perform bidi- rectional communication with each other. Recently, two-way relaying for multi-user scenarios has attracted more attention and has been considered in [12–14]. In [12], a multi-antenna RS assists a Base Station to perform bidirectional communi- cation with multiple nodes. A different multi-user scenario is treated in [13, 14] where two sets of nodes perform two- 2009 International ITG Workshop on Smart Antennas – WSA 2009, February 16–18, Berlin, Germany