Joint Relay Selection and Analog Network Coding Using Differential Modulation in Two-Way Relay Channels

Abstract

In this paper, we consider a general bidirectional relay network with two sources and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> relays when neither the source nodes nor the relays know the channel-state information (CSI). A joint relay-selection and analog-network coding using differential modulation (RS-ANC-DM) is proposed. In the proposed scheme, the two sources employ differential modulations and transmit the differential modulated symbols to all relays at the same time. The signal received at the relay is a superposition of two transmitted symbols, which we call analog network-coded symbols. Then, a single relay that has minimum-sum symbol error rate (SER) is selected out of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> relays to forward the ANC signals to both sources. To facilitate the selection process, in this paper, we also propose a simple suboptimal Min-Max criterion for relay selection, where a single relay that minimizes the maximum SER of two source nodes is selected. Simulation results show that the proposed Min-Max selection has almost the same performance as the optimal selection but is much simpler. The performance of the proposed RS-ANC-DM scheme is analyzed, and a simple asymptotic SER expression is derived. The analytical results are verified through simulations.