Network-Coded Cooperative Spatial Multiplexing in Two-Way Relay Channels

Abstract

In this paper, for a two-way relay channel comprising two multi-antenna transceivers and $L$ single-antenna potential relay nodes, we propose three network-coded cooperative spatial multiplexing (CSM) schemes that effectively overcome the rate loss incurred due to the half-duplex limitation of the transceivers and the relay nodes and achieve high spectral efficiency. In the following, these three schemes are referred to as time-division broadcast (TDBC)-CSM , incremental (I)-TDBC-CSM and multiple-access broadcast (MABC)-CSM . We investigate these schemes in terms of the outage probability, the average transmission rate, the asymptotic behavior, and the diversity-multiplexing tradeoff. The analysis of the paper shows that, first, the I-TDBC-CSM scheme achieves the full diversity of order $L\min (M_1,M_2)+M_1M_2$ , where $M_1$ and $M_2$ are the numbers of antennas employed by the two transceivers; second, the TDBC-CSM and MABC-CSM schemes achieve the diversity of order $L\min (M_1,M_2)$ , where this quantity is the maximum achievable diversity gain in the absence of the direct link between the transceivers; third, the TDBC-CSM and I-TDBC-CSM schemes effectively overcome the rate loss incurred due to the half-duplex limitation of the relay nodes; fourth, the MABC-CSM scheme not only overcomes the half-duplex limitation of the relay nodes but also mitigates the spectral efficiency loss incurred due to the half-duplex limitation of the transceivers; and fifth, if one or both of the transceivers are equipped with a massive antenna array, the asymptotic average rate of the CSM-based schemes scales linearly with the number of potential relay nodes, as opposed to the conventional relaying schemes, in which the average rate is not scalable with $L$ . We provide extensive simulation results to confirm the theoretical analysis of the paper. The simulation results show that for a given outage probability, the proposed schemes outperform the conventional relaying schemes in terms of the average transmission rate.