Physical Layer Network Coding for Mobile Communications
Final Report Abstract
In this project, we have investigated several equalization approaches which can be employed in two-way relaying transmission systems using physical layer network coding (PNC). PNC with single-carrier transmission operating in flat fading environments has been studied extensively before, yet only a few approaches for tackling the problem of extending PNC to environments causing frequency-selective fading and synchronization imperfections could be found in the literature. In the first part of the project, we have developed three trellis-based equalization schemes that can be used at the relay node to retrieve the data to be relayed in PNC in the presence of intersymbol interference (ISI). While two of the schemes perform (close to) optimum, they suffer from a high computational complexity and can be used only for channels with very short impulse responses. The third scheme is less complex but exhibits a performance far away from the optimum. In order to enable low-complexity linear equalization (LE) and decision-feedback equalization (DFE), respectively, at the relay node, transmit filtering at the source nodes is necessary for creating identical overall source-to-relay channel impulse responses. We have derived transmit filters for both equalization schemes according to the zero-forcing (ZF) and minimum mean-squared error (MMSE) criterion, respectively, maximizing the signal-to-noise ratio (SNR) after equalization. In addition, suboptimum trellis-based equalization in form of delayed decision-feedback sequence estimation (DDFSE) at the relay node was studied. This scheme also mandates the use of transmit filters at the source nodes, however, it is not feasible to implement the optimal filters according to the matched filter bound criterion. As a consequence, the optimal DFE transmit filters are used instead, which is a valid approach since DFE can be seen as a complexity reduced DDFSE scheme with only a single trellis state. Furthermore, we have derived the optimum filters for Tomlinson-Harashima precoding (THP) used in the uplink. THP exhibits almost an identical performance compared to optimal ZF-DFE at the relay node but can be combined with channel coding in a straightforward manner, unlike DFE. However, the optimal filters are different to those for ZF-DFE, in contrast to classical single-link communications. The designed uplink THP scheme has been complemented by a novel downlink compromise precoding approach combined with LE at the destination nodes which is able to achieve some gains over pure LE. Since single-carrier frequency-division multiple access (SC-FDMA) modulation has already shown its viability in wireless communications, we have studied the adoption of SC-FDMA for PNC transmission. SC-FDMA may be viewed as a single-carrier modulation format but shows some important differences to traditional single-carrier schemes. In particular, when an SC-FDMA transmission is employed, it has to be taken into account that the conventional convolution operation related to the channel effects becomes circular. Therefore, our LE and DFE based approaches have been modified in order to adjust them to the peculiarities of SC-FDMA. All of the presented optimal filtering approaches provide a considerable performance gain compared to simple benchmark schemes. Considering also the low computational complexity of the proposed schemes, they are candidates for real-world two-way relaying applications where single-carrier transmission is used, e.g. in 5G or sensor networks.
Publications
- “Maximum SNR Transmit Filtering for Linear Equalization in Physical Layer Network Coding”, in Proc. IEEE Global Communications Conference (GLOBECOM 2012) – Broadband Wireless Access Workshop (BWA), Anaheim, CA, USA, Dec. 2012
A. Schmidt, W. Gerstacker, and R. Schober
- “Trellis-based Equalization Schemes for Physical Layer Network Coding”, in Proc. IEEE International Conference on Communications (ICC), Ottawa, Canada, June 2012
A. Schmidt and W. Gerstacker
- “Maximum SNR Transmit Filtering for Decision-Feedback Equalization in Physical Layer Network Coding”, in Proc. 9th International ITG Conference on Systems, Communications and Coding (SCC 2013), Munich, Germany, Jan. 2013
A. Schmidt, W. Gerstacker, and R. Schober
- “Optimal Tomlinson- Harashima Precoding for Physical Layer Network Coding”, in Proc. IEEE WCNC 2013 – Workshop New Advances for Physical Layer Network Coding, Shanghai, P.R. China, Apr. 2013
A. Schmidt, R. Schober, and W. Gerstacker
- “Single-Carrier Frequency- Division Multiple Access Transmission with Physical Layer Network Coding over ISI Channels”, in Proc. European Wireless (EW), Budapest, Hungary, May 2015
A. Schmidt, R. Schober, and W. Gerstacker
- “Nonlinear Equalization Approaches for Physical Layer Network Coding”, submitted to IEEE Transactions on Wireless Communications, Volume: 16 , Issue: 2 , Feb. 2017
A. Schmidt, R. Schober, and W. Gerstacker
(See online at https://doi.org/10.1109/TWC.2016.2630694)
