Differential modulation for two-way wireless communications: a perspective of differential network coding at the physical layer

This work considers two-way relay channels (TWRC), where two terminals transmit simultaneously to each other with the help of a relay node. For single antenna systems, we propose several new transmission schemes for both amplify-and-forward (AF) protocol and decode-and-forward (DF) protocol where the channel state information is not required. These new schemes are the counterpart of the traditional noncoherent detection or differential detection in point-to-point communications. Differential modulation design for TWRC is challenging because the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF protocols, where the latter can be considered as performing differential network coding at the physical layer. As the exact ML detector is prohibitively complex, we propose several suboptimal alternatives including decision feedback detectors and prediction-based detectors. All these strategies work well as evidenced by the simulation results. The proposed protocols are especially useful when the required average data rate is high. In addition, we extend the protocols to the multiple-antenna case and provide the design criterion of the differential unitary space time modulation (DUSTM) for TWRC

Achieving full diversity in multi-antenna two-way relay networks via symbol-based physical-layer network coding

This paper considers physical-layer network coding (PNC) with M-ary phase-shift keying (MPSK) modulation in two-way relay channel (TWRC). A low complexity detection technique, termed symbol-based PNC (SPNC), is proposed for the relay. In particular, attributing to the outer product operation imposed on the superposed MPSK signals at the relay, SPNC obtains the network-coded symbol (NCS) straightforwardly without having to detect individual symbols separately. Unlike the optimal multi-user detector (MUD) which searches over the combinations of all users’ modulation constellations, SPNC searches over only one modulation constellation, thus simplifies the NCS detection. Despite the reduced complexity, SPNC achieves full diversity in multi-antenna relay as the optimal MUD does. Specifically, antenna selection based SPNC (AS-SPNC) scheme and signal combining based SPNC (SC-SPNC) scheme are proposed. Our analysis of these two schemes not only confirms their full diversity performance, but also implies when SPNC is applied in multi-antenna relay, TWRC can be viewed as an effective single-input multiple-output (SIMO) system, in which AS-PNC and SC-PNC are equivalent to the general AS scheme and the maximal-ratio combining (MRC) scheme. Moreover, an asymptotic analysis of symbol error rate (SER) is provided for SC-PNC considering the case that the number of relay antennas is sufficiently large