Achieving Full Diversity in Multi-Antenna Two-Way Relay Networks via Symbol-Based Physical-Layer Network Coding

Abstract

Abstract-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 multiantenna 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.Index Terms-Physical-layer network coding (PNC), singleinput multiple-output (SIMO), two-way relay, multi-antenna relay, diversity analysis.

Phase-Rotation-Aided Relay Selection in Two-Way Decode-and-Forward Relay Networks

“…For example, it is demonstrated that according to outage capacity, MaxMin-RS without any preprocessing is capable of obtaining full diversity gain [15]. However, our previous work has shown SER performance does not exhibit any diversity gain by applying MaxMin-RS straightforwardly [14]. This paper indeed provides insights into how PR strategy enhance the capability of MaxMin-RS on achieving diversity gains in SER performance.…”

“…To be more specific, in [13], [14], the received signals from all relay antennas are combined, which allows both diversity gain and array gain to be achieved. The signal combining operation employed in [13], [14] obstructs its application in the distributed scenario, where the multiple relay antennas are distributed among several single-antenna relays. This limitation is removed by the distributed-antenna space-time coding (DSTC) based scheme [9] and a variety of antenna selection (AS) based schemes [10]- [12].…”

A More Accurate Outage Analysis for ZF-Based MIMO AF Two-Way Relaying by Order Statistics

“…where ρ U (m) 1 and ρ U (m) 2 are defined in (5). It can be observed that ρ U (m) 1 and ρ U (m) 2 are statistically independent, but ρ m , for m ∈ {1 · · · M r }, are possibly dependent random variables.…”

Diversity of Coded Beamforming in MIMO-OFDM AF Relaying Systems With Direct Link

“…Among various relaying protocols, the amplify-and-forward (AF) protocol which forwards the amplified version of the received signal at the relay to the destination has drawn considerable attention due to its simple implementation and low processing delay. Assuming flat fading channels, a large amount of research efforts have been devoted to design linear precoders and analyze the performance of MIMO AF relaying systems in [3]- [6] and references therein. In addition, for wideband frequency selective channels, the incorporation of orthogonal frequency division multiplexing (OFDM) for MIMO AF relaying systems has been studied in [7]- [9].…”