Adaptive Transmission Combining Physical-Layer Network Coding and Successive Interference Cancellation for Two-Way Relay System

In this chapter, two-way relaying networks using Physical-Layer Net- work Coding (PLNC) are considered with practical constraints. In a Multiple Access (MA) phase, two users transmit messages simultaneously on the same physical resources. The relay constructs a relay message based on the superimposed receive signal of both users. This message is broadcasted to the users which are able to extract the desired data from the other user. However, as the relay is not able to resolve shifts in time and frequency for the individual channels, the transmission scheme needs to be adjusted, if perfect synchronization cannot be ensured. This chapter deals with the proper selection of waveforms for multi-carrier systems in the Two-Way-Relay Channel (TWRC) using PLNC. We address Generalized Frequency Division Multiplexing (GFDM) compared to Orthogonal Frequency Division Multi-plexing (OFDM) under practical constraints like Carrier Frequency Offsets (CFOs) and Timing Offsets (TOs) within double dispersive channels. For OFDM rectangular transmit filters are used, which have a broad spectrum shape and are sensitive to shifts, especially in frequency domain. GFDM applies Gaussian waveforms that are inherently less susceptible to synchronization offsets than theirs rectangular counterparts, but additional interference is introduced even in a perfectly synchronized and flat fading channel. Thus, interferences caused by the channel or by the non-orthogonal Gaussian impulse shape are treated by an equalizer at the relay. The simulation results show that the Gaussian waveform outperforms the conventional OFDM system if the nodes are not perfectly synchronized.

Adaptive physical layer network coding (PNC) has been shown to be effective in two-way relay communications (TWRC). Given that the existing PNC methods were developed for frequency-flat fading channels, this paper studies adaptive PNC in OFDM systems operating over frequency-selective fading channels. Proposed and investigated are three methods to determine a common clustering for all subcarriers in order to reduce the overhead information required in the broadcast phase. The "Min-SER" method is given based on the analysis of the error event in the multiple access phase, while the "Max-fade-SER" and "Min-fade-distance" methods are recommended to further reduce the computational complexity in determining the common clustering. Considering the trade-off among performance, overhead and complexity, the "Max-fade-SER" method is the most attractive clustering method for applying adaptive PNC in OFDM systems.

In this paper, the authors show that using physical layer network coding (PNC) in wireless relay systems does not always increase throughput performance, and to achieve maximum throughput, PNC should be exploited intelligently regarding to the channel conditions. In this study, they propose a selective PNC (SPNC) scheme in bidirectional relay systems for binary phase shift keying. In the proposed scheme, the relay chooses either to detect network-coded data from superimposed signal by PNC scheme or single source data by a so-called single node detection (SND) scheme, based on which offers more end-to-end throughput for current channel realisation. They analytically determine the region of channel state plane in which SPNC selects SND scheme. Also, they obtain expressions for instantaneous bit error rates (BERs) of PNC and SND protocols. Moreover, they derive upper bounds in closed-form for average BERs of PNC and SND schemes during multiple access phase at the relay. Then, they investigate SPNC with high-order modulations. Simulations and analytical results confirm that SPNC achieves considerable throughput gain over PNC in Rayleigh fading channels.

In this paper, we consider a decode-and-forward (DF) two-way relay (TWR) system in power line communication (PLC). The DF TWR employs physical- layer network coding (PNC). We derive analytic expressions for the average capacity and the outage probability of the system over a log-normal fading channel. Analytic results are verified through Monte Carlo simulations. From the results, the TWR is able to mitigate the half-duplex (HD) spectral efficiency loss incurred by one-way relaying. The impact of the impulsive noise on the system performance is also highlighted in the simulation results. It is shown that higher impulsive probability degrades system performance.

The growing demand for high-speed data, quality of service (QoS) assurance and energy efficiency has triggered the evolution of 4G LTE-A networks to 5G and beyond. Interference is still a major performance bottleneck. This paper studies the application of physical-layer network coding (PNC), a technique that exploits interference, in heterogeneous cellular networks. In particular, we propose a rate-maximising relay selection algorithm for a single cell with multiple relays based on the decode-and-forward strategy. With nodes transmitting at different powers, the proposed algorithm adapts the resource allocation according to the differing link rates and we prove theoretically that the optimisation problem is log-concave. The proposed technique is shown to perform significantly better than the widely studied selection-cooperation technique. We then undertake an experimental study on a software radio platform of the decoding performance of PNC with unbalanced SNRs in the multiple-access transmissions. This problem is inherent in cellular networks and it is shown that with channel coding and decoders based on multiuser detection and successive interference cancellation, the performance is better with power imbalance. This paper paves the way for further research in multi-cell PNC, resource allocation, and the implementation of PNC with higher-order modulations and advanced coding techniques.

This paper investigates noncoherent detection in a two-way relay channel operated with physical- layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. We design a noncoherent detector that jointly estimates relative phase and detects data using a belief propagation algorithm. Numerical results show that our detector performs as well as a "fictitious" optimal detector that has perfect knowledge of the relative phase. Although this paper focuses on PNC with FSK modulation, we believe the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve detection performance.

In bidirectional relaying using Physical Layer Network Coding (PLNC), it is generally assumed that users employ same modulation schemes in the Multiple Access phase. However, as observed by Zhang et al., it may not be desirable for the nodes to always use the same modulation schemes, particularly when node-relay channels are not equally strong. Such a scheme is called Heterogeneous PLNC. However, the above approach uses the computationally intensive Closest Neighbour Clustering algorithm to find the network coding maps to be applied at the relay. Also, the treatment is specific to certain cases of heterogeneous modulations. In this paper, we show that, when users employ heterogeneous symmetric-PSK modulations, the network coding maps and the mapping regions in the fade state plane can be obtained analytically. Performance results are provided in terms of relay error rate and bit error rate.

In this paper, a vertical physical-layer network coding (VPNC) scheme based pulse amplitude modulation (PAM) for two-way relay channel (TWRC) is proposed. Different from the conventional physical layer network coding (PNC) scheme in which the relay superimposes two users' signals of the same constellation, in the proposed VPNC scheme two users transmit PAM signals with vertical constellation and the relay superimposes two signals of vertical constellation in the multiple access (MA) phase. In addition, when the VPNC is exploited in conjunction with channel coding, joint channel VPNC is proposed to further improve the BER performance. Simulation results show that the proposed VPNC scheme outperforms the conventional PNC scheme on BER performance.

A two-way relay (TWR) channel is considered where two users exchange their messages with the help of a single relay. With the assumption of separate relay power budget and user power budget, we maximize the sum-rate of the TWR channel using physical-layer network coding (PNC) with flexible time fraction. We propose an optimal power allocation scheme between users and find that in high signal-to-noise ratio (SNR) regime, the user power should be allocated inversely proportional to the channel gains. Moreover, the bidirectional streams of the PNC-TWR enjoy full diversity gain. The analysis of the equal time fraction case and the numerical results of the flexible time fraction case both imply that the PNC relaying performs better than the decode-and-forward based TWR (DF-TWR) if the channel gains are similar, while the DF relaying performs better if the channel gains are quite different.

We present a novel adaptive physical layer network coding (PLNC) at the relay, called pseudo exclusive-or (PXOR), for LDPC coded two-way relay (TWR) block fading channels. Based on the pairwise check decoding (PCD), the check relationship table generated by the proposed PXOR mapping obtains the same Hamming distances of the PLNC mapped codewords as that of conventional XOR mapping. In the meantime, the PXOR mapping optimizes the Euclidean distances by adjusting the symbol distances dynamically as far as possible in order to compensate the amplitude fading and phase deviation of the TWR block fading channels. For the system end-to-end error probability, simulation results show that the proposed coded PXOR considerably outperforms the coded conventional XOR and achieves the same performance as the complicated coded CNC for considered two TWR block fading channels.

In this paper, we consider the two-way relay channel (TWRC) over which communication is performed using space-time block codes (STBC) with physical-layer network coding (PNC) protocol. The three-node two-way relaying (TWR) model consists of two end nodes (sources) simultaneously communicating with each other over a relay node where each node is equipped with two antennas and uses Alamouti's STBC to provide diversity. We consider non-reciprocal channels where fading channel coefficients are independent for opposite directions of the same link. We first derive closed form expressions for the outage probability of the STBC-TWR system and uncoded TWRC assuming equal transmit power at each node and decode-and-forward (DF) strategy at the relay. We show that the STBC-TWR system significantly improves the uncoded TWRC outage performance. Then, to further improve the performance, we propose an optimal power allocation in TWR scheme employing Alamouti's STBC and PNC protocol. The optimal power allocation is obtained by maximizing the sum-rate under the total power constraint. We show that the optimal power allocation considerably improve the outage performance as well as the sum-rate compared to the equal-power case.

In this paper we consider a two-way relaying system, where two users A and B wish to exchange information with the help of a common relay R., To decode the superimposed signal from A and B efficiently, we propose a new scheme of jointing physical layer network coding (PNC) and channel decoding for multiple-access channel based on trellis coded modulation (TCM). Since TCM combines channel coding with modulation, the scheme improves the free distance of the coding sequence, thus more encoding gain is achieved. In addition, taking advantage of the linearity of convolutional code and MAC-XOR NC code, the digital bits of network coding are estimated directly. In a word, we propose a novel scheme which considers channel coding, modulation and PNC at the same time, so that not only the information transmission rate is increased, but also the reliability is improved.

In this paper, while considering the impact of antenna correlation and the interference from neighboring users, we study the problem of channel estimation and training sequence design in multi-input multi-output (MIMO) two-way relaying (TWR) systems. To this end, we propose to decompose the bidirectional transmission links into two phases, i.e., the multiple access (MAC) and the broadcast (BC) phases. By deriving the optimal linear minimum mean-square-error estimators, the corresponding training design problems for the MAC and BC phases are formulated and solved. Subsequently, algorithms and, in some special cases, closed-form solutions for obtaining the optimal training sequences for channel estimation in TWR systems are derived. Moreover, to further reduce channel estimation overhead, the minimum required length of the training sequences are determined. Simulation results verify the effectiveness of the proposed training designs in improving channel estimation performance in TWR systems.

Performance analysis and optimization for cellular two-way relay networks with cooperative NOMA transmission

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