Compute-and-forward for two-way relay

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.

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.

We propose a new joint channel coding and physical layer network coding (CPNC) scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs). At the heart of the scheme lies a key technique referred to as eigen-direction alignment (EDA) precoding. This technique efficiently creates multiple aligned parallel channels which facilitates the deployment of multi-stream CPNC. Our analysis shows that the achievable rate of the scheme can approach the capacity upper bound in the median to high signal-to-noise (SNR) region when n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> > n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</inf> , where n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> and n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</inf> denote the number of antennas of each user and that of relay, respectively. The gap to the capacity upper bound diminishes as n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> /n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</inf> increases. Numerical results demonstrate that the proposed scheme significantly outperform other well-known schemes in the literature.

A noncoherent two-way relaying system is developed using physical-layer network coding for improved throughput over conventional relaying in a fading channel. Energy-efficient noncoherent operation is achieved using multitone frequency shift keying (FSK). A novel soft-output demodulator is developed for the relay, and corresponding achievable exchange rates are found for Rayleigh fading and AWGN channels. Bit-error rate performance approaching the achievable rate is realized using a capacity-approaching channel code and a receiver architecture, which iterates between demodulation and channel decoding. Iterative decoding is performed feeding information back from the channel decoder to the demodulator. In addition, the error-rate performance is made to approach the achievable rate more closely by optimizing LDPC codes for this system. The energy efficiency improvement obtained by increasing the modulation order is more dramatic for the proposed physical-layer network coding scheme than it is for a conventional point-to-point system. Using optimized LDPC codes, the bit-error rate performance is improved by as much as 1.1 dB over a widely known standardized LDPC code, and comes to within 0.7 dB of the limit corresponding to the achievable rate. Throughout this paper, the performance for physical-layer network coding is compared with conventional network coding. When noncoherent FSK is used, physical-layer network coding enables higher achievable rates, and conventional network coding exhibits better energy efficiency at low rates.

This paper proposes a channel coded linear physical-layer network coding (LPNC) scheme for two-way relay (TWR) fading channel, where only the relay possesses the channel state information (CSI) in the multiple access (MAC) phase. This scheme employs the spectrally efficient Ring-Trellis Coded Modulation (Ring-TCM) codes to achieve a better performance for TWR communication systems that employs LPNC. The design criterion of the Ring-TCM code for TWR fading channel is discussed. We also propose a new algorithm to find the optimal network coding coefficients to resemble the channel fading coefficients of the node-to-relay channels. The relay estimates the end nodes' message using the maximum a posteriori (MAP) decoding algorithm based on a joint trellis. Our simulation results show that the coded LPNC scheme significantly outperforms the uncoded LPNC scheme. It can also outperform the coded scheme that employs complete decoding (CD) scheme. Our simulation results also show that the proposed scheme can approach the cut-set bound at the high signal-to-noise ratio (SNR).

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.

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.

This study proposes an optimal time allocation scheme for two‐way relay channel (TWRC) using the physical‐layer network coding (PNC). In other words, this study analytically determines the optimal transmit time durations for the first and the second time slot, which maximise the achievable sum rate under a sum time constraint for a given squared magnitude of the channel coefficients and transmit power values. Numerical results show that the achievable sum rate for the proposed optimal time allocation is greater than or equal to that for equal time allocation.

Radio channel is characterized by a multipath propagation that is suitable for application of network coding (NC) to improve the network capacity. In particular, physical layer network coding (PNC) scheme is known to double the network capacity of bi-directional communication between pairs of end users assisted by a relay terminal in a Gaussian channel. Recently, analog network coding (ANC) has been proposed with a simpler implementation complexity in comparison with PNC scheme, but the same achievable network capacity. On the other hand, an important question is how much the channel capacity is improved over a conventional point-to-point communication in a frequency-selective fading channel. In this paper, we present the ergodic channel capacity analysis of bi-directional transmission with analog network coding in a frequency-selective fading channel. The channel capacity expression for transmission with frequency domain equalization (FDE) is derived based on the Gaussian approximation of the inter-symbol interference (ISI) after FDE.

The physical-layer network coding (PNC) can greatly improve the throughput of wireless network communications. However, critical synchronization in both time domain and frequency domain is required. Orthogonal frequency division multiplexing (OFDM) solves the problem of the synchronization in time domain while more critical synchronization in frequency domain is required. In this paper, we investigate the inter-channel interference (ICI) issue for OFDM-based physical-layer network coding (FPNC) over the two-way relay channel (TWRC). An approximate formula that calculates the ICI is derived. The compensation frequency, used by intermediate node to obtain minimal ICI power, has also been calculated. We find that average compensation is the optimal compensation method in the symmetric TWRC system while a different compensation method should be adopted in the asymmetric TWRC system. In addition, it is observed that bit error rate (BER) performance is not only decided by the power of the ICI but also by the distribution of it. At last, numerical results indicate that our approximate formula is accurate enough to calculate the ICI and can be applied to other 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.

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.

Zero-forcing dirty paper coding aided physical-layer network coding for MIMO two-way relaying channels with multiple users

This paper investigates the sum-bit error rate (BER) performance of amplify-and-forward (AF) energy harvesting two-way relay networks (TWRNs), where two source nodes communicate with each other through a self-sustaining wireless relay node using time switching-based relaying (TSR) protocol. Two physical layer network coding (PNC) schemes are considered, namely two-time-slot and three-time-slot PNC, denoted by 2-PNC and 3-PNC, respectively. We derive analytical expressions for the sum-BER of these two schemes and propose to appropriately time share between modulation schemes of different dimensions according to the energy harvesting time fraction in order to normalize the spectral efficiency. Simulation and numerical experiments are performed to verify our analysis. It is observed that 3-PNC outperforms 2-PNC in terms of sum-BER when the energy harvesting time fraction is small. However, this fraction can be optimized such that the 2-PNC scheme achieves better overall sum-BER performance.