Resource allocation for two-way relaying with network coding

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.

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.

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.

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 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, compute-and-forward physical layer network coding (PNC) scheme is investigated for wireless two-way relay channel. The achievable rates are reviewed both for AWGN channel and fading channel. New transmit schemes by using channel inversion precoding are proposed over fading channel to achieve much higher rates. It is revealed that with the proposed channel aware precoding scheme, the performance of compute-and-forward improves enormously. For two-way relay channel, compute-and-forward can achieve the maximum degree of freedom (DoF) of 2 without the limitation of Diophantine tradeoff, which indicates that compute-and-forward is the most suitable relaying scheme for two-way relay channel.

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.

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.

When two wireless terminals exchange information through an intermediate relay, physical-layer network coding (PNC) improves the spectrum efficiency by allowing concurrent message transmission. In two-way relay systems, the performance gain of PNC under practical limits has been investigated. The results show that generally the performance would be significantly degraded by channel impairments like asymmetric channel gain at the multiple-access phase. As an alternative interference exploitation scheme, successive interference cancellation (SIC) works well when multiple sources’ signals have different power levels at the destination to successfully decoding. In this paper, an adaptive transmission scheme combing PNC and SIC is proposed for the two-way relay systems. Separate sum-rate simulation results for PNC and SIC show the opposite tendency with the channel impairment in two-way relaying, which means combining them would get a smooth sum-rate gain and let the system be more robust to dynamic scenarios.

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 this paper, we consider the three-node two-way relay channel (TWRC) over which communication is performed using space-time block codes (STBC) with physical-layer network coding (PNC) protocol. Two end nodes simultaneously communicate with each other over a relay node where each node is equipped with two antennas and uses Alamouti's STBC to provide diversity. First, a closed form expression for the outage probability of the STBC-TWR system is derived, assuming nonreciprocal channels, equal transmit power at each node and decode-and-forward (DF) strategy at the relay. It is shown that the STBC-TWR system significantly improves the uncoded TWRC outage performance. Then, to further improve the performance, an optimal power allocation to maximize the sum-rate under the total power constraint, is proposed. It is shown that the optimal power allocation considerably improve the sum-rate as well as the outage performance compared to the equal-power case.

Traditional communication system typically separates the configuration of the physical layer from the network traffic load and topology. In this paper, we study how to apply physical-layer network coding considering the locations and traffic loads of multiple nodes in multiple-input multiple-output (MIMO) networks. We propose the heterogeneous-modulation physical-layer network coding (HePNC) design for MIMO networks with asymmetric two- way relay channel (TWRC), where all nodes are equipped with multiple antennas. Comparing to the single-antenna case, we study how to ensure the goodput with a fixed per-bit-energy can be scaled up w.r.t. the number of antennas, and also achieve performance gains in terms of end-to-end bit error rate (BER). The MIMO HePNC transmission includes the multiple access (MA) and broadcast (BC) stages. As the global channel state information (CSI) may be too costly to obtain, we propose two practical MIMO HePNC protocols based on maximum likelihood (ML) multi-user detector (MUD) that do not rely on global CSI. The first protocol is a heuristic one evolved from the single-input single-output (SISO) HePNC, and the second protocol upgrades the design and performance of both of the MA and BC stages. Analytical and extensive simulations demonstrated that, with two antennas each, the proposed MIMO HePNC protocols can not only double the goodput, but also achieve a substantial reduction on error rate, which indicates that combining HePNC and MIMO is a very promising cross-layer solution. We further discuss the impacts of the bottleneck link and provide guidelines on the relay location selection.

This paper investigates the outage performance of simultaneous wireless information and power transfer (SWIPT) in two-way relay channels, where two sources exchange their information via an energy harvesting (EH) relay with digital network coding (NC) employed. The relay harvests energy from the received radio-frequency (RF) signals transmitted from the two sources and then use it to forward the received signals. For such a system, we study the power splitting-based two-way relay (PS-TWR) transmission strategy and analytically derive an explicit expression of the system outage probability. In order to explore the system outage performance limit, we formulate an optimization problem to minimize the system outage probability by jointly optimizing the power splitting ratio and the time assignment ratio. Since the problem is non-convex and have no known solution method, we present a genetic algorithm (GA) to solve it. Numerical results demonstrate our theoretical analysis and show that the power splitting ratio and the time assignment ratio greatly affect the system outage performance. Moreover, it is also shown that for the SWIPT-enabled two-way relay system, the relay node should be deployed closer to the source with better channel quality and when it is positioned on the middle point between the two sources, the system gets the worst outage performance, which is very different from traditional non-SWIPT two-way relay systems.

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.