A novel adaptive cross-layer optimal power allocation (OPA) scheme over physical layer and data-link layer for two-way relaying system with amplify-and-forward policy (TWR-AF) is proposed in this paper. Our goal is to find the optimal power allocation factors under each channel state information (CSI) to maximize the sum throughput of two sources under total transmit power constraint in the physical layer while guaranteeing the statistical delay quality-of-service (QoS) requirement in the data-link layer. By integrating information theory with the concept of effective capacity, the OPA problem is formulated into an optimization problem to maximize the sum effective capacity. It is solved through Lagrange multiplier approach, and the optimal power allocation factors are presented. Simulations are developed and the results show that the proposed cross-layer OPA scheme can achieve the best sum effective capacity with relatively low complexity when compared with other schemes. In addition, the proposed cross-layer OPA scheme achieves the maximal sum effective capacity when the relay is located in (or near) the middle of the two source nodes, and the sum effective capacity becomes smaller when the difference between two QoS exponents becomes larger.

In this paper, we analyze the impact of channel estimation errors in an amplify-and-forward (AF)-based two-way relaying network (TWRN) where adaptive modulation (AM) is employed in individual relaying path. In particular, the performance degradation caused by channel estimation error is investigated over Nakagami-m fading channels. We first derive an end-to-end signal-to-noise ratio (SNR), a cumulative distribution function, and a probability density function in the presence of channel estimation error for the AF-based TWRN with adaptive modulation (TWRN-AM). By utilizing the derived SNR statistics, we present accurate expressions of the average spectral efficiency and bit error rates with an outage-constraint in which transmission does not take place during outage events of bidirectional communications. Based on our derived analytical results, an optimal power allocation scheme for TWRN-AM is proposed to improve the average spectral efficiency by minimizing system outages.

In this paper, we study simultaneous wireless information and power transfer (SWIPT) in two-way relay channels where two users exchange information with each other via a multi-antenna relay node. The signals forwarded by the relay node are also used to supply the power to two users. We formulate a max-min optimization problem aiming to maximize the minimum harvested energy between two users to achieve fairness. We jointly optimize the relay beamforming matrix and allocating powers at the two users subject to the quality of service (QoS) constraints. To be specific, we consider the amplify-and-forward (AF) relay strategy and the time splitting SWIPT strategy. To this end, we propose two different time splitting protocols to enable relay to supply power to two users. To solve the non-convex joint optimization problem, we propose to split the original optimization problem into two subproblems and solving them iteratively to obtain the final solution. It is shown that the first subproblem dealing with the beamforming matrix can be optimally solved by using the technique of relaxed semidefinite programming (SDR), and the second subproblem, which deals with the power allocation, can be solved via linear programming. The performance comparison of two schemes as well as the one-way relaying scheme are provided and the effectiveness of the proposed schemes is verified.

In this paper, we investigate the capacity performance of an in-band full-duplex (IBFD) amplify-and-forward two-way relay system under the effect of residual loop-back-interference (LBI). In a two-way IBFD relay system, two IBFD nodes exchange data with each other via an IBFD relay. Both two-way relaying and IBFD one-way relaying could double the spectrum efficiency theoretically. However, due to imperfect channel estimation, the performance of two-way relaying is degraded by self-interference at the receiver. Moreover, the performance of the IBFD relaying is deteriorated by LBI between the transmit antenna and the receive antenna of the node. Different from the IBFD one-way relay scenario, the IBFD two-way relay system will suffer from an extra level of LBI at the destination receiver. We derive accurate approximations of the average end-to-end capacities for both the IBFD and half-duplex modes. We evaluate the impact of the LBI and channel estimation errors on system performance. Monte Carlo simulations verify the validity of analytical results. It can be shown that with certain signal-to-noise ratio values and effective interference cancellation techniques, the IBFD transmission is preferable in terms of capacity. The IBFD two-way relaying is an attractive technique for practical applications.

In this paper, we study the impact of imperfect channel information on an amplify-and-forward (AF)-based two-way relaying network (TWRN) with adaptive modulation which consists of two end-terminals and multiple relays. Specifically, we consider a single-relay selection scheme of the TWRN in the presence of outdated channel state information (CSI) and channel estimation errors. First, we choose the best relay based on outdated CSI, and perform adaptive modulation on both relaying paths with channel estimation errors. Then, we discuss the impact of the outdated CSI on the statistics of the signal-to-noise ratio (SNR) per hop. In addition, we formulate the end-to-end SNRs with channel estimation errors and offer statistic analyses in the presence of both the outdated CSI and channel estimation errors. Finally, we provide the performance analyses of the proposed TWRN with adaptive modulation in terms of average spectral efficiency, average bit error rate, and outage probability. Numerical examples are given to verify our obtained analytical results for various system conditions.

This work presents the exact outage performance and throughput of two-way cognitive decode-and-forward relaying wireless sensor networks with realistic transceiver relay. The relay is a self-powered wireless node that harvests radio frequency energy from the transmitted signals. We consider four configurations of a network with formed by combining two bidirectional relaying protocols (multiple access broadcast protocol and time division broadcast protocol), and two power transfer policies (dual-source energy transfer and single-fixed-source energy transfer). Based on our analysis, we provide practical insights into the impact of transceiver hardware impairments on the network performance, such as the fundamental capacity ceiling of the network with various configurations that cannot be exceeded by increasing transmit power given a fixed transmission rate and the transceiver selection strategy for the network nodes that can optimize the implementation cost and performance tradeoff.

The acquisition of accurate channel state information at the transmitter (CSIT) is a difficult task in multiple-input multiple-output (MIMO) systems. Partial CSIT is a more realistic assumption, especially for high-mobility mobile users (MUs) whose channel varies very rapidly. In this letter, we propose a MIMO two-way relaying (MTWR) scheme, in which the communication between the BS and a high-mobility MU is assisted by other low-mobility MUs serving as relays. This produces a beamforming effect that can significantly improve the performance of the high-mobility MU, especially for a large number of MUs and unreliable CSIT.

Network coding on the physical-layer has recently been widely discussed as a potentially promising solution to the wireless access problem in a relay network. However, the existing research on physical-layer network coding (PNC), usually assumes that the symbol timing of the nodes is fully synchronized and hardly investigates the unavoidable symbol timing errors. Similar to many telecommunication systems, symbol timing plays a critical role in PNC and precise alignment has to be provided for the encoding. In this work, we propose a novel symbol timing algorithm with a low oversampling factor (samples per symbol) based on the a priori knowledge of the transmitted pulse shape. The proposed algorithm has the dual advantages of the low oversampling rate and high precision. The mean square error (MSE) performance is verified by simulations to be at least one order of magnitude better than that of the conventional optimum phase (OP) algorithm for a signal noise ratio (SNR) greater than 5dB.

This paper presents the design of an ad hoc two-way two-hop relay network using physical-layer network coding (PNC) in which multiple antennas are used at all nodes. In the considered network, the Alamouti's space-time block code (STBC) is used for transmission while linear detection is used for signal recovery. In order to facilitate linear estimation, we develop an equivalent multiuser STBC model for the proposed network and design the sum-and-difference matrix which allows convenient combination of the transmitted symbols from the end nodes. In addition, a simple relay selection method based on minimum mean square error (MSE) is proposed for performance improvement. Simulation results show that the proposed network achieves diversity order 2 while requiring only polynomial complexity. Moreover, it is possible to achieve significant bit error rate (BER) performance improvement when the proposed relay selection algorithm is used.

In this letter, we combine minimum-shift keying (MSK) with physical-layer network coding (PNC) to form a new scheme, i.e., MSK-PNC, for two-way relay channels (TWRCs). The signal detection of the MSK-PNC scheme is investigated, and two detection methods are proposed. The first one is orthogonal demodulation and mapping (ODM), and the second one is two-state differential detection (TSDD). The error performance of the proposed MSK-PNC scheme is evaluated through simulations.

We analyze the outage probability of the multiuser two-way relay network (TWRN) where the N-th best mobile user (MU) out of M MUs and the base station (BS) exchange messages with the aid of an amplify-and-forward relay. In the analysis, we focus on the practical unbalanced Nakagami-m fading between the MUs-relay link and the relay-BS link. We also consider both perfect and outdated channel state information (CSI) between the MUs and the relay. We first derive tight closed-form lower bounds on the outage probability. We then derive compact expressions for the asymptotic outage probability to explicitly characterize the network performance in the high signal-to-noise ratio regime. Based on our asymptotic results, we demonstrate that the diversity order is determined by both Nakagami-m fading parameters, M, and N when perfect CSI is available. When outdated CSI is available, the diversity order is determined by Nakagami-m fading parameters only. In addition, we quantify the contributions of M, N, and the outdated CSI to the outage probability via the array gain.

This paper studies an underlay-based cognitive two-way relay network which consists of a primary network (PN) and a secondary network (SN). Two secondary users (SUs) exchange information with the aid of multiple single-antenna amplify-and-forward relays while a primary transmitter communicates with a primary receiver in the same spectrum. Unlike the existing contributions, the transmit powers of the SUs and the distributed beamforming weights of the relays are jointly optimized to minimize the sum interference power from the SN to the PN under the quality-of-service (QoS) constraints of the SUs determined by their output signal-to-interference-plus-noise ratio (SINR) and the transmit power constraints of the SUs and relays. This approach leads to a non-convex optimization problem which is computationally intractable in general. We first investigate two necessary conditions that optimal solutions should satisfy. Then, the non-convex minimization problem is solved analytically based on the obtained conditions for single-relay scenarios. For multi-relay scenarios, an iterative numerical algorithm is proposed to find suboptimal solutions with low computational complexity. It is shown that starting with an arbitrarily initial feasible point, the limit point of the solution sequence derived from the iterative algorithm satisfies the two necessary conditions. To apply this algorithm, two approaches are developed to find an initial feasible point. Finally, simulation results show that on average, the proposed low-complexity solution considerably outperforms the scheme without source power control and performs close to the optimal solution obtained by a grid search technique which has prohibitively high computational complexity.

In this paper, we consider a two-way multi-relay scenario and analyze the bit error rate (BER) and outage performance of an amplify-and-forward (AF) relaying protocol. We first investigate the bit error probability by considering channel estimation error. With the derivation of effective signal-to-noise ratio (SNR) at the transceiver and its probability density function (PDF), we can obtain a closed form formulation of the total average error probability of two-way multi-relay system. Furthermore, we also derive exact expressions of the outage probability for two-way relay through the aid of a modified Bessel function. Finally, numerical experiments are performed to verify the analytical results and show that our theoretical derivations are exactly matched with simulations.

This paper proposes an opportunistic feedback and user selection method for a multiuser two-way relay channel (MU-TWRC) in a time-varying environments where a base station (BS) and a selected mobile station (MS), one of K moving MSs, exchange messages during two time slots via an amplify-and-forward relay station. Specifically, under the assumption of perfect channel reciprocity, we analyze the outage probabilities of several channel feedback scenarios, including the proposed scheme. Based on the analysis, the transmission rates are optimized and the optimal user selection method is proposed to maximize the expected sum throughput. The simulation results indicate that, with opportunistic feedback, the performance can be significantly improved compared to that without feedback. Moreover, the performance is nearly identical to that with full feedback, and close to the case of perfect channel state information at BS for low mobility MSs.

This paper analyzes the performance of a two-way relay network experiencing co-channel interference from multiple interferers due to aggressive frequency reuse in cellular networks. We discuss two different scenarios: Outages are declared individually for each user (individual outage) and an outage is declared simultaneously for all users (common outage). We derive the closed-form expressions for the individual and common outage probabilities of the two-way relay network with multiple interferers. The validity of our analytical results is verified by a comparison with simulation results. It is shown that the analytical results perfectly match the simulation results of the individual and common outage probabilities. Also, it is shown that the individual and common outage probabilities increase as the number of interferers increases.

This letter investigates the outage performance of a joint transmit and receive antenna selection scheme in an amplify-and-forward two-way relaying system with channel estimation error. A closed-form approximate outage probability expression is derived, based on which the asymptotic outage probability expression is derived to get an insight on system's outage performance at high signal-to-noise (SNR) region. Monte Carlo simulation results are presented to verify the analytical results.

In this paper, we study the problem of joint resource allocation in the two-way relay system, where a pair of multi-antenna users wish to exchange information via multi-antenna amplify-and-forward relay under orthogonal frequency-division multiplexing (OFDM) modulation. We formulate a sum-rate maximization problem subject to a limited power constraint for each user and relay. Our resource allocation strategy aims at finding the best pairing scheme and optimal power allocation over subchannels in frequency and space domains. This turns out to be a mixed integer programming problem. We then derive an asymptotically optimal solution though the Lagrange dual decomposition approach. Finally, simulation results are provided to demonstrate the performance gain of the proposed algorithms.

MIMO two-way multi-hop networks are considered in which the radio resource is fully reused in all multi-hop links to increase spectrum efficiency while the adjacent interference signals are cancelled by MIMO processing. In addition, the nodes in the multi-hop network optimize their transmit powers to mitigate the remaining overreach interference. Our main contribution in this paper is to investigate an efficient relay placement method with power allocation in such networks. We present two formulations, namely QoS-constrained optimization and SINR balancing, and solve them using a sequential geometric programming method. The proposed algorithm takes advantage of convex optimization to find an efficient configuration. Simulation results show that relay placement has an important impact on the effectiveness of power allocation to mitigate the interference. Particularly, we found that an uniform relay location is optimal only in power-limited scenarios. With optimal relay locations, significant end-to-end rate gain and power consumption reduction are achieved by SINR balancing and QoS-constrained optimization, respectively. Furthermore, the optimal number of hops is investigated in power or interference-limited scenarios.

Physical-layer network coding with binary turbo coding in a two-way relay channel is considered. A two-user turbo decoding scheme is proposed with a simplified sum trellis. For two-user iterative decoding at a relay, the component decoder with its simplified sum trellis decodes the superimposed signal to the arithmetic sum of two users' messages. The simplified sum trellis is obtained by removing one of the states in a pair of mutual symmetrical states from a sum trellis. This removal reduces the decoding complexity to half of that with the sum trellis, and does not degrade decoding performance over AWGN channel since two output sequences from the pair of mutual symmetrical states are the same.

A specific physical layer network coding (PNC) scheme is proposed for the two-way relay channel. Unlike the traditional binary PNC that focuses mainly on BPSK modulation, the proposed PNC scheme is tailored for general MPSK modulation. In particular, the product of the two modulated signals is considered as a network-coded symbol. The proposed network coding operation occurs naturally in the inner or outer product of the received signal. A novel PNC-specific detection principle is then developed to estimate the network-coded symbol. Simulations show that the proposed scheme achieves almost optimal performance in terms of end-to-end bit error rate (BER), where the relay node is equipped with multiple antennas.