Optimal power allocation for two-way decode-and-forward relay networks with equal transmit power at source nodes

In this paper, we investigate the optimal power and time allocation for a wireless relay network, called BCFR (Broadcasting Channel with Fixed Relay), where the relay node is limited by the half-duplex operation. Introducing a relay in two-node broadcasting channel for a node which has a link of bad quality or requires higher transmission rate enlarges the rate region with well-designed power and time allocation. Also, BCFR is a common component of many relay networks, in which either orthogonal or non-orthogonal transmission can be adopted at the information source node. In particular, for the non-orthogonal transmission, the layered transmission with superposition coding is applied at the source node. By deriving the optimal power and time-fraction allocation at each node of BCFR, we show that the non-orthogonal structure enhances the capacity region and achieves higher log-sum capacity than the orthogonal transmission.

In this paper, a distributed power control algorithm is proposed for wireless relay networks in interference-limited environments. The objective is to minimize the total transmission power while satisfying the signal-to-interference-plus-noise ratio (SINR) requirements. Two forwarding techniques, i.e., decode- and-forward (DF) and amplify-and-forward (AF), are considered. The proposed algorithm only requires locally measured SINR on the relay nodes (RNs) and the destination nodes (DNs), based on which each cooperation unit (defined as one source node (SN) and DN pair with the RN associated to it) iteratively updates the transmission power of the SN and the RN by solving a local optimization problem. We prove that the convergence is guaranteed when the parameters adopted in the algorithm are sufficiently large, and then a parameter adjusting method is also designed. Simulation results indicate that the proposed algorithm converges fast and leads to only 7% more power consumption than the optimal power allocation in the considered scenarios. It is also shown that even in interference-limited environments, relaying can still improve system performance substantially in terms of outage and power consumption.

We investigate a power allocation optimization problem under the scenario of multiple cooperative relays and one destination with multiple receiving antennas. We consider the relay protocol, decode and forward (DAF). An optimal power allocation scheme (OPA), through singular value decomposition (SVD) of the channel matrix, is developed among the relay nodes under a certain power constraint to achieve the maximum channel capacity. The expression of the optimal power allocation coefficient is derived using Lagrange multiplier. Simulation results show that the OPA can obtain higher capacity gain and lower outage probability comparing with the uniform power allocation (UPA) scheme. Moreover, we show that the OPA with DAF has better performance than it with AAF.

In this paper, we propose a dynamic power allocation scheme for a single-relay network based on orthogonal frequency division multiplexing (OFDM) modulation with limited feedback.We consider an Amplify-and-Forward (AF) cooperative diversity model, where one source node communicates with one destination node assisted by one half duplex relay. The power allocation scheme employs a codebook of quantized power allocation vectors designed offline equipped on the source, relay, and destination. The destination, who has full knowledge of channel state information (CSI), chooses the best power allocation vector and sends back its index to the source and relay nodes, which results in a dramatic reduced overhead over conventional resource allocation. First we achieve the optimal power allocation solution as the function of channel realizations with maximum capacity. Then we present an adaptation of the Lloyd algorithm to construct a codebook to quantize the optimal power allocation vectors subject to the amount of feedback. Simulations show that a negligible performance loss could be achieved with just a few feedback bits at different levels of SNRs.

Through simultaneous energy and information transfer, radio frequency (RF) energy harvesting (EH) reduces the energy consumption of the wireless networks. It also provides a new approach for the wireless devices to share each other’s energy storage, without relying on the power grid or traffic offloading. In this paper, we study RF energy harvesting enabled power balancing within the decode-and-forward (DF) relaying-enhanced cooperative wireless system. An optimal power allocation policy is proposed for the scenario where both source and relay nodes can draw power from the radio frequency signals transmitted by each other. To maximize the overall throughput while meeting the energy constraints imposed by the RF sources, an optimization problem is formulated and solved. Based on different harvesting efficiency and channel condition, closed form solutions for optimal joint source and relay power allocation are derived.

In Part II of this two-part paper, a sum-rate-maximizing power allocation\nwith minimum power consumption is found for multiple-input multiple-output\n(MIMO) decode-and-forward (DF) two-way relaying (TWR) in a network optimization\nscenario. In this scenario, the relay and the source nodes jointly optimize\ntheir power allocation strategies to achieve network optimality. Unlike the\nrelay optimization scenario considered in part I which features low complexity\nbut does not achieve network optimality, the network-level optimal power\nallocation can be achieved in the network optimization scenario at the cost of\nhigher complexity. The network optimization problem is considered in two cases\neach with several subcases. It is shown that the considered problem, which is\noriginally nonconvex, can be transferred into different convex problems for all\nbut two subcases. For the remaining two subcases, one for each case, it is\nproved that the optimal strategies for the source nodes and the relay must\nsatisfy certain properties. Based on these properties, an algorithm is proposed\nfor finding the optimal solution. The effect of asymmetry in the number of\nantennas, power limits, and channel statistics is also considered. Such\nasymmetry is shown to have a negative effect on both the achievable sum-rate\nand the power allocation efficiency in MIMO DF TWR. Simulation results\ndemonstrate the performance of the proposed algorithm and the effect of\nasymmetry in the system.\n

This paper investigates the optimal precoder design and power allocation between the source and relay for a half-duplex single-relay non-orthogonal amplify-and-forward (NAF) system. Based on the pair-wise error probability (PEP) analysis, an optimal class of 2 × 2 precoders is first derived for the traditional power allocation scheme, where one-third of the system power is spent at the relay node, while two-thirds are spent at the source node. Different from optimal unitary precoders proposed earlier, the derived class of precoders indicates that the source should spend all its power transmitting a superposition of the symbols in the broadcast phase, while being silent in the cooperative phase, for optimal asymptotic performance. We then further address the problem of jointly optimal precoder and power allocation for the system under consideration. It is shown that the total power should be equally distributed to the source and the relay, and the source should again spend no power during the cooperative phase for the best asymptotic performance. Analytical and simulation results reveal that the proposed precoders not only exploit full cooperative diversity, but also provide significant coding gain over the optimal unitary precoders. For instance, a coding gain of around 1dB can be attained at the practical BER level of 10 − 5 for various modulation schemes.

In this paper, the capacity of MIMO relay channel with decode and forward (DF) scheme is investigated, where each node within the system quipped with multiple antennas and located in an environment with distance-dependent path loss. In order to achieve the maximum capacity of the system, the optimal power allocation (OPA) among the nodes and the transmit antennas is analyzed under the assumption that relay node knows all channels instantaneous state information (CSI), and an implement algorithm of the OPA is derived. Numerical results demonstrate that adopting the proposed power allocation algorithm, the capacity of MIMO relay channel with DF relay scheme can be significantly improved.

In this paper, we study the power allocation of suggested cognitive relay network model to minimize the system outage probability subject to total and individual power constraints for cognitive relays and subject to interference constraints for primary user nodes. In suggested model, a source is assisted by cognitive relay nodes which allow coexisting with primary user nodes by imposing severe constraints on the transmission power so that they operate below the noise floor of primary nodes. A relay transmission scheme, namely, amplify-and-forward (AF) is considered. We present an optimal power allocation (OPA) scheme to minimize the system outage probability, based on complete channel state information among the source, destination and relay nodes and mean channel gains between primary user nodes and cognitive relays. The analytical power allocation strategies have been validated through numerical simulations. The results indicate that the AF with OPA has significantly better outage behavior and average throughput than AF scheme.

In this paper, we consider simultaneous wireless information and energy transfer in an orthogonal-frequency-division-multiple-access decode-and-forward relay network, in which an energy-constrained relay node harvests energy from a source node and uses the harvested energy to forward information to multiple destination nodes. Our objective is to maximize the end-to-end sum rate by resource allocation, subject to transmit power constraint at the source and energy-harvesting (EH) constraint at the relay. A non-convex and mixed-integer programming (MIP) problem is formulated to optimize time-switching (TS) ratios of EH and information decoding at the relay, TS ratio of information transmission from relay to destinations, subcarrier allocation as well as power allocation (PA) over all subcarriers at source and relay. We propose to decouple this problem into a convex problem and an MIP problem in fractional form. To solve the MIP problem, we transform it into an equivalent optimization problem in subtractive form which has a tractable solution. As a result, we propose a novel scheme to achieve jointly optimal TS ratios, subcarrier allocation and PA. Simulation results verify the optimality of our proposed resource allocation scheme.

A two-hop multiple-input multiple-output (MIMO) relay network which comprises a multiple antenna source, an amplify-and-forward MIMO relay and many potential users are studied in this paper. Consider the achievable sum rate as the performance metric, a joint design method for the processing units of the BS and relay node is proposed. The optimal structures are given, which decompose the multiuser MIMO relay channel into several parallel single-input single-output relay channels. With these structures, the signal-to-noise ratio at the destination users is derived; and the power allocation is proved to be a convex problem. We also show that high sum rate can be achieved by pairing each link according to its magnitude. The sum rate of three broadcast strategies, time division multiple access (TDMA) to the strongest user, dirty paper coding (DPC), and beamforming (BF) are investigated. The sum rate bounds of these strategies and the sum capacity (achieved by DPC) gain over TDMA and BF are given. With these results, it can be easily obtained that how far away TDMA and BF are from being optimal in terms of the achievable sum rate.

In this paper, we focused on the achievable rate of multi-hop buffer-aided relay networks, where one source node is supposed to deliver message with the assistance of multi-hop buffer-aided relays to one destination node in a decode-and-forward manner. Unlike previous research efforts, not only buffer-aided transmission scheduling, but also adaptive power allocation at source node and all intermediate relays are taken into considerations to derive the theoretically achievable end-to-end rate. Analysis results showed that, both buffer-aided transmission strategy and optimal power allocations can significantly improve the end-to-end achievable rate.

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 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 letter, energy-efficient transmission and power allocation for fixed-gain amplify-and-forward relay networks with partial channel state information (CSI) are studied. In the energy-efficiency problem, the total power consumed is minimized while keeping the signal-to-noise-ratio (SNR) above a certain threshold. In the dual problem of power allocation, the end-to-end SNR is maximized under individual and global power constraints. Closed-form expressions for the optimal source and relay powers and the Lagrangian multiplier are obtained. Numerical results show that the optimal power allocation with partial CSI provides comparable performance as optimal power allocation with full CSI at low SNR.