Optimized constellations for two-way wireless relaying with physical network coding
01 Jun 2009-IEEE Journal on Selected Areas in Communications (Institute of Electrical and Electronics Engineers)-Vol. 27, Iss: 5, pp 773-787
TL;DR: The proposed modulation scheme can significantly improve end-to-end throughput for two-way relaying systems and is applicable to a relaying system using higher-level modulations of 16QAM in the MA stage.
Abstract: We investigate modulation schemes optimized for two-way wireless relaying systems, for which network coding is employed at the physical layer. We consider network coding based on denoise-and-forward (DNF) protocol, which consists of two stages: multiple access (MA) stage, where two terminals transmit simultaneously towards a relay, and broadcast (BC) stage, where the relay transmits towards the both terminals. We introduce a design principle of modulation and network coding, considering the superposed constellations during the MA stage. For the case of QPSK modulations at the MA stage, we show that QPSK constellations with an exclusive-or (XOR) network coding do not always offer the best transmission for the BC stage, and that there are several channel conditions in which unconventional 5-ary constellations lead to a better throughput performance. Through the use of sphere packing, we optimize the constellation for such an irregular network coding. We further discuss the design issue of the modulation in the case when the relay exploits diversity receptions such as multiple-antenna diversity and path diversity in frequency-selective fading. In addition, we apply our design strategy to a relaying system using higher-level modulations of 16QAM in the MA stage. Performance evaluations confirm that the proposed scheme can significantly improve end-to-end throughput for two-way relaying systems.
Citations
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03 Oct 2011
TL;DR: Numerical results with QPSK show that substantially higher rates are achievable with the proposed approach than those achievable by always using a fixed function or adapting the function at the relay but coding over GF(4).
Abstract: We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits the recovery of a class of functions at the relay. We define such a class of functions and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that substantially higher rates are achievable with our proposed approach than those achievable by always using a fixed function or adapting the function at the relay but coding over GF(4).
49 citations
Cites background from "Optimized constellations for two-wa..."
...The broadcast stage is fairly standard and is identical to that considered in [2], [3]....
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...In this paper, the complex channel coefficients hA and hB are assumed to be perfectly estimated at each receiver but unknown to each transmitter....
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TL;DR: It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a regions in which the choice of the network coding maps affects the performance.
Abstract: The design of modulation schemes for the physical layer network-coded two-way relaying scenario is considered with a protocol which employs two phases: multiple access (MA) phase and broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of MA interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, that this relationship can be used to get the network coding maps satisfying the exclusive law. The channel fade states for which the minimum distance of the effective constellation at the relay become zero are referred to as the singular fade states. For M- PSK modulation ( M any power of 2), it is shown that there are (M2/4- M/2+1 )M singular fade states. Also, it is shown that the constraints which the network coding maps should satisfy so that the harmful effects of the singular fade states are removed, can be viewed equivalently as partially filled Latin Squares (PFLS). The problem of finding all the required maps is reduced to finding a small set of maps for M- PSK constellations ( M any power of 2), obtained by the completion of PFLS. Even though the completability of M ×M PFLS using M symbols is an open problem, specific cases where such a completion is always possible are identified and explicit construction procedures are provided. Having obtained the network coding maps, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map chosen in a particular region. It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for 4-PSK signal set by Koike-Akino et al. when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by Koike-Akino et al.
49 citations
Cites background or methods from "Optimized constellations for two-wa..."
...6....
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...…to the same as the one obtained using computer search for 4-PSK signal set by Koike-Akino et al., when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by…...
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...12) Simulation results for 8-PSK signal set show that the proposed scheme performs better than the pure XOR network code and in some conditions outperforms the scheme proposed in [7] (see Section VIII)....
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...V. T. Muralidharan and B. S. Rajan are with the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560012, India (e-mail: tmvijay@ece.iisc.ernet.in; bsrajan@ece.iisc.ernet.in)....
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...It is shown in Section III that the problem of obtaining clusterings which remove all the singular fade states reduces to completing a finite number of PFLS, which completely avoids the problem of performing exhaustive search for an uncountably infinite number of values....
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Dissertation•
01 Jul 2013
TL;DR: In this article, the authors investigated the impact of the receiver on the BS total power consumption in direct transmission cellular networks and proposed a relay cooperation scheme for advanced relay-aided cellular networks.
Abstract: Wireless communication networks are traditionally designed to operate at high spectral efficiency with less emphasis on power consumption as it is assumed that endless power supply is available through the power grid where the cells are connected to. As new generations of mobile networks exhibit decreasing gains in spectral efficiency, the mobile industry is forced to consider energy reform policies in order to sustain the economic growth of itself and other industries relying on it. Consequently, the energy efficiency of conventional direct transmission cellular networks is being examined while alternative green network architectures are also explored. The relay-aided cellular network is being considered as one of the potential network architecture for energy efficient transmission. However, relaying transmission incurs multiplexing loss due to its multi-hop protocol. This, in turn, reduces network spectral efficiency. Furthermore, interference is also expected to increase with the deployment of Relay Stations (RSs) in the network. This thesis examines the power consumption of the conventional direct transmission cellular network and contributes to the development of the relay-aided cellular network. Firstly, the power consumption of the direct transmission cellular network is investigated. While most work considered transmitter side strategies, the impact of the receiver on the Base Station (BS) total power consumption is investigated here. Both the zero-forcing and minimum mean square error weight optimisation approaches are considered for both the conventional linear and successive interference cancellation receivers. The power consumption model which includes both the radio frequency transmit power and circuit power is described. The influence of the receiver interference cancellation techniques, the number of transceiver antennas, circuit power consumption and inter-cell interference on the BS total power consumption is investigated. Secondly, the spectral-energy efficiency trade-off in the relay-aided cellular network is investigated. The signal forwarding and interference forwarding relaying paradigms are considered with the direct transmission cellular network taken as the baseline. This investigation serves to understand the dynamics in the performance trade-off. To select a suitable balance point in the trade-off, the economic efficiency metric is proposed whereby the spectral-energy efficiency pair which maximises the economic profitability is found. Thus, the economic efficiency metric can be utilised as an alternative means to optimise the relay-aided cellular network while taking into account the inherent spectral-energy efficiency trade-off. Finally, the method of mitigating interference in the relay-aided cellular network is demonstrated by means of the proposed relay cooperation scheme. In the proposed scheme, both joint RS decoding and independent RS decoding approaches are considered during the broadcast phase while joint relay transmission is employed in the relay phase. Two user selection schemes requiring global Channel State Information (CSI) are considered. The partial semi-orthogonal user selection method with reduced CSI requirement is then proposed. As the cooperative cost limits the practicality of cooperative schemes, the cost incurred at the cooperative links between the RSs is investigated for varying degrees of RS cooperation. The performance of the relay cooperation scheme with different relay frequency reuse patterns is considered as well. In a nutshell, the research presented in this thesis reveals the impact of the receiver on the BS total power consumption in direct transmission cellular networks. The relayaided cellular network is then presented as an alternative architecture for energy efficient transmission. The economic efficiency metric is proposed to maximise the economic profitability of the relay network while taking into account the existing spectral-energy efficiency trade-off. To mitigate the interference from the RSs, the relay cooperation scheme for advanced relay-aided cellular networks is proposed. To my family & closest of friends
49 citations
TL;DR: A practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs) and exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS).
Abstract: We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs) In the proposed scheme, an irregular repeat–accumulate (IRA) MC over $\textrm{GF}(q)$ with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS) We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs For example, our designed codes over GF(7) and GF(3) with a code rate of 3/4 are within 1 and 12 dB of the TWRC capacity, respectively Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations
49 citations
Cites background or methods from "Optimized constellations for two-wa..."
...The main difficulty lies in that the existing multi-level coding (MLC) and bit-interleaved coded-modulation (BICM) schemes [10] based on binary channel codes do not exhibit the ambiguity-free mapping property [13]....
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...In the prime size field, the modulo-q addition and multiplication can be used as the addition and multiplication operators of the finite field, which can avoids the ambiguity problem [13]....
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...In [13], [14], the authors considered using an adaptive non-linear PNC modulation design method, which is difficult to be scalable for large constellations and has high computational complexity....
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TL;DR: This work focuses on a two-way denoise-and-forward relaying system using non-coherent Differential Binary Phase-Shift Keying (DBPSK) modulation, which has the well-defined relay denoising function when channel state information is unknown.
Abstract: This work focuses on a two-way denoise-and-forward relaying system using non-coherent Differential Binary Phase-Shift Keying (DBPSK) modulation, which has the well-defined relay denoising function when channel state information is unknown. We first design the relay denoising function and source decoders using Maximum Likelihood (ML) principles for the general case with K parallel relays. As the ML denoising function is hard to manipulate, we approximate it as a multi-user detector followed by a physical layer network coding encoder and obtain the closed-form relay decoding error. For the single-relay case, we show that the ML source decoder is actually equivalent to the typical DBPSK decoder for the relay-source channel and thus derive the exact end-to-end Bit Error Rate (BER). To minimize the average BER, we also investigate the power allocation problem by use of asymptotic analysis at high Signal-to-Noise Ratio (SNR). We show that the optimal source power is inversely proportional to the square root of the channel gain of the source-relay channel, and the optimal relay power decreases with SNR. For the multi-relay case, though the exact analysis is intractable, we develop upper bound and lower bound on BER and show that the diversity order is exactly ⌈κ/2⌉.
48 citations
Cites methods from "Optimized constellations for two-wa..."
...To optimize the end-to-end error performance, we shall also investigate the power allocation problem....
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References
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Book•
01 Jan 1991TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Abstract: Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
45,034 citations
"Optimized constellations for two-wa..." refers background in this paper
...Since Shannon firstly considered a two–way channel in [10], some theoretical investigations on the bidirectional relaying have emerged so far [ 11 ]....
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TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
Abstract: We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.
8,533 citations
"Optimized constellations for two-wa..." refers background in this paper
...W IRELESS network coding has recently received a lot of attention in research community, although the concept of network coding has been around for almost a decade [2]....
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Book•
01 Dec 1987
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Abstract: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.
4,564 citations
TL;DR: The results show that using COPE at the forwarding layer, without modifying routing and higher layers, increases network throughput, and the gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
Abstract: This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20-node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that using COPE at the forwarding layer, without modifying routing and higher layers, increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
2,190 citations
TL;DR: Two new half-duplex relaying protocols are proposed that avoid the pre-log factor one-half in corresponding capacity expressions and it is shown that both protocols recover a significant portion of the half- duplex loss.
Abstract: We study two-hop communication protocols where one or several relay terminals assist in the communication between two or more terminals. All terminals operate in half-duplex mode, hence the transmission of one information symbol from the source terminal to the destination terminal occupies two channel uses. This leads to a loss in spectral efficiency due to the pre-log factor one-half in corresponding capacity expressions. We propose two new half-duplex relaying protocols that avoid the pre-log factor one-half. Firstly, we consider a relaying protocol where a bidirectional connection between two terminals is established via one amplify-and-forward (AF) or decode-and-forward (DF) relay (two-way relaying). We also extend this protocol to a multi-user scenario, where multiple terminals communicate with multiple partner terminals via several orthogonalize-and-forward (OF) relay terminals, i.e., the relays orthogonalize the different two-way transmissions by a distributed zero-forcing algorithm. Secondly, we propose a relaying protocol where two relays, either AF or DF, alternately forward messages from a source terminal to a destination terminal (two-path relaying). It is shown that both protocols recover a significant portion of the half-duplex loss
1,728 citations
"Optimized constellations for two-wa..." refers background in this paper
...In [6, 18 ], the amplify–and–forward (AF) bidirectional relaying is introduced, where the terminal nodes simultaneously transmit to the relaying node, and subsequently the relay broadcasts the received signal after amplification....
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