The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized.
The original motivation for the compute-and-forward strategy was the possibility of relaying in a multi-hop network while avoiding the harmful effects of interference between users (by decoding linear combinations) as well as noise accumulation (by decoding at every relay). Several works have investigated and improved upon the performance of the original compute-and-forward framework in the context of multi-hop relaying @cite_73 @cite_25 @cite_85 @cite_42 @cite_62 @cite_76 . Our expanded framework can improve performance further by permitting relays to employ unequal powers and decode multiple linear combinations when appropriate. Following the conference publication of this work, Tan al @cite_9 noted that our proposed message representation may be inefficient for multi-hop relaying if each relay naively treats a linear combination over @math as @math information symbols for the next hop. They proposed a lattice-based solution to this issue. It is also possible to resolve this issue directly over the message representation by having each relay only use some of its @math received symbols as information symbols for the next hop. See [Section III.F] ncncarxiv for details.
@cite_62 @cite_9 @cite_85 @cite_42 @cite_76 @cite_73 @cite_25
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The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized. In this paper, a point-to-point orthogonal-frequency- division multiplexing (OFDM) system with a decode-and- forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus, each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate and outperform the existing methods in various channel conditions. This paper introduces and analyzes relaying techniques that increase the achievable throughput in multi-hop wireless networks by applying network coding over bi-directional traffic flows. We term each such technique as bi-directional amplification of throughput (BAT)-relaying. While network coding is normally performed by combining decoded packets, here we introduce a relaying method based on amplify-and-forward (AF), where the relay node utilizes the inherent combining of packets provided by simultaneous transmissions over a multiple access channel. Under low noise levels, AF BAT-relaying offers a superior throughput performance. The unconventionality of AF BAT relaying opens many possibilities for further research. This paper investigates the impact of inter-user non-orthogonality and asynchronous communication on the information-outage probability performance of multi-user decode-and-forward (DF) cooperative diversity in a code-division multiple-access (CDMA) uplink. Each user in the proposed system transmits its own data towards the base station and also serves as a relay for other users. We assume full-duplex communication so that each user can transmit and receive simultaneously at the same frequency. Each user attempts to decode the messages of a plurality of other users and forwards the superposition of multiple re-encoded and re-spread messages. Our cooperative scheme employs a sub-optimum decorrelating receiver to suppress the multi-user interference at both the base station and the relay-side. We evaluate the information-outage probability performance of the proposed scheme in an underloaded, fully-loaded and overloaded CDMA uplink. We consider combining schemes at the base station where the source information is code combined with the relayed information, while the information from multiple relays is either code combined or diversity combined. Under the system parameters contemplated in this paper, diversity combining of the relayed information is nearly as good as code combining because of the associated probabilities of decoding at the relays. We then examine the effect of using practical modulation formats on the information-outage probability performance of the proposed DF multi-user sharing scheme under diversity combining. We see that the performance loss due to modulation constraints and the use of diversity combining instead of code combining is relatively small. We consider a two-hop relaying network in which orthogonal frequency division multiplexing (OFDM) is employed for the source-to-destination, the source-to-relay and the relay- to-destination links. Amplify-and-forward (AF) and decode-and- forward (DF) policies are both discussed with or without two-hop diversity, respectively, for the relaying network with a sum-power constraint. An unified approach is used for optimal power allocation in the four different relaying scenarios. First, equivalent channel gains are developed for any given subcarrier pair in each scenario, and then optimal power allocation can be obtained by applying the classic water-filling method. Moreover, we provide the proof to the optimality of sorted subcarrier pairing for AF and DF relaying without diversity, which, combined with optimal power allocation, can offer further performance gain. This paper considers relaying techniques that increase the achievable throughput in multi-hop wireless networks by taking advantage of the bi-directional traffic flow. Such a relaying technique is termed relaying with Bi-directional Amplification of Throughput (BAT-relaying). The BAT-relaying is utilizing the concept of anti-packets, defined for bi-directional traffic flows. The relay node combines the anti-packets that are destined for different nodes and broadcasts the combined packet. Two BAT-relaying techniques have been proposed previously, Decode-and-Forward (DF) BAT-relaying and Amplify-and-Forward (AF) BAT-relaying. While in DF the relay node combines the packets by an XOR operation, AF BAT-relaying utilizes the inherent packet combining provided by the multiple access channel. In an errorless channel, AF has always higher achievable throughput than DF, but in noisy channels the noise amplification can severely degrade the performance of AF. In this paper we introduce a new scheme for BAT-relaying, termed Denoise-And-Forward (DNF) BAT-Relaying. The DNF BAT-relaying also makes use of the combining provided by the multiple access channel, but it removes the noise from the combined anti-packets before broadcasting to the destinations. While in the noiseless channel DNF and AF offer the same throughput performance which is superior to DF BAT-relaying, in large regions of the lower SNR values DNF BAT-relaying has the best throughput performance of all three schemes. Due to the unconventional nature of the BAT-relaying schemes, there are many open issues for further investigation. The design of a practical DNF scheme concerns several protocol layers, including modulation and coding. We consider transmission of packets in two-hop wireless ad hoc networks in which relay nodes are deployed between the source-destination pairs. Based on results from extreme value theory and product tails, we derive throughput scaling laws when opportunistic relay selection is performed. Assuming partial channel state information at each transmitter (CSIT) and decode- and-forward, half-duplex relays, we investigate how the per-hop throughput depends on the channel gain asymptotic distribution and the relay deployment. In dense networks with lambda t nodes per m 2 and fixed relay distances, we provide specific scaling laws for Rayleigh, lognormal, and Weibull fading, showing that the throughput is upper bounded by thetas(radic(lambda t )). Interestingly, with variable relay distances and location-aware relay selection, we analytically show that regularly varying channel distributions result in enhanced multi-relay diversity gain, achieving linear throughput scaling thetas(radic(lambda t )). Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information. We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the functional-decode-forward coding strategy, the relay decodes functions of the users' messages without needing to decode individual messages. The functions to be decoded by the relay are defined such that when the relay broadcasts the functions back to the users, every user is able to decode the messages of all other users. We consider a frequency-flat fading multihop network with a single active source-destination pair terminals communicating over multiple hops through a set of intermediate relay terminals. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) for a simple communication protocol based on time-division decode-and-forward relaying in meaningful asymptotic regimes of signal-to-noise ratio (SNR) under a system-wide power constraint on source and relay transmissions. The impact of multi-hopping and channel fading on the key performance measures of the high and low SNR regimes is investigated to shed new light on the possible enhancements in power bandwidth efficiency and link reliability. In contrast to the common belief that in fading environments communicating over multiple hops suffers significantly in performance due to the worst link limitation, our results indicate that hopping could significantly improve the outage behavior over slow-fading networks and stabilize links against the random channel fluctuations. In particular, we prove that there exists an optimal number of hops that minimizes the end-to-end outage probability and characterize the dependence of this optimal number on the fading statistics and target energy and spectral efficiencies. Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for two-hop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decode-and-forward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closed-form jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)-based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVD-based cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming. For a centralized encoder and decoder, a channel matrix is simply a set of linear equations that can be transformed into parallel channels. We develop a similar approach to multi-user networks: we view interference as creating linear equations of codewords and that a receiverpsilas goal is to collect a full rank set of such equations. Our new relaying technique, compute-and-forward, uses structured codes to reliably compute functions over channels. This allows the relays to efficiently recover a linear functions of codewords without recovering the individual codewords. Thus, our scheme can work with the structure of the interference while removing the effects of the noise at the relay. We apply our scheme to a Gaussian relay network with interference and achieve better rates than either compress-and-forward or decode-and-forward for certain regimes. In order to adapt to time-varying wireless channels, various channel-adaptive schemes have been proposed to exploit inherent spatial diversity in mobile wireless ad hoc networks where there are usually alternate next-hop relays available at a given forwarding node. However, current schemes along this line are designed based on heuristics, implying room for performance enhancement. To seek a theoretical foundation for improving spatial diversity gain, we formulate the selection of the next-hop as a sequential decision problem and propose a general "optimal stopping relaying (OSR)" framework for designing such next-hop diversity schemes. As a particular example, assuming Rayleigh fading channels, we implement an OSR strategy to optimize information efficiency (IE) in a protocol stack consisting of greedy perimeter stateless routing (GPSR) and IEEE 802.11 MAC protocols. We present mathematical analysis of the proposed OSR together with other strategies in literature for a single forwarding node. In addition, we perform extensive simulations (using QualNet) to evaluate the end-to-end performance of these relaying strategies in a multi-hop network. Both the mathematical and simulation results demonstrate the superiority of OSR over other existing schemes. We consider a time-slotted two-hop wireless system in which the sources transmit to the relays in the even time slots (first hop) and the relays forward the packets to the destinations in the odd time slots (second hop). Each source may connect to multiple relays in the first hop. In the presence of interference and without tight coordination of the relays, it is not clear which relays should transmit the packet. We propose four decentralized methods of relay selection, some based on location information and others based on the received signal strength (RSS).We provide a complete analytical characterization of these methods using tools from stochastic geometry. We use simulation results to compare these methods in terms of end-to-end success probability. We consider multi-hop OFDM relaying systems employing either decode-and-forward (DF) or amplify-and-forward (AF) relaying protocols in this paper. We propose adaptive power allocation (PA) algorithms under joint transmit power constraint at source and relays in order to maximize system capacity with channel state information (CSI) known at all nodes. The paring of subcarriers is also discussed. Simulation results show that the proposed adaptive PA algorithms achieve higher system capacity than uniform PA algorithms. If paring techniques are employed, system capacity can be further enhanced. We consider a dual-hop wireless network where an energy constrained relay node first harvests energy through the received radio-frequency signal from the source, and then uses the harvested energy to forward the source's information to the destination node. The throughput and delay metrics are investigated for a decode-and-forward relaying mechanism at finite blocklength regime and delay-limited transmission mode. We consider ultra-reliable communication scenarios under discussion for the next fifth-generation of wireless systems, with error and latency constraints. The impact on these metrics of the blocklength, information bits, and relay position is investigated. This paper investigates performance limits of a two-hop multi-antenna amplify-and-forward (AF) relay system in the presence of a multi-antenna energy harvesting receiver. The source and relay nodes of the two-hop AF system employ orthogonal space-time block codes for data transmission. We derive joint optimal source and relay precoders to achieve different tradeoffs between the energy transfer capability and the information rate, which are characterized by the boundary of the so-called rate-energy (R-E) region. Numerical results demonstrate the effect of different parameters on the boundary of the R-E region. Abstract Recently, unmanned aerial vehicles (UAVs) acting as relay platforms have attracted considerable attention due to the advantages of extending coverage and improving connectivity for long-range communications. Specifically, in the scenario where the access point (AP) is mobile, a UAV needs to find an efficient path to guarantee the connectivity of the relay link. Motivated by this fact, this paper proposes an optimal design for beamforming (BF) and UAV path planning. First of all, we study a dual-hop amplify-and-forward (AF) wireless relay network, in which a UAV is used as relay between a mobile AP and a fixed base station (BS). In the network, both of the AP and the BS are equipped with multiple antennas, whereas the UAV has a single antenna. Then, we obtain the output signal-to-noise ratio (SNR) of the dual-hop relay network. Based on the criterion of maximizing the output SNR, we develop an optimal design to obtain the solution of the optimal BF weight vector and the UAV heading angle. Next, we derive the closed-form outage probability (OP) expression to investigate the performance of the dual-hop relay network conveniently. Finally, computer simulations show that the proposed approach can obtain nearly optimal flying path and OP performance, indicating the effectiveness of the proposed algorithm. Furthermore, we find that increasing the antenna number at the BS or the maximal heading angle can significantly improve the performance of the considered relay network. The multi-user communication channel, in which multiple users exchange information with the help of a single relay terminal, called the multi-way relay channel, is considered. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal is the enabler of communication. A relevant metric to study in this scenario is the symmetric rate achievable by all users, which we identify for amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF) protocols. We also present an upper bound for comparison. The two extreme cases, namely full data exchange, in which every user wants to receive messages of all other users, and pairwise data exchange, consisting of multiple two-way relay channels, are investigated and presented in detail. We consider a two-hop relay model in which multiple sources communicate with a single destination via multiple distributed relays. We propose an asymmetric Compute-and-Forward (CoF) scheme that allows lattice coding with different coarse and fine lattices at the sources. The proposed scheme is motivated by the observation that, in an asymmetric CoF system, a higher transmission power at a source does not necessarily translate to a higher achievable information rate. We show that significant performance enhancement can be achieved by optimizing the transmission powers of the sources below their respective budgets. Further, the asymmetric construction of lattice coding allows the relays to conduct different modulo operations to reduce their forwarding rates, thereby supporting higher rates at the sources. However, modulo operations in general incur information loss, and so need to be carefully designed to ensure that the destination can successfully recover the source messages. As such, we propose a novel successive recovering algorithm for decoding at the destination, and establish sufficient conditions to guarantee successful recovery. Numerical results are provided to verify the superiority of our proposed scheme over other schemes.