Showing papers on "Relay published in 2010"

Improving Wireless Physical Layer Security via Cooperating Relays

Abstract: Physical (PHY) layer security approaches for wireless communications can prevent eavesdropping without upper layer data encryption. However, they are hampered by wireless channel conditions: absent feedback, they are typically feasible only when the source-destination channel is better than the source-eavesdropper channel. Node cooperation is a means to overcome this challenge and improve the performance of secure wireless communications. This paper addresses secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers. Three cooperative schemes are considered: decode-and-forward (DF), amplify-and-forward (AF), and cooperative jamming (CJ). For these schemes, the relays transmit a weighted version of a reencoded noise-free message signal (for DF), a received noisy source signal (for AF), or a common jamming signal (for CJ). Novel system designs are proposed, consisting of the determination of relay weights and the allocation of transmit power, that maximize the achievable secrecy rate subject to a transmit power constraint, or, minimize the transmit power subject to a secrecy rate constraint. For DF in the presence of one eavesdropper, closed-form optimal solutions are derived for the relay weights. For other problems, since the optimal relay weights are difficult to obtain, several criteria are considered leading to suboptimal but simple solutions, i.e., the complete nulling of the message signals at all eavesdroppers (for DF and AF), or the complete nulling of jamming signal at the destination (for CJ). Based on the designed relay weights, for DF in the presence of multiple eavesdroppers, and for CJ in the presence of one eavesdropper, the optimal power allocation is obtained in closed-form; in all other cases the optimal power allocation is obtained via iterative algorithms. Numerical evaluation of the obtained secrecy rate and transmit power results show that the proposed design can significantly improve the performance of secure wireless communications.

Practical physical layer network coding for two-way relay channels: performance analysis and comparison

Abstract: This paper investigates the performance of practical physical-layer network coding (PNC) schemes for two-way relay channels. We first consider a network consisting of two source nodes and a single relay node, which is used to aid communication between the two source nodes. For this scenario, we investigate transmission over two, three or four time slots. We show that the two time slot PNC scheme offers a higher maximum sum-rate, but a lower sum-bit error rate (BER) than the four time slot transmission scheme for a number of practical scenarios. We also show that the three time slot PNC scheme offers a good compromise between the two and four time slot transmission schemes, and also achieves the best maximum sum-rate and/or sum-BER in certain practical scenarios. To facilitate comparison, we derive new closed-form expressions for the outage probability, maximum sum-rate and sum-BER. We also consider an opportunistic relaying scheme for a network with multiple relay nodes, where a single relay is chosen to maximize either the maximum sum-rate or minimize the sum-BER. Our results indicate that the opportunistic relaying scheme can significantly improve system performance, compared to a single relay network.

Joint Physical Layer Coding and Network Coding for Bidirectional Relaying

Abstract: We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1/2 log(1 + snr) bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel. We show that, using lattice codes and lattice decoding, we can obtain a rate of 1/2 log(1/2 + snr) bits per transmitter, which is essentially optimal at high SNR. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1/2 log(1/2 + snr). The proposed scheme can be thought of as a joint physical-layer network-layer code which outperforms other recently proposed analog network coding schemes.

Capacity of the Gaussian Two-Way Relay Channel to Within ${1\over 2}$ Bit

Abstract: In this paper, a Gaussian two-way relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in full-duplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. Unlike conventional nested lattice codes, our codes utilize two different shaping lattices for source nodes based on a three-stage lattice partition chain, which is a key ingredient for producing the best gap-to-capacity results to date. Specifically, for all channel parameters, the achievable rate region of our scheme is within 1/2 bit from the capacity region for each user and its sum rate is within log3/2 bit from the sum capacity.

Cooperation With an Untrusted Relay: A Secrecy Perspective

Abstract: We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show, by means of the achievable secrecy rate based on compress-and-forward, that by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover-Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the source-destination link is not worse than the source-relay link, by matching with achievable rate we present.

Voluntary Energy Harvesting Relays and Selection in Cooperative Wireless Networks

Abstract: The use of energy harvesting (EH) nodes as cooperative relays is a promising and emerging solution in wireless systems such as wireless sensor networks. It harnesses the spatial diversity of a multi-relay network and addresses the vexing problem of a relay's batteries getting drained in forwarding information to the destination. We consider a cooperative system in which EH nodes volunteer to serve as amplify-and-forward relays whenever they have sufficient energy for transmission. For a general class of stationary and ergodic EH processes, we introduce the notion of energy constrained and energy unconstrained relays and analytically characterize the symbol error rate of the system. Further insight is gained by an asymptotic analysis that considers the cases where the signal-to-noise-ratio or the number of relays is large. Our analysis quantifies how the energy usage at an EH relay and, consequently, its availability for relaying, depends not only on the relay's energy harvesting process, but also on its transmit power setting and the other relays in the system. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results demonstrate how a system that uses EH relays differs in significant ways from one that uses conventional cooperative relays.

Optimal Distributed Beamforming for Two-Way Relay Networks

Abstract: In this paper, we consider a relay network which consists of two single-antenna transceivers and nr single-antenna relay nodes. Considering a two time slot two-way relaying scheme, each relay adjusts the phase and the amplitude of the mixture signal it receives from the two transceivers during the first time slot, by multiplying it with a complex beamforming coefficient. Then each relay transmits the so-obtained signal in the second time slot. Aiming at optimally calculating the beamforming coefficients as well as the transceiver transmit powers, we study two different approaches. In the first approach, we minimize the total transmit power (dissipated in the whole network) subject to two constraints on the transceivers' received signal-to-noise ratios (SNRs). We prove that such a power minimization technique has a unique solution. We also show that the optimal weight vector can be obtained through a simple iterative algorithm which enjoys a linear computational complexity per iteration. We also prove that for symmetric relaying schemes (where the two constraints on the transceiver SNRs are the same), half of the minimum total transmit power will be allocated to the two transceivers and the remaining half will be shared among the relaying nodes. In the second approach, we will study an SNR balancing technique. In this technique, the smaller of the two transceiver SNRs is maximized while the total transmit power is kept below a certain power budget. We show that this problem has also a unique solution which can be obtained through an iterative procedure with a linear computational complexity per iteration. We also prove that this approach leads to a power allocation scheme, where half of the maximum power budget is allocated to the two transceivers and the remaining half will be shared among all the relay nodes. For both approaches, we devise distributed schemes which require a minimal cooperation among the two transceivers and the relays. In fact, we show that both techniques can be implemented such that the bandwidth, required to obtain the beamforming weights in a distributed manner, remains constant as the size of the network grows.

Relay device for transferring information between a sensor system and a fluid delivery system

Abstract: A relay device transfers information between a sensor system, which measures a physiological characteristic level of a user, and a fluid delivery system, which infuses a fluid into a user. The relay device includes a sensor system receiver for receiving communications from the sensor system in a sensor system format. The relay device also includes a processor for processing the communications from the sensor system and converting the communications for transmission in a delivery system format. The relay device further includes a delivery system transmitter for transmitting the converted communications in the delivery system format to the fluid delivery system. The sensor system and delivery system formats may utilize different frequencies and/or different communication protocols for communications transmitted between the sensor system and the fluid delivery system through the relay device.

Noisy Network Coding

Abstract: A noisy network coding scheme for sending multiple sources over a general noisy network is presented. For multi-source multicast networks, the scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover and El Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The scheme involves message repetition coding, relay signal compression, and simultaneous decoding. Unlike previous compress--forward schemes, where independent messages are sent over multiple blocks, the same message is sent multiple times using independent codebooks as in the network coding scheme for cyclic networks. Furthermore, the relays do not use Wyner--Ziv binning as in previous compress-forward schemes, and each decoder performs simultaneous joint typicality decoding on the received signals from all the blocks without explicitly decoding the compression indices. A consequence of this new scheme is that achievability is proved simply and more generally without resorting to time expansion to extend results for acyclic networks to networks with cycles. The noisy network coding scheme is then extended to general multi-source networks by combining it with decoding techniques for interference channels. For the Gaussian multicast network, noisy network coding improves the previously established gap to the cutset bound. We also demonstrate through two popular AWGN network examples that noisy network coding can outperform conventional compress-forward, amplify-forward, and hash-forward schemes.

Multiuser Two-Way Amplify-and-Forward Relay Processing and Power Control Methods for Beamforming Systems

Abstract: In this paper, multiple-input multiple-output (MIMO) relay transceiver processing is proposed for multiuser two-way relay communications. The relay processing is optimized based on both zero-forcing (ZF) and minimum mean-square-error (MMSE) criteria under relay power constraints. Various transmit and receive beamforming methods are compared including eigen beamforming, antenna selection, random beamforming, and modified equal gain beamforming. Local and global power control methods are designed to achieve fairness among all users and to maximize the system signal-to-noise ratio (SNR). Numerical results show that the proposed multiuser two-way relay processing can efficiently eliminate both co-channel interference (CCI) and self-interference (SI).

Relay Attacks on Passive Keyless Entry and Start Systems in Modern Cars.

Abstract: We demonstrate relay attacks on Passive Keyless Entry and Start (PKES) systems used in modern cars. We build two efficient and inexpensive attack realizations, wired and wireless physical-layer relays, that allow the attacker to enter and start a car by relaying messages between the car and the smart key. Our relays are completely independent of the modulation, protocol, or presence of strong authentication and encryption. We perform an extensive evaluation on 10 car models from 8 manufacturers. Our results show that relaying the signal in one direction only (from the car to the key) is sufficient to perform the attack while the true distance between the key and car remains large (tested up to 50 meters, non line-of-sight). We also show that, with our setup, the smart key can be excited from up to 8 meters. This removes the need for the attacker to get close to the key in order to establish the relay. We further analyze and discuss critical system characteristics. Given the generality of the relay attack and the number of evaluated systems, it is likely that all PKES systems based on similar designs are also vulnerable to the same attack. Finally, we propose immediate mitigation measures that minimize the risk of relay attacks as well as recent solutions that may prevent relay attacks while preserving the convenience of use, for which PKES systems were initially introduced.

Subcarrier-pair based resource allocation for cooperative multi-relay OFDM systems

Abstract: In this paper, we study the joint allocation of three types of resources, namely, power, subcarriers and relay nodes, in multi-relay assisted dual-hop cooperative OFDM systems. All the relays adopt the amplify-and-forward protocol and assist the transmission from the source to destination simultaneously but on orthogonal subcarriers. The objective is to maximize the system transmission rate subject to individual power constraints on each node or a total network power constraint. We formulate such a problem as a subcarrier-pair based resource allocation that seeks the joint optimization of subcarrier pairing, subcarrier-pair-to-relay assignment, and power allocation. Using a dual approach, we solve this problem efficiently in an asymptotically optimal manner. Specifically, for the optimization problem with individual power constraints, the computational complexity is polynomial in the number of subcarriers and relay nodes, whereas the complexity of the problem with a total power constraint is polynomial in the number of subcarriers.We further propose two suboptimal algorithms for the former to trade off performance for complexity. Simulation studies are conducted to evaluate the average transmission rate and outage probability of the proposed algorithms. The impact of relay location is also discussed.

Performance analysis of adaptive decode-and-forward cooperative diversity networks with best-relay selection

Abstract: Cooperative diversity is a relatively new technique that can be used to improve the performance of the wireless networks. The main advantage of this technique is that the diversity gain can be achieved without the need to install multiple antennas at the transmitter or the receiver. In this paper, we investigate the performance of the best-relay selection scheme where the "best" relay only participates in the relaying. Therefore, two channels only are needed in this case (one for the direct link and the other one for the best indirect link) regardless of the number of relays (M). The best relay is selected as the relay node that can achieve the highest signal-to-noise ratio at the destination node. A general mathematical probability model is developed to study the outage performance of the best-relay selection adaptive decode-and-forward cooperative networks. In particular, closed-form expressions for the outage probability and average channel capacity are derived. Results show that the best-relay selection not only reduces the amount of required resources but also can maintain a full diversity order.

Fault-Tolerant Relay Node Placement in Heterogeneous Wireless Sensor Networks

Abstract: Existing work on placing additional relay nodes in wireless sensor networks to improve network connectivity typically assumes homogeneous wireless sensor nodes with an identical transmission radius. In contrast, this paper addresses the problem of deploying relay nodes to provide fault tolerance with higher network connectivity in heterogeneous wireless sensor networks, where sensor nodes possess different transmission radii. Depending on the level of desired fault tolerance, such problems can be categorized as: 1) full fault-tolerant relay node placement, which aims to deploy a minimum number of relay nodes to establish k(k ? 1) vertexdisjoint paths between every pair of sensor and/or relay nodes and 2) partial fault-tolerant relay node placement, which aims to deploy a minimum number of relay nodes to establish k(k ? 1) vertex-disjoint paths only between every pair of sensor nodes. Due to the different transmission radii of sensor nodes, these problems are further complicated by the existence of two different kinds of communication paths in heterogeneous wireless sensor networks, namely, two-way paths, along which wireless communications exist in both directions; and one-way paths, along which wireless communications exist in only one direction. Assuming that sensor nodes have different transmission radii, while relay nodes use the same transmission radius, this paper comprehensively analyzes the range of problems introduced by the different levels of fault tolerance (full or partial) coupled with the different types of path (one-way or two-way). Since each of these problems is NP-hard, we develop O(?k2)-approximation algorithms for both one-way and two-way partial fault-tolerant relay node placement, as well as O(?k3)-approximation algorithms for both one-way and two-way full fault-tolerant relay node placement (? is the best performance ratio of existing approximation algorithms for finding a minimum k-vertex connected spanning graph). To facilitate the applications in higher dimensions, we also extend these algorithms and derive their performance ratios in d-dimensional heterogeneous wireless sensor networks (d ? 3). Finally, heuristic implementations of these algorithms are evaluated via QualNet simulations.

IMT-advanced relay standards [WiMAX/LTE Update]

Abstract: There are two candidates for IMT-Advanced (4 G) standards, LTE-Advanced by 3 GPP and 802.16 m by IEEE. This article focuses on relay architectures in 16 m and LTE-A, and discusses design principles and trade-offs leading to decisions in each standards group. Basically, 16 m relay and LTE-A Release 10 relay are very similar technologies where the relay is essentially an orthogonal frequency-division multiple access base station with a wireless backhaul link. However, some open issues, such as mobility, power saving, multihop architecture, transparent relaying, multi-arrier transmission, and cooperative transmission, are still left as challenges for engineers and researchers. This article provides insights to both relay standards that could be helpful for readers to fully comprehend practical ways of incorporating relays into 4 G wireless broadband networks.

Degrees of Freedom of the MIMO Y Channel: Signal Space Alignment for Network Coding

Abstract: In this paper, we study a network information flow problem for a multiple-input-multiple-output (MIMO) Gaussian wireless network with three users each equipped with M antennas and a single intermediate relay equipped with N antennas. In this network, each user intends to convey independent messages for two different users via the intermediate relay while receiving two independent messages from the other two users. This is a generalized version of the two-way relay channel for the three-user case. We will call it a "MIMO Y channel." For this MIMO Y channel, we show that the capacity is 3M log(SNR) + o(log(SNR)) if N ≥ ⌈3M/2⌉ by using two novel signaling techniques, which are signal space alignment for network coding, and network-coding-aware interference nulling beamforming.

Ergodic Capacity Analysis of Amplify-and-Forward MIMO Dual-Hop Systems

Abstract: This paper presents an analytical characterization of the ergodic capacity of amplify-and-forward (AF) MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. In contrast to prior results, our expressions apply for arbitrary numbers of antennas and arbitrary relay configurations. We derive an expression for the exact ergodic capacity, simplified closed-form expressions for the high SNR regime, and tight closed-form upper and lower bounds. These results are made possible by employing recent tools from finite-dimensional random matrix theory, which are used to derive new closed-form expressions for various statistical properties of the equivalent AF MIMO dual-hop relay channel, such as the distribution of an unordered eigenvalue and certain random determinant properties. Based on the analytical capacity expressions, we investigate the impact of the system and channel characteristics, such as the antenna configuration and the relay power gain. We also demonstrate a number of interesting relationships between the dual-hop AF MIMO relay channel and conventional point-to-point MIMO channels in various asymptotic regimes.

Dual-hop systems with noisy relay and interference-limited destination

Abstract: In this letter, we analyze the outage performance of a dual-hop relay fading channel in an interference-limited environment. We first derive closed-form expressions for the outage probability of both the amplify-and-forward (AF) and the decode-and-forward (DF) relay channels, based on which, the diversity analysis is conducted. In addition, we show that in terms of the outage probability performance, the worst scenario appears to be the case with equal received-power interferers, for a given total received interference power.

Optimal Coordination of Directional Overcurrent Relays Considering Different Network Topologies Using Interval Linear Programming

Abstract: In real power systems, the network topology is subjected to uncertainty due to single-line outage contingencies, maintenance activities, and network reconfigurations. These changes in the network topology may lead to miscoordination of directional overcurrent relays (DOCRs). To overcome this drawback, corresponding to each primary/backup relay pair, a set of inequality coordination constraints which is related to different network topologies should be satisfied. In this paper, a new approach based on the interval analysis is introduced to solve the DOCRs coordination problem considering uncertainty in the network topology. The basic idea is to convert the set of inequality constraints corresponding to each relay pair to an interval constraint. In this situation, the DOCR coordination problem is formulated as an interval linear programming (ILP) problem. Using well-known mathematical theorems, the obtained ILP problem, which has no equality constraints, can be converted to standard linear programming (LP). As a result, the number of coordination constraints is significantly reduced in the proposed methods. The application of the proposed method to the IEEE 14- and 30-bus test systems proves the ability of the interval method in modeling topology uncertainty in the large-scale coordination problem.

Joint Optimization for One and Two-Way MIMO AF Multiple-Relay Systems

Abstract: This paper considers both one-way and two-way relaying systems with multiple relays between two terminal nodes where all nodes have multiple-input multiple-output (MIMO) antennas. We propose a unified algorithm which computes the optimal linear transceivers jointly at the source node and the relay nodes for amplify-and-forward (AF) protocols. First, optimization designs based on the sum-rate and the mean-square error (MSE) criteria are formulated for the two-way AF relaying channel. Due to non-convexity of the given problems, the proposed schemes iteratively identify local-optimal source and relay filters by deriving the gradients of the cost functions for a gradient descent algorithm. Then, the proposed algorithm can optimize a one-way multiple relay system as a special case of the two-way channel. Finally, we prove the global optimality of the maximum sum-rate scheme under an asymptotically large antenna assumption. From simulation results, it is confirmed that the proposed methods yield the near optimum result for the MIMO multiple relay channel even with a moderate number of antennas. Consequently, we show that the proposed algorithm outperforms conventional schemes in terms of the sum-rate and the error performance for both one-way and two-way protocols.

Metropolitan all-pass and inter-city quantum communication network

Abstract: We have demonstrated a metropolitan all-pass quantum communication network in field fiber for four nodes. Any two nodes of them can be connected in the network to perform quantum key distribution (QKD). An optical switching module is presented that enables arbitrary 2-connectivity among output ports. Integrated QKD terminals are worked out, which can operate either as a transmitter, a receiver, or even both at the same time. Furthermore, an additional link in another city of 60 km fiber (up to 130 km) is seamless integrated into this network based on a trusted relay architecture. On all the links, we have implemented protocol of decoy state scheme. All of necessary electrical hardware, synchronization, feedback control, network software, execution of QKD protocols are made by tailored designing, which allow a completely automatical and stable running. Our system has been put into operation in Hefei in August 2009, and publicly demonstrated during an evaluation conference on quantum network organized by the Chinese Academy of Sciences on August 29, 2009. Real-time voice telephone with one-time pad encoding between any two of the five nodes (four all-pass nodes plus one additional node through relay) is successfully established in the network within 60 km.

Opportunistic relay selection for cooperative networks with secrecy constraints

Abstract: This study deals with opportunistic relay selection in cooperative networks with secrecy constraints, where an eavesdropper node tries to overhead the source message. Previously reported relay selection techniques are optimised for non-eavesdropper environments and cannot ensure security. Two new opportunistic relay selection techniques, which incorporate the quality of the relay-eavesdropper links and take into account secrecy rate issues, are investigated. The first scheme assumes an instantaneous knowledge of the eavesdropper channels and maximises the achievable secrecy rate. The second one assumes an average knowledge of the eavesdropper channels and is a suboptimal selection solution appropriate for practical applications. Both schemes are analysed in terms of secrecy outage probability and their enhancements against conventional opportunistic selection policies are validated via numerical and theoretical results.

Performance Analysis of Two Hop Amplify-and-Forward Systems with Interference at the Relay

Abstract: We analyze the performance of a two hop channel state information (CSI)-assisted amplify-and-forward system, with co-channel interference at the relay. The system's outage probability and the average bit error rate (BER) in the presence of Rayleigh faded multiple interferers are investigated. We derive an exact expression for the outage probability and an accurate bound for the system's average BER. Simulation results show the validity of the analysis and point out the effect of interference.

Robust Joint Design of Linear Relay Precoder and Destination Equalizer for Dual-Hop Amplify-and-Forward MIMO Relay Systems

Abstract: This paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, with Gaussian random channel uncertainties in both hops. By taking the channel uncertainties into account, two robust design algorithms are proposed to minimize the mean-square error (MSE) of the output signal at the destination. One is an iterative algorithm with its convergence proved analytically. The other is an approximated closed-form solution with much lower complexity than the iterative algorithm. Although the closed-form solution involves a minor relaxation for the general case, when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix, no relaxation is needed and the proposed closed-form solution is the optimal solution. Simulation results show that the proposed algorithms reduce the sensitivity of the AF MIMO relay systems to channel estimation errors, and perform better than the algorithm using estimated channels only. Furthermore, the closed-form solution provides a comparable performance to that of the iterative algorithm.

Constrained relay node placement in wireless sensor networks: formulation and approximations

Abstract: One approach to prolong the lifetime of a wireless sensor network (WSN) is to deploy some relay nodes to communicate with the sensor nodes, other relay nodes, and the base stations. The relay node placement problem for wireless sensor networks is concerned with placing a minimum number of relay nodes into a wireless sensor network to meet certain connectivity or survivability requirements. Previous studies have concentrated on the unconstrained version of the problem in the sense that relay nodes can be placed anywhere. In practice, there may be some physical constraints on the placement of relay nodes. To address this issue, we study constrained versions of the relay node placement problem, where relay nodes can only be placed at a set of candidate locations. In the connected relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with a base station through a bidirectional path. In the survivable relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with two base stations (or the only base station in case there is only one base station) through two node-disjoint bidirectional paths. For each of the two problems, we discuss its computational complexity and present a framework of polynomial time O(1) -approximation algorithms with small approximation ratios. Extensive numerical results show that our approximation algorithms can produce solutions very close to optimal solutions.

Noisy network coding

Abstract: A new coding scheme for multicasting multiple sources over a general noisy network is presented. The scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover-El Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The key idea is to use block Markov message repetition coding and simultaneous decoding. Instead of sending multiple independent messages over several blocks and decoding them sequentially as in previous relaying schemes, the same message is sent multiple times using independent codebooks and the decoder performs joint typicality decoding on the received signals from all the blocks without explicitly decoding the compression indices. New results on semideterministic relay networks and Gaussian networks demonstrate the potential of noisy network coding as a robust and scalable scheme for communication over wireless networks.

Distributed Optimal Relay Selection in Wireless Cooperative Networks With Finite-State Markov Channels

Abstract: Relay selection is crucial in improving the performance of wireless cooperative networks. Most previous works for relay selection use the current observed channel conditions to make the relay-selection decision for the subsequent frame. However, this memoryless channel assumption is often not realistic given the time-varying nature of some mobile environments. In this paper, we consider finite-state Markov channels in the relay-selection problem. Moreover, we also incorporate adaptive modulation and coding, as well as residual relay energy in the relay-selection process. The objectives of the proposed scheme are to increase spectral efficiency, mitigate error propagation, and maximize the network lifetime. The formulation of the proposed relay-selection scheme is based on recent advances in stochastic control algorithms. The obtained relay-selection policy has an indexability property that dramatically reduces the computation and implementation complexity. In addition, there is no need for a centralized control point in the network, and relays can freely join and leave from the set of potential relays. Simulation results are presented to show the effectiveness of the proposed scheme.

Filter-and-Forward Distributed Beamforming in Relay Networks With Frequency Selective Fading

Abstract: A new approach to distributed cooperative beamforming in relay networks with frequency selective fading is proposed. It is assumed that all the relay nodes are equipped with finite impulse response (FIR) filters and use a filter-and-forward (FF) strategy to compensate for the transmitter-to-relay and relay-to-destination channels. Three relevant half-duplex distributed beamforming problems are considered. The first problem amounts to minimizing the total relay transmitted power subject to the destination quality-of-service (QoS) constraint. In the second and third problems, the destination QoS is maximized subject to the total and individual relay transmitted power constraints, respectively. For the first and second problems, closed-form solutions are obtained, whereas the third problem is solved using convex optimization. The latter convex optimization technique can be also directly extended to the case when the individual and total power constraints should be jointly taken into account. Simulation results demonstrate that in the frequency selective fading case, the proposed FF approach provides substantial performance improvements as compared to the commonly used amplify-and-forward (AF) relay beamforming strategy.

Tensor-Based Channel Estimation and Iterative Refinements for Two-Way Relaying With Multiple Antennas and Spatial Reuse

Abstract: Relaying is one of the key technologies to satisfy the demands of future mobile communication systems. In particular, two-way relaying is known to exploit the radio resources in a very efficient manner. In this contribution, we consider two-way relaying with amplify-and-forward (AF) MIMO relays. Since AF relays do not decode the signals, the separation of the data streams has to be performed by the terminals themselves. For this task both nodes require reliable channel knowledge of all relevant channel parameters. Therefore, we examine channel estimation schemes for two-way relaying with AF MIMO relays. We investigate a simple Least Squares (LS) based scheme for the estimation of the compound channels as well as a tensor-based channel estimation (TENCE) scheme which takes advantage of the special structure in the compound channel matrices to further improve the estimation accuracy. Note that TENCE is purely algebraic (i.e., it does not require any iterative procedures) and applicable to arbitrary antenna configurations. Then we demonstrate that the solution obtained by TENCE can be improved by an iterative refinement which is based on the structured least squares (SLS) technique. In this application, between one and four iterations are sufficient and consequently the increase in computational complexity is moderate. The iterative refinement is optional and targeted for cases where the channel estimation accuracy is critical. Moreover, we propose design rules for the training symbols as well as the relay amplification matrices during the training phase to facilitate the estimation procedures. Finally, we evaluate the achievable channel estimation accuracy of the LS-based compound channel estimation scheme as well as the tensor-based approach and its iterative refinement via numerical computer simulations.

Bandwidth and Power Allocation for Cooperative Strategies in Gaussian Relay Networks

Abstract: Achievable rates with amplify-and-forward (AF) and decode-and-forward (DF) cooperative strategies are examined for relay networks. Motivated by sensor network applications, power-constrained networks with large bandwidth resources and a large number of nodes are considered. It is shown that AF strategies do not necessarily benefit from the available bandwidth. Rather, transmitting in the optimum AF bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with the available network power. The optimum power allocation among the AF relays, shown to be a form of maximal ratio combining, indicates the favorable relay positions. Orthogonal node transmissions are also examined. While the same optimum bandwidth result still holds, the relay power allocation in this case can be viewed as a form of water-filling. In contrast, the DF strategy will optimally operate in the wideband regime and is shown to require a different choice of relays. Thus, in a large scale network, the choice of a coding strategy goes beyond determining a coding scheme at a node; it also determines the operating bandwidth, as well as the set of relays and best distribution of the relay power.