Parallel Relay Network Research Articles

DMT analysis and optimal scheduling for two-hop parallel relay networks

Two-hop parallel networks with half-duplex relays over quasi-static Rayleigh fading channels are considered. Assuming relays have only local channel state information, optimal communication schemes for these networks in terms of the diversity multiplexing trade-off (DMT) are obtained. It is shown that the dynamic quantize-map-and-forward (DQMF) and the static quantize-map-and-forward (SQMF) communication strategies achieve the optimal DMT at different ranges of the multiplexing gain. In the DQMF scheme, a relay sets its transmitting/listening times according to the instantaneous source-relay channel condition. However, in the SQMF scheme, a relay sets its transmitting/listening times to be a constant independent of the instantaneous source-relay channel gain. Essentially, we calculate the DMT of the network under the general setting for arbitrary average signal-to-noise ratios over links and it is shown that the DMT of the proposed schemes matches the upper bounds. Moreover, the optimal transmitting/listening times of the half-duplex relays as functions of the instantaneous channel realizations are derived for different communication strategies in the general setting. Finally, various simulation scenarios are considered and the DMT of the proposed schemes and the dynamic decode and forward communication strategy are compared.

Parallel Relay Network with Orthogonal Components: Capacity and Power Allocation

The authors consider a relay network in which the source-destination pair is augmented by a set of parallel relays. In this relay network, the source transmits to the destination and the relays over multiple orthogonal channel components. Practically, orthogonal channel components is motivated by the fact that a relay cannot receive and then transmit by using the same frequency band. For this relay network, lower bound on the capacity is shown to match the upper bound, and thus establish the capacity of the discrete memoryless physically degraded relay channel. Then, the capacity result is extended to the case of additive white Gaussian noise channel. Finally, rigorous simulation results are carried out to verify the analytical results.

Lossy Forwarding HARQ for Parallel Relay Networks

This paper proposes Lossy-Forwarding Hybrid Automatic Repeat reQuest (LF-HARQ) schemes to improve bit-error-rate, packet-error-rate and throughput performances of dual-hop wireless parallel relaying systems. In contrast to the conventional lossless decode-and-forward schemes, where erroneous packets are always discarded at the relay, we introduce Lossy-Forwarding concept to HARQ technique that allows the relay nodes to forward them to the next hop, referred to as Fully LF-HARQ (FLF-HARQ) scheme. We then propose Partially LF-HARQ (PLF-HARQ) scheme, where the relaying nodes select either forwarding the erroneous packets or requesting retransmission. The mode selection is based on the confidence indicator (CI) expressing the reliability of the received packets. Since the channels are assumed to suffer from block Rayleigh fading, the CI is calculated via online measurement of mutual information, block-by-block. Results of computer simulations to verify the superiority of the proposed techniques are presented.

New Soft-Encoding Relay (SoER) Mechanisms for Wireless Relay Systems: Convolutional and Turbo Constructions

A two-hop parallel-relay network is considered in this paper. Conventional schemes investigating the coding strategies at the relay(s) have largely focused on hard encoding, with the exception of one pioneering strategy that proposed a soft distributed encoding using the soft estimate (tanh-based) information. To fully harness the gain promised by soft encoding, this paper focuses on distributed soft encoding strategies at the relays. Unlike the previous work that favors the tanh form for soft encoding, we advocate the range-limited log-likelihood ratios (rLLR) as a better way for the relays to capture the reliability of the messages sent by the sender, and especially to further soft-encode these messages. Based on this, we develop a simple but effective soft-encoding relay (SoER) strategy that exploits the useful features of rLLR. Specifically, the close resemblance of rLLR to the tanh form allows us to derive a very simple convolutional encoding, and the piece-wise linearity of rLLR allows us to evaluate the codeword probability density function (PDF) analytically, which further allows us to derive a Viterbi decoding algorithm using a more precise PDF (in addition to the Gaussian-approximated Viterbi algorithm). We finally extend the nonrecursive convolutional SoER strategy to the turbo SoER strategy. Simulation results confirm the efficiency of the new proposed SoER schemes.

Opportunistic Noisy Network Coding for Fading Relay Networks Without CSIT

The parallel relay network is studied, in which a single source node sends a message to a single destination node with the help of $N$ parallel relays. Channel coefficients are assumed to vary over time and channel state information (CSI) is causally available only at the receiver side (CSIR). Opportunistic noisy network coding is proposed for intelligently exploiting CSIR at each relay in a distributed manner by operating the noisy network coding scheme with adaptive compression. More specifically, each relay opportunistically vector-quantizes the collection of received symbols that is received with channel gains larger than a certain threshold. It then forwards the digital compression information to the destination node using independently generated Gaussian codes. For independent and identically distributed (i.i.d.) Rayleigh fading, the proposed scheme is shown to achieve the ergodic capacity in the large number of relays regime. Furthermore, the proposed scheme is extensively compared with several alternative schemes, the decode-forward scheme, the adaptive amplify-forward scheme, and the non-adaptive noisy network coding scheme over geometric models. We show that the new proposed scheme provides significant gain over these schemes in various cases.

Delay Bounds for Random Linear Coding in Parallel Relay Networks

We consider the problem of transmitting a collection of packets from a source node to a destination node across a relaynetwork. We analyze a simple random network coding scheme where each node transmits a random linear combination of packets each time it has an opportunity to transmit. The main result of this paper is an upper bound on the expected time to transmit ageneration of packets across the network. We show that the expected time is bounded by the generation size divided by the capacityof the minimum cut separating the source from the destination, plus a term that grows as the square root of the generation size. We then use this bound to provide a queueing analysis of a strategy that dynamically creates generations as packets arrive in a queue at the network’s source node. To facilitate our analysis, we model the relay network by a continuous-time Markov chain. Our primaryanalytical tool is a general method for computing upper bounds on hitting times associated with continuous-time Markov chains. We believe that this approach also provides a method for analyzing transmission times associated with more general network topologies.

Approximate Secrecy Capacity of Gaussian Parallel Relay Networks

We consider a Gaussian relay network, which has to protect the message from a powerful eavesdropper, which has the possibility of listening to the transmitted signals on orthogonal channels. The secrecy capacity of the Gaussian network is approximated by considering the corresponding network in the deterministic discrete superposition model. Upper and lower bounds on the secrecy capacity are found in terms of the deterministic model, which are potentially easier to evaluate. We perform this evaluation for the particular topology of the parallel relay network, where the relays form a parallel layer between the source and the destination. By analyzing the deterministic model, we approximate the secrecy capacity within a constant gap. The approximation can be expressed just in terms of the channel gains of the network. It is therefore possible to deduct that the simple scheme of hiding the transmitted signals in noise is approximately optimal.

Optimal Amplify-and-Forward Scheme for Parallel Relay Networks with Correlated Relay Noise

This paper studies a parallel relay network where the relays employ an amplify-and-forward (AF) relaying scheme and are subjected to individual power constraints. We consider correlated effective relay noise arising from practical scenarios when the relays are exposed to common interferers. Assuming that the noise covariance and the full channel state information are available, we investigate the problem of finding the optimal AF scheme in terms of maximum end-to-end transmission rate. It is shown that the maximization problem can be equivalently transformed to a convex semi-definite program, which can be efficiently solved. Then an upper bound on the maximum achievable AF rate of this network is provided to further evaluate the performance of the optimal AF scheme. It is proved that the upper bound can be asymptotically achieved in two special regimes when the transmit power of the source node or the relays is sufficiently large. Finally, both theoretical and numerical results are given to show that, on average, noise correlation is beneficial to the transmission rate — whether the relays know the noise covariance matrix or not.

Opportunistic relaying with analogue and digital network coding for two‐way parallel relay network

A pair of terminals exchanging information via a layer of parallel relay nodes under slow fading is considered. Two protocols are proposed based on the combination of opportunistic relaying (OR) with analogue network coding (ANC), named ORANC, or with digital network coding (DNC), named ORDNC, respectively. Two schemes/versions of ORDNC, including 2-phase ORDNC (2P-ORDNC) and 3-phase ORDNC (3P-ORDNC) are proposed. Their outage performances are investigated. ORANC and 2P-ORDNC are proved to achieve optimal diversity-multiplexing tradeoff (DMT), whereas 3P-ORDNC is proved to be suboptimal. However, from diversity viewpoint only, all the above schemes are proven to achieve full diversity order. Simulation results verify the analysis, and show that 3P-ORDNC and ORANC shows advantage at low- and high-data rate regions, respectively.

Rematch-and-Forward: Joint Source–Channel Coding for Parallel Relaying With Spectral Mismatch

The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multiple-access channel from the relays to the final destination (decoder), where all noises are independent. This setup exhibits an inherent conflict between digital and analog relaying; while analog relaying [known as amplify-and-forward (AF however, it is limited to white channels of equal bandwidth. In this paper, we present a generalization of the analog approach to the case of bandwidth mismatch. Our strategy, coined rematch and forward (R&F), is based upon applying joint source-channel coding techniques that belong to a certain class of maximally analog schemes. Using such techniques, R&F converts the bandwidth of the broadcast section to that of the multiple-access section, creating an equivalent matched-bandwidth network over which A&F is applied. It is shown that this strategy exploits the full bandwidth of the individual channels, without sacrificing the coherence gain offered by A&F. Specifically, for given individual-link capacities, R&F remains within a constant gap from the network capacity for any number of relays and any bandwidth ratio between the sections. Finally, the approach is extended to the case of colored channels.

Soft forwarding technique for unitary space‐time modulation

The authors propose two soft forwarding schemes for unitary space-time modulation, namely estimate-and-forward (EF) and mutual information-based forwarding (MIF), which are ideally suited for rapid piecewise-constant fading scenarios with no channel state information both at transmitters and receivers. In the EF scheme, the relay regenerates signal via the conditional expectation of the source unitary space-time (UST) signal given the received matrix at the relay node instead of hard decisions. The MIF scheme employs the instantaneous mutual information between the source UST signal and received matrix at the relay node as a measurement for maximum-likelihood detection. The authors provide the relay forwarding functions, the normalisation factors, and the detection methods at the destination firstly. Above all, the generalised signal-to-noise ratio (SNR) at the destination for our unitary space-time modulated relaying system is analysed and simulated firstly. Simulation results reveal that the proposed EF and MIF schemes can outperform the existing amplify-and-forward (AF) and detect-and-forward (DF) schemes in terms of bit-error-rate performances in most scenarios. For a parallel relay network with two relays, the proposed EF scheme achieves 2 and 3 dB SNR gain over AF and DF schemes, respectively. Moreover, the MIF scheme can further give about 1.5 dB SNR gain.

Diversity-Multiplexing Tradeoff in Multiantenna Multirelay Networks: Improvements and Some Optimality Results

This paper investigates the benefits of amplify-and-forward (AF) relaying in the setup of multiantenna wireless networks. For this purpose, random sequential (RS) relaying is studied. It is shown that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better diversity-multiplexing tradeoff (DMT) as compared to the traditional AF relaying. First, the RS scheme is proved to achieve the optimum DMT for a multiantenna full-duplex single-relay two-hop network. Applying this result, a new achievable DMT is derived for the case of multiantenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multiantenna two parallel noninterfering half-duplex relays. Furthermore, random unitary matrix multiplication is shown to also improve the DMT of the nonorthogonal AF relaying scheme for the case of a multiantenna single relay channel. Finally, the general case of multiantenna full-duplex relay networks is studied. First, a new lower-bound is derived on its DMT using the RS scheme. Furthermore, maximum multiplexing gain of the network is also shown to be achievable by traditional amplify-forward relaying. The gain value is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes.

Achieving high diversity and multiplexing gains in the asynchronous parallel relay network

A single source-destination pair communicating via a layer of parallel relay nodes under quasi-static slow fading environment is investigated. The time delays from the source to the destination via different relays are assumed to be different. For such an asynchronous environment, a new transmission scheme is constructed so as to achieve better diversity-multiplexing tradeoff (DMT). More specifically, both the source and the destination adopts orthogonal frequency division multiplexing technique to solve the asynchronous problem; the relays cooperatively apply the distributed generalised complex orthogonal design, a form of orthogonal space–time coding, for high-rate transmission. Each relay is assumed to use the adaptive amplify-and-forward relaying strategy. To optimise its outage performance, a distributed on-off power control rule applied to the relays is analytically derived and is proved to yield full spatial diversity order. Compared with an existing protocol, our proposed scheme is shown to achieve the same DMT when there are four relay nodes and better DMT when there are more. Besides, the DMT gap between our scheme and the existing one increases with the number of relay nodes. Copyright © 2013 John Wiley & Sons, Ltd.

The Approximate Capacity of the Gaussian $N$-Relay Diamond Network

We consider the Gaussian “diamond” or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log4(N)) of capacity with preconstant in the order notation independent of the channel gains.

Joint source and relay optimization for parallel MIMO relay networks

Abstract In this article, we study the optimal structure of the source precoding matrix and the relay amplifying matrices for multiple-input multiple-output (MIMO) relay communication systems with parallel relay nodes. Two types of receivers are considered at the destination node: (1) The linear minimal mean-squared error (MMSE) receiver; (2) The nonlinear decision feedback equalizer based on the minimal MSE criterion. We show that for both receiver schemes, the optimal source precoding matrix and the optimal relay amplifying matrices have a beamforming structure. Using such optimal structure, joint source and relay power loading algorithms are developed to minimize the MSE of the signal waveform estimation at the destination. Compared with existing algorithms for parallel MIMO relay networks, the proposed joint source and relay beamforming algorithms have significant improvement in the system bit-error-rate performance.

A Game-Theoretic Approach to Anonymous Networking

Anonymous wireless networking is studied when an adversary monitors the transmission timing of an unknown subset of the network nodes. For a desired quality of service (QoS), as measured by network throughput, the problem of maximizing anonymity is investigated from a game-theoretic perspective. Quantifying anonymity using conditional entropy of the routes given the adversary's observation, the problem of optimizing anonymity is posed as a two-player zero-sum game between the network designer and the adversary: The task of the adversary is to choose a subset of nodes to monitor so that anonymity of routes is minimum, whereas the task of the network designer is to maximize anonymity by choosing a subset of nodes to evade flow detection by generating independent transmission schedules. In this two-player game, it is shown that a unique saddle-point equilibrium exists for a general category of finite networks. At the saddle point, the strategy of the network designer is to ensure that any subset of nodes monitored by the adversary reveals an identical amount of information about the routes. For a specific class of parallel relay networks, the theory is applied to study the optimal performance tradeoffs and equilibrium strategies. In particular, when the nodes employ transmitter-directed signaling, the tradeoff between throughput and anonymity is characterized analytically as a function of the network parameters and the fraction of nodes monitored. The results are applied to study the relationships between anonymity, the fraction of monitored relays, and the fraction of hidden relays in large networks.

Soft Information Relaying in Fading Channels

This letter considers the mutual information based soft forwarding (MIF) scheme for a memoryless parallel relay network in Rayleigh fading channels. The exact analytical expression for soft noise variance in Rayleigh fading channels is first given. A tight upper bound of the soft noise variance of the relayed signal and the input-output relationship at the relay is then derived. Furthermore, it is revealed that the MIF scheme in Rayleigh fading channels can achieve a full diversity order. Simulation results show that the MIF scheme yields about 0.8 - 1.8 dB signal-to-noise ratio (SNR) gains compared to the various full diversity-achieving schemes in the literature.

Using Superposition Codebooks and Partial Decode-and-Forward in Low-SNR Parallel Relay Networks

A new communication scheme for Gaussian parallel relay networks based on superposition coding and partial decoding at the relays is presented. Some specific examples are proposed in which two codebook layers are superimposed. The first level codebook is constructed with symbols from a binary or ternary alphabet while the second level codebook is composed of codewords chosen with Gaussian symbols. The new communication scheme is a generalization of decode-and-forward, amplify-and-forward, and bursty-amplify-and-forward. The asymptotic low SNR regime is studied using achievable rates and minimum energy-per-bit as performance metrics. It is shown that the new scheme outperforms all previously known schemes for some channels and parameter ranges.

The Impact of Incomplete Information on Games in Parallel Relay Networks

This paper considers the impact of incomplete information on incentives for node cooperation in parallel relay networks with one source node, one destination node, and multiple relay nodes. All nodes are selfish and strategic, interested in maximizing their own profit instead of the social welfare. The paper considers the practical situation where the channel state on any given relay path is not observable to the source or to the other relays. Different bargaining relationships between the source and the relays are considered, and a framework for studying the efficiency loss induced by incomplete information is proposed. The source of the efficiency loss is analyzed, and the amount of inefficiency which results is quantified.

Cooperative Transmission for a Vector Gaussian Parallel Relay Network

In this paper, we consider a parallel relay network where two relays cooperatively help a source transmit its message to a destination. We assume the source and the destination nodes are equipped with multiple antennas. Three basic schemes and their achievable rates are studied: Decode-and-Forward (DF), Amplify-and-Forward (AF), and Compress-and-Forward (CF). For the DF scheme, the source transmits two private signals, one for each relay, where dirty paper coding (DPC) is used between the two private streams, and a common signal for both relays. The relays make efficient use of the common information to introduce a proper amount of correlation in the transmission to the destination. We show that the DF scheme achieves the capacity under certain conditions. We also show that the AF and CF schemes are asymptotically optimal in the high relay power limit if the relays-to-destination channel is full rank. The relative advantages of the three schemes are discussed with numerical results.