About this Journal Submit a Manuscript Table of Contents
ISRN Communications and Networking
Volume 2011 (2011), Article ID 186783, 8 pages
doi:10.5402/2011/186783
Research Article

Energy-Efficient Relaying Strategy with Network Coding in Two-Way Parallel Channels

1Research Institute of Information Technology, Tsinghua University, Beijing 100084, China
2Communication Systems, Royal Institute of Technology (KTH), 16440 Stockholm, Sweden

Received 25 November 2010; Accepted 11 January 2011

Academic Editor: A. Maaref

Copyright © 2011 Ning Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a two-way communication assisted by parallel regenerative decode-and-forward relays operating in orthogonal channels. In a system with limited channel state information at each source and relay node, an optimum distributed power allocation strategy is proposed to minimize the total transmit power, providing a target signal-to-noise ratio at each destination with a target outage probability. Moreover, combined with opportunistic relaying and network coding, a distributed decision mechanism is proposed for the relay node to decide whether to help the transmission or not. In this proposal, each source works out the transmit power and the decision threshold then broadcasts them. The selected relay compares the decision threshold with the channel gain of its weaker relay-to-destination link, then determines whether to forward the networkcoded data or not. Simulation results show the advantage of this strategy in terms of energy efficiency for a two-hop two-way communication scenario. The proposed strategy is very flexible as it can trade outage to power consumption and vice versa.

1. Introduction

Wireless relaying offers space diversity to extend the transmission range and to enhance end-to-end transmission performance such as outage probability and data rate. In conventional single link communication, the transmission between the source and the destination suffers from severe fading due to multipath fading effects and path loss, which results in unreliable communication. Fortunately, relays can provide cooperative diversity [1], and save power to improve the reliability without the need of physical antenna arrays. Recently, some works such as [24] introduced network coding [5] to the bidirectional cooperation. Especially, [2, 3] focus on the bit-level transmission, and working out the optimum system throughput provided that both the two source-to-relay channels are better than the direct channel between the two sources in the three-node model. As shown in Figure 1, two source nodes (𝑆1 and 𝑆2) exchange messages with the help of a relay (namely, 𝑅), using time-division scheme in two-way communications. The traditional method [2] needs four phases (Figure 1(a)) to complete the exchange of information. However, by using network coding (a bitwise XOR operation at the relay node), only three phases are needed (Figure 1(b)). In such a three-phase relaying scheme, the messages from 𝑆1 and 𝑆2 are first decoded at the relay node, network coded, re-encoded, and then sent as one message to both destinations simultaneously. Here in this paper, we extend the three-node case to the scenario in which there are multiple relay candidates that could assist the source nodes in the two-way communication as shown in Figure 2.

fig1
Figure 1: (a) Traditional relaying; (b) three-phase relaying.
186783.fig.002
Figure 2: Two-way communication with multiple candidates.

When there are multiple relay node candidates, the multiple relays could simultaneously assist the transmission [68], or the most suitable single relay could be selected for transmission according to the channel state information (CSI). This opportunistic idea is based on instantaneously selecting an “on-peak” receiver with the “good” channel condition to improve system performance [912]. These works focused on the multirelay transmission in one-way transmissions (i.e., the messages are sent from 𝑆1 to 𝑆2, but no messages come from 𝑆2 to 𝑆1). Meanwhile, they assume that either the destination cannot directly receive the signals from the source [9], or that the complete CSI of all communication channels can be available at the source node [10, 12].

In addition, from the control mechanism's point of view, the cooperative strategies can be categorized into two types: central control strategy and distributed strategy. In most cases of practical systems, the distributed strategy is more practical since it only needs local and partial CSI, which overcomes the obstacles of a centralized architecture such as the substantial feedback requirements, overhead and delay, and so forth. For example, in [13], users select cooperation partners based on a priority list in a distributed manner for multiuser networks with coded cooperation. Reference [14] provides a relay selection algorithm based on instantaneous channel measurements obtained by each relay node locally, which reduces the cooperative costs among relays work in but only the one-way transmission is considered in [8, 13, 14].

Especially in [8], several optimum distributed power allocation strategies minimize the total transmit power while providing a target signal-to-noise ratio at the destination with a target outage probability. Due to the one-way transmission, [8] only needs to consider the relay-to-destination link after the relays successfully decode the messages. When network coding is introduced to decrease the transmission phases in two-way communications, as shown in Figure 1(b), the outage probability should be investigated on both 𝑅𝑆1 and 𝑅𝑆2 links in the third transmission phase after the relay has correctly decoded the messages from the two source nodes.

In this paper, our design target is to maximize power efficiency in two-way relay systems. Due to the limited knowledge of CSI at both source nodes, our distributed strategy mainly focuses on the forwarding decision and distributed power allocation. Firstly, a single relay node will be chosen as the opportunistic relay. Then, the opportunistic relay makes a decision whether to forward the source data according to a proper forwarding threshold. Moreover, the distributed power allocation based on the decode-and-forward (DaF) scheme [15] works out the corresponding transmit powers (𝑃𝑆1,𝑃𝑆2) and the forwarding threshold (𝛼𝑡) at the source nodes. The source nodes broadcast the optimum pair ((𝑃𝑆1,𝛼𝑡) and (𝑃𝑆2,𝛼𝑡)) to be used by the relay nodes.

The remainder of this paper is organized as follows. The next section describes the system model. The analysis of the distributed strategy is performed in Section 3. Simulation results can be found in Section 4. Finally, concluding remarks are given in Section 5.

2. System Model and Background

As shown in Figure 2, we consider a relay network consisting of an 𝑆1𝑆2 two-way pair and 𝑀 relay nodes employing DaF. For simplicity, we denote relay 𝑖 by 𝑅𝑖. We assume that the relaying operates in orthogonal time-division channels. Let 1𝑖 and 2𝑖 denote the fading coefficient of the 𝑆1𝑅𝑖 and 𝑅𝑖𝑆2 channels for the 𝑖th relay node, respectively, 𝑖=1,,𝑀. The fading coefficient of the 𝑆1𝑆2 link is denoted by 0. Assume that each channel is slowly varying flat fading, and {1𝑖,2𝑖,0} are all independent realizations of zero-mean complex Gaussian random variables with variance 𝜎21𝑖, 𝜎22𝑖 and 𝜎20, respectively. We define 𝛽1𝑖=1/𝜎21𝑖, 𝛽2𝑖=1/𝜎22𝑖, and 𝛽0=1/𝜎20.

Firstly, the relay selection is prior to the forwarding decision and the distributed power allocation. That is, in the opportunistic relaying, the “good” relay is chosen prior to the transmission among a collection of 𝑀 possible candidates and source nodes. As shown in Figure 1(b), in the first transmission phase, 𝑆1 broadcasts 𝑋1 with power 𝑃𝑆1, then 𝑆2 broadcasts 𝑋2 with power 𝑃𝑆2. The corresponding destinations (i.e., 𝑆2 node and 𝑆1 node) observe 𝑦2 and 𝑦1 as𝑦2=𝑃𝑆10𝑋1+𝑍2,𝑦1=𝑃𝑆20𝑋2+𝑍1,(1) and the opportunistic relay 𝑅𝑟 observes 𝑦1𝑟 from the 𝑆1𝑅𝑟 link and 𝑦2𝑟 from the 𝑆2𝑅𝑟 as𝑦1𝑟=𝑃𝑆11𝑟𝑋1+𝑍1𝑟,𝑦2𝑟=𝑃𝑆22𝑟𝑋2+𝑍2𝑟,(2) where 𝑍2, 𝑍1, 𝑍1𝑟, and 𝑍2𝑟 are additive white Gaussian noise (AWGN) terms at the corresponding destinations and the selected relay, respectively. Without loss of generality, they are of variance 𝑁0.

The opportunistic relay is chosen based on the following criterion: 𝑖||=min1𝑖||2,||2𝑖||2,𝑖=1,,𝑀,𝑟=argmax𝑖𝑖,(3) which is similar to that in [9, 16].

That is, a single “good” relay is selected based on the end-to-end instantaneous wireless channel conditions from the 𝑀 relay candidates to act as the cooperative partner. Among the 𝑀 relay candidates, the relay node that maximizes 𝑖 is defined as the “good” relay 𝑅𝑟. We denote min{|1𝑟|2,|2𝑟|2} by 𝐴𝑟. We use this relay selection criterion because the quality of the signals received by each destination depends on the quality of the weaker link [16]. Assume this opportunistic relay node can decode 𝑋1 and 𝑋2 correctly when its received signal-to-noise ratio (SNR) from 𝑆1 and 𝑆2 satisfiesΓ1𝑟=𝑃𝑆1||1𝑟||2𝑁0𝛾target,Γ2𝑟=𝑃𝑆2||2𝑟||2𝑁0𝛾target,(4) where 𝛾target is the given SNR constraint for correctly decoding. By using network coding, a bitwise XOR operation at the selected relay node encodes the messages from both 𝑆1 and 𝑆2, then the encoded messages are sent to each destination node where 𝑆1 and 𝑆2 could get the desired messages by performing an XOR operation [5]. Thus, it only needs three phases (Figure 1(b)). The destination processes, the messages from the source, and the relay jointly when the decoder operates with log likelihood ratios [2] to achieve the performance gain of maximal ratio combining (MRC). Then, the received SNR at the destination 𝑆2 is Γ2=𝑃𝑆1||0||2+𝑃𝑟||2𝑟||2𝑁0.(5) And the resulting SNR at the destination 𝑆1 is Γ1=𝑃𝑆2||0|2+𝑃𝑟||1𝑟|2𝑁0.(6)

Assume each destination can correctly receive the source data whenever Γ2𝛾target and Γ1𝛾target. Based on the assumption above, the problem of power efficiency for DaF relay networks with parallel channels can be modeled as in Problem (𝑄1): min{PS1,PS2,Pr,𝛾}𝑃𝑆1+𝑃𝑆2+𝑃𝑟𝑃subjectto𝑆1||0||2+𝑃𝑟||2𝑟||2𝑁0𝛾target𝑃𝑆2||0||2+𝑃𝑟||1𝑟||2𝑁0𝛾target𝑃𝑆1||1𝑟||2𝑁0𝛾target𝑃𝑆2||2𝑟||2𝑁0𝛾target.(𝑄1)

Since the traditional two-way relaying is decomposed into two one-way transmissions (Figure 1(a)), the optimum power allocation strategy for one-way transmission in DaF relay networks [8] is briefly restated as follows. Assume the one-way transmission is from 𝑆1 to 𝑆2, then [8] works out the optimum power 𝑃𝑆1 and the forwarding threshold 𝛼𝑡𝑃𝑆1 can only be one of 𝑀+1 discrete values {𝛾target𝑁0/|0|2, 𝛾target𝑁0/|11|2, 𝛾target𝑁0/|12|2,,𝛾target𝑁0/|1𝑀|2}. The parameters {𝑃𝑆1,𝛾} are obtained based on that the channel gain of relay-to-destination, |2𝑖|2 is exponentially distributed, which does not find out the “bottle-neck” of transmission (i.e., the weaker link of the relays). When relaying is selected (i.e., 𝑃𝑆1<𝛾target𝑁0/|0|2), the source node broadcasts {𝑃𝑆1,𝛼𝑡} to all the candidates. If the channel gain of relay-destination link is greater than the forwarding threshold, namely, |2𝑖|2𝛼𝑡, then the selected relays forward the source data. It implies that multiple relays could participate in the relaying simultaneously.

In the model with network coding and opportunistic relaying, as shown in Figure 1(b), when relaying is selected, 𝑃𝑆1=𝛾target𝑁0/|1𝑟|2, the target SNR can be guaranteed at the selected relay during the transmission from 𝑆1 to the selected relay. And it is the same to 𝑆2 when 𝑃𝑆2=𝛾target𝑁0/|2𝑟|2. But the outage event may occur in the third transmission phase because the instantaneous channel gain of forwarding links may be less than 𝛼𝑡, which is calculated by the statistics of all the links. Thus, given the target SNR, 𝛾target, at each destination with a target outage probability, 𝜌target, in two-way communications, we rewrite Problem (𝑄1) as Problem (𝑄2). 𝐸[𝑃𝑟] is the expected value of the transmit power of opportunistic relay. Problem (𝑄2) is the problem of power efficiency in two-way relay networks.min{PS1,PS2,Pr,𝛾}𝑃𝑆1+𝑃𝑆2𝑃+𝐸𝑟subjectto𝑃rob𝑃𝑆1|0|2+𝑃𝑟||2𝑟||2𝑁0𝛾target𝜌target𝑃rob𝑃𝑆2||0||2+𝑃𝑟||1𝑟||2𝑁0𝛾target𝜌target𝑃𝑆1||1𝑟||2𝑁0𝛾target𝑃𝑆2||2𝑟||2𝑁0𝛾target.(𝑄2)

Obviously, the transmission through the relaying could be more power efficient than the direct transmission on the condition that each relaying link is better than the direct link (i.e., |1𝑟|2|0|2 and |2𝑟|2|0|2 ). In this paper, we will work out this problem.

3. Distributed Relaying Decision and Power Allocation Strategy

In this section, a distributed relaying decision mechanism followed by distributed power allocation strategy is proposed to crack the obstacles of centralized mechanism, using the limited CSI at each node.

When 𝑆1 transmits the training messages, due to the broadcast nature of wireless medium, all relay nodes and 𝑆2 can simultaneously estimate their 𝑆1𝑅 and 𝑆1𝑆2 fading coefficients {1𝑖,𝑖=1,,𝑀},{0}, respectively. Similarly, when the relay and 𝑆2 transmit the training bits, {0,11,12,,𝑖𝑀} can be estimated at 𝑆1. However, {21,22,,2𝑀} may not be available at 𝑆1. Thus, the distributed strategy is proposed with the realizations {0,1𝑖,12,,1𝑀}, the statistics of all the links available at the source 𝑆1, and the realizations {0,21,22,,2𝑀}, the statistics of all the links available at 𝑆2. The relay nodes are assumed to have their local CSI, that is, 1𝑖 and 2𝑖 for 𝑅𝑖,𝑖=1,2,,𝑀.

The nature of the distributed strategy requires that each relay should make its decision only on its local CSI. Since the opportunistic relay has been chosen in advance (as mentioned in Section 2), the selected relay only needs to decide whether to forward the source data or not. In this paper, the selected relay broadcasts the network-coded data when its minimal channel gain of relay-to-destination satisfies 𝐴𝑟||=min1𝑟||2,||2𝑟||2𝛼𝑡,(7) where 𝛼𝑡 is the forwarding threshold value. One reason is because this network coding needs both ends to decode at the same rate, another reason is that the transmission data rate broadcast by the relay is limited by the weaker link. Thus, the opportunistic relay forwards the decoded signals with sufficient power 𝑃𝑟𝑃𝑟=𝛾target𝑁0𝐴𝑟=max0,𝛾target𝑁0𝑃𝑆𝑘||𝑘𝑟||2||min1𝑟||2,||2𝑟||2(8)max0,𝛾target𝑁0𝑃𝑆𝑘||𝑘𝑟||2𝛼𝑡,(9) where 𝛾target denotes the SNR contribution from the relay.

We note that such a distributed decision mechanism results in a nonzero probability that none of the relay nodes satisfies (7), and hence a nonzero outage probability. A large value of 𝛼𝑡 means that the selected relay will transmit with less power and less often, which saves power but at the expense of a high outage probability. On the other hand, a small value for 𝛼𝑡 means that the selected relay will transmit possibly higher power and more often, which results in a low outage probability but possibly high power. Hence, the source nodes should work out the pairs {𝑃𝑆1,𝛼𝑡} and {𝑃𝑆2,𝛼𝑡} to meet a system-given specification, that is, an outage probability requirement 𝜌target.

From the source's point of view, the transmit power of the selected relay node is a random variable with the known statistics, since the realizations of the forwarding link are not available at the source node. Due to (3), we have the cumulative distribution function (CDF) of 𝐴𝑟𝐹𝐴𝑟(𝑥)=𝑀𝑖=11𝑒𝛽𝑖𝑥,𝑥0,(10) and its probability density function (pdf) is given by 𝑓𝐴𝑟(𝑥)=𝑀𝑘=1𝛽𝑘𝑒𝛽𝑘𝑥𝑀𝑖=1,𝑖𝑘1𝑒𝛽𝑖𝑥,𝑥0,(11) where 𝛽𝑖=2𝑘=1𝛽𝑖𝑘, 𝑖=1,,𝑀 (refer to the appendix).

Having the pdf of 𝐴𝑟, the expected value of the transmit power of the selected relay 𝑅𝑟 is obtained as 𝐸𝑃𝑟=𝛼𝑡max0,𝛾target𝑁0𝑃𝑆𝑘||0||2𝑥𝑓𝐴𝑟(𝑥)𝑑𝑥,(12) where 𝑘=argmax{𝑗}{|𝑗𝑟|2}, 𝑗=1,2. The factor max{0,𝛾target𝑁0𝑃𝑆𝑘|0|2} means that the relay should pay more power according to the channel gain of weaker link to guarantee the correct decoding at both ends in the third transmission phase.

From (3) and (7), the forwarding threshold 𝛼𝑡 should be chosen as the value that satisfies the outage probability with equality, that is, 𝜌target𝐴=Pr𝑟<𝛼𝑡=𝐹𝐴𝑟𝛼𝑡=𝑀𝑖=11𝑒𝛽𝑖𝛼𝑡.(13) Exact expression for the threshold 𝛼𝑡 is difficult to obtain but it is possible to derive bounds for it. For instance, by letting 𝛽min=min{𝛽1,𝛽2,,𝛽𝑀} and 𝛽max=max{𝛽1,𝛽2,,𝛽𝑀}, we can bound the outage probability as 1𝑒𝛽max𝛼𝑡𝑀𝑀𝑖=11𝑒𝛽𝑖𝛼𝑡1𝑒𝛽min𝛼𝑡𝑀.(14) Therefore, 𝛼𝑡 is bounded as 1𝛽maxln1𝜌1/𝑀target𝛼𝑡1𝛽minln1𝜌1/𝑀target.(15) The value of 𝛼𝑡 can be obtained by a search in the given range in (15) numerically.

In addition, the transmit power of the source nodes can be calculated by Theorem 1, which provides the following optimal solution.

Theorem 1. The optimum transmit power of the source nodes, 𝑃𝑆1 and 𝑃𝑆2, can only be one of the discrete values in the following sets: 𝛾target𝑁0||1𝑟||2,𝛾target𝑁0||0||2,𝛾(16)target𝑁0||2𝑟||2,𝛾target𝑁0||0||2.(17) respectively.
Each source node's transmit power is equal to 𝛾target𝑁0/|0|2 when the direct transmission is preferred. And the source nodes transmit power 𝛾target𝑁0/|1𝑟|2, 𝛾target𝑁0/|2𝑟|2, respectively, when the relaying is preferred. Thus, the power consumption of relaying is less than that of direct transmission, that is, 𝑃𝑆1+𝛼𝑡max0,𝛾target𝑁0𝑃𝑆1||0||2𝑥𝑓𝐴𝑟𝛾(𝑥)𝑑𝑥target𝑁0||0||2,𝑃(18)𝑆2+𝛼𝑡max0,𝛾target𝑁0𝑃𝑆2||0||2𝑥𝑓𝐴𝑟𝛾(𝑥)𝑑𝑥target𝑁0||0||2.(19)

Proof. Here, the distributed strategy is based on the opportunistic relaying and network coding. Due to the opportunistic relaying, the “good” relay is chosen prior to the transmission (3). And the source nodes can work out the forwarding threshold 𝛼𝑡 with the known statistics of all the links (𝛼𝑡 is the same to both 𝑆1 node and 𝑆2 node) by (15). Then, 𝑆1 node can evaluate (18) to make a decision whether to perform relaying based on the knowledge of 0 and 1𝑟 (for 𝑃𝑆1). At the same time, 𝑆2 node can also evaluate (19) based on the knowledge of 0 and 2𝑟 (for 𝑃𝑆2). Consequently, 𝑆1 and 𝑆2 nodes can exchange “1 bit” signaling information (here, this “1 bit” signaling information is little overhead and can be achieved by a one-time handshaking protocol between the two source nodes.) to finally decide whether to transmit the source data by the direct link or relaying link.
We consider the scenario in which the relaying is preferred. Clearly, the target SNR at the selected relay can be achieved without an outage event in each source-to-relay link with the source transmit power 𝛾target/|1𝑟|2, 𝛾target/|2𝑟|2, respectively.
Since each source node only knows the statistics of all the links without the knowledge of the realizations of channel gain in the relay-to-destination link, the outage event may occur in the third phase. Due to (13), the target outage probability can be satisfied when the forwarding threshold 𝛼𝑡 is calculated from (15). In the following content, it can be shown that the target SNR at destination can be satisfied. Assume the 𝑅𝑟𝑆2 link is weaker than the 𝑅𝑟𝑆1 link, that is, |2𝑟|2|1𝑟|2. From (8), we can get 𝑃𝑟=(max{0,𝛾target𝑁0𝑃𝑆1|0|2})/|2𝑟|2, 𝑃𝑆1=𝛾target𝑁0/|1𝑟|2𝛾target𝑁0/|2𝑟|2 (i.e., the transmit power of 𝑆1 is less than that of souce2, 𝑃𝑆1𝑃𝑆2).
At 𝑆2, the received SNR is 𝑃𝑆1||0||2+𝑃𝑟||2𝑟||2=𝑃𝑆1||0||2+max0,𝛾target𝑁0𝑃𝑆1||0||2||2𝑟||2||2𝑟||2𝛾target.(20) At 𝑆1, the received SNR is 𝑃𝑆2||0||2+𝑃𝑟||1𝑟||2=𝑃𝑆2||0||2+max0,𝛾target𝑁0𝑃𝑆1||0||2||2𝑟||2||1𝑟||2𝑃𝑆2||0||2+max0,𝛾target𝑁0𝑃𝑆1||0||2||2𝑟||2||2𝑟||2𝛾target.(21)
Using the expression in (12), the expected value of total transmit power is as follows: 𝐸𝑃total=𝑃𝑆1+𝑃𝑆2𝑃+𝐸𝑟=𝑃𝑆1+𝑃𝑆2+𝛼𝑡max0,𝛾target𝑁0𝑃𝑆1||0||2𝑥𝑓𝐴𝑟(𝑥)𝑑𝑥.(22)
Therefore, the target SNR and the target outage probability can be satisfied. Theorem 1 is proved.

The proposed “energy-efficient relaying strategy with network coding” in two-way parallel channels is summarized in Table 1. Here, the opportunistic relaying is applied to decrease the cooperative costs, to save power, and capture the nice link for the practical system. Moreover, the network coding is introduced to save power.

tab1
Table 1: Energy-efficient relaying strategy with network coding in two-way parallel channels.

4. Simulation Results

In this section, we will consider the following three different cooperative schemes.(i)The proposed distributed strategy (for relaying decision and power allocation) combined with opportunistic relaying and network coding (DSON for short). (ii)The optimum distributed power allocation (ODPA) scheme [8]. (iii)Single relay model (SRM) [8].

The traditional two-way relaying is decomposed into two one-way transmissions (as shown in Figure 1(a)). Moreover, to the best of our knowledge, (ii) and (iii) outperform the existing distributed schemes in one-way relaying, so we focus on comparing the performance of (i) with that of (ii) and (iii). We consider the two-way transmission consisting of 𝑆1 node and 𝑆2 node 100 m apart, and 𝑀 relay nodes between the source nodes. The fading model is considered as [15], that is, the variance of the channel gain is proportional to the distance between nodes. Here, we have 𝜎2𝑘𝑖=0.5𝐶𝑑𝛼𝑆𝑘𝑅𝑖𝜎,𝑘=1,2,20=0.5𝐶𝑑𝛼𝑆1𝑆2,(23) where 𝑑𝑗𝑖 is the distance between node 𝑗 and node 𝑖, the path-loss exponent is denoted by 𝛼, the factor 0.5 is due to the above variances defined by two dimension. 𝐶 is a constant that is expressed as 𝐶=𝐺𝑡𝐺𝑟𝜆2/𝐿(4𝜋)2, where 𝐺𝑡 is the transmitter antenna gain, 𝐺𝑟 is the receiver antenna gain, 𝜆 is the wavelength, and 𝐿 is the system loss factor not related to propagation (𝐿1). The values 𝛼=3, 𝐺𝑡=𝐺𝑟=1, 𝜆=(1/3)𝑚, 𝐿=1, are used in the simulations. Assume the AWGN variances on all links to be 𝑁0=1010 and the target SNR (𝛾target) to be 10 dB.

We first consider the case in which {𝑑𝑆1𝑅𝑖}𝑀𝑖=1={0.2,0.8}, {𝑑𝑅𝑖𝑆2}𝑀𝑖=1={0.8,0.2}, and 𝑀=2. Figure 3 illustrates the numerical results of the expected value of the total power 𝐸[𝑃total] as a function of the target outage probability 𝜌out. It is observed that the proposed strategy (DSON) outperforms the existing schemes at practical values of outage probability. For instance, for an outage 𝜌out=0.05, approximately 22%, 37% is saved by the DSON scheme as compared to the ODPA and the SRM schemes, respectively. The performance of the DSON scheme is not better than that of the ODPA and the SRM at the higher outage probability regimes but we know, as fact, that the high outage probability is prohibited in practical systems.

186783.fig.003
Figure 3: 𝐸[𝑃total] versus the outage probability 𝜌out for the different distributed strategies with {𝑑𝑆1𝑅𝑖}𝑀𝑖=1={0.2,0.8}, {𝑑𝑅𝑖𝑆2}𝑀𝑖=1={0.8,0.2}, and 𝑀=2.

Generally, the relays are located in the midst of two source nodes. The following simulation results are based on the scenario in which all the relay nodes are in the midst of two source nodes. Namely, {𝑑𝑆1𝑅𝑖}𝑀𝑖=1={𝑑𝑅𝑖𝑆2}𝑀𝑖=1={0.5,,0.5}.

Figure 4 illustrates the numerical results of the expected value of the total power 𝐸[𝑃total] as a function of the target outage probability 𝜌out for the case 𝑀=2. Similarly to the results of Figure 3, Figure 4 shows that the proposed scheme (DSON) outperforms both (ii) and (iii) at the lower 𝜌out regime. It is also observed that the relative gain of the proposed scheme is larger in comparison to the case of Figure 3. For instance, at outage of 𝜌out=0.05, approximately 30%, 31% is saved by the DSON with respect to the ODPA and the SRM, respectively. It is clear that, when the relays are in the middle between the two source nodes, they provide good help to both source nodes. With only two relays (𝑀=2), the opportunistic relaying has less spatial channels to choose from (less spacial diversity) and suffers from broadcasting the network-coded data according to the weaker link in the third transmission phase; this is the implication on the performance of the DSON scheme at higher outage probability regime.

186783.fig.004
Figure 4: 𝐸[𝑃total] versus the outage probability 𝜌out for the different distributed strategies with 𝑀=2.

Figure 5 illustrates the numerical results for the case when the number of relay nodes is 𝑀=8. Here, it is observed that the DSON strategy has improved considerably in comparison to the case of one- and two-relay nodes. The DSON strategy now enjoys more spatial diversity in the presence of more relay nodes as the candidates. Though the ODPA and the SRM also have more spatial diversities, both the ODPA and the SRM select relays mainly based on source-to-relay links, so their spatial dimension is half of that of the DSON strategy. Moreover, the DSON with network coding only has three transmission phases, this results in more saving in power consumption.

186783.fig.005
Figure 5: 𝐸[𝑃total] versus the outage probability 𝜌out for the different distributed strategies with 𝑀=8.

5. Conclusions

In this paper, an energy-efficient relaying strategy with network coding in two-way parallel channels is proposed. In the first stage of this proposal, based on the opportunistic relaying strategy, only one relay is selected to assist the transmission. It decreases the cooperative costs among relays, which is preferred in practical systems. Meanwhile, it guarantees that the DSON chooses the relay from both source-to-relay and relay-to-destination links. Moreover, network coding decreases the transmission phases from four to three. Combined with the opportunistic relaying and network coding, distributed relaying decision and power allocation strategy is applied to obtain the optimal power efficiency. Since only limited CSIs needed in this scheme, it is practical for real applications in two-way relaying networks.

Of course, the DSON suffers from broadcasting the network-coded data according to the weaker link in the third transmission phase for satisfying the requirements of target SNR and target outage probability. From a power saving point of view, the DSON outperforms the ODPA and the SRM in a two-way relaying communication link.

Appendix

For purposes of completeness, we briefly summarize a result from [16], Lemma A.

Lemma A (see [16]). Random variables 𝐴𝑖,𝐴𝑖1,,𝐴𝑖𝐾, (𝑖=1,,𝑀), 𝐴𝑖1,,𝐴𝑖𝐾 are independently exponential distributed with parameter 𝛽𝑖1,,𝛽𝑖𝐾, respectively, 𝐴𝑖=min{𝐴𝑖1,,𝐴𝑖𝐾}. Let 𝑟=argmax𝑖𝐴𝑖, for 𝐹𝐴𝑟(𝑥), the CDF of 𝐴𝑟, there is 𝐹𝐴𝑟(𝑥)=𝑀𝑖=11𝑒𝛽𝑖𝑥,(A.1) where 𝛽𝑖=𝐾𝑘=1𝛽𝑖𝑘, 𝑖=1,,𝑀.

Acknowledgments

This paper was supported by the International Science and Technology Cooperation Program (2008DFA12160), China's 863 Project no. 2009AA011501, National Natural Science Foundation of China no. 60832008, China's Major Project no. 2009ZX03003-009, Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT), National Science and Technology Pillar Program no. 2008BAH30B09, and National Basic Research Program of China no. 2007CB310608.

References

  1. A. Sendonaris, E. Erkip, and B. Aazhang, “Increasing uplink capacity via user cooperation diversity,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT '98), p. 156, Cambridge, Mass, USA, August 1998.
  2. P. Larsson, N. Johansson, and K. E. Sunell, “Coded bi-directional relaying,” in Proceedings of the IEEE 63rd Vehicular Technology Conference (VTC '06), pp. 851–855, May 2006. View at Scopus
  3. P. Popovski and H. Yomo, “Physical network coding in two-way wireless relay channels,” in Proceedings of the IEEE International Conference on Communications (ICC '07), pp. 707–712, Glasgow, Scotland, June 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. C.-H. Liu and F. Xue, “Network coding for two-way relaying: rate region, sum rate and opportunistic scheduling,” in Proceedings of the IEEE International Conference on Communications (ICC '08), pp. 1044–1049, Beijing, China, April 2008. View at Publisher · View at Google Scholar
  5. R. Ahlswede, N. Cai, S. Y. R. Li, and R. W. Yeung, “Network information flow,” IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1204–1216, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. K. Azarian, H. El Gamal, and P. Schniter, “On the achievable diversity-vs-multiplexing tradeoff in half-duplex cooperative channels,” IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4152–4172, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Transactions on Information Theory, vol. 49, no. 10, pp. 2415–2425, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Chen, S. Serbetli, and A. Yener, “Distributed power allocation strategies for parallel relay networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 2, Article ID 4450823, pp. 552–561, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Bletsas, H. Shin, and M. Z. Win, “Outage-optimal cooperative communications with regenerative relays,” in Proceedings of the 40th Annual Conference on Information Sciences and Systems (CISS '06), pp. 632–637, March 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Knopp and P. A. Humblet, “Information capacity and power control in single-cell multiuser communications,” in Proceedings of the IEEE International Conference on Communications (ICC '95), vol. 1, pp. 331–335, June 1995. View at Scopus
  11. Q. Ren and Q. Liang, “Opportunistic media access control and rate adaptation for wireless ad hoc networks,” in Proceedings of the IEEE International Conference on Communications (ICC '04), vol. 1, pp. 154–158, June 2004. View at Scopus
  12. W. Yang, L. Li, W. Sun, and Y. Wang, “Energy-efficient relay selection and optimal relay location in cooperative cellular networks with asymmetric traffic,” Journal of China Universities of Posts and Telecommunications, vol. 17, no. 6, pp. 80–88, 2010.
  13. T. E. Hunter and A. Nosratinia, “Distributed protocols for user cooperation in multi-user wireless networks,” in Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '04), pp. 3788–3792, December 2004. View at Scopus
  14. A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple cooperative diversity method based on network path selection,” IEEE Journal on Selected Areas in Communications, vol. 24, no. 3, pp. 659–672, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: efficient protocols and outage behavior,” IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–3080, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Peng, Q. Zhang, M. Zhao, and Y. Yao, “On the performance analysis of network-coded cooperation in wireless networks,” in Proceedings of the 26th IEEE International Conference on Computer Communications (INFOCOM '07), pp. 1460–1468, May 2007. View at Publisher · View at Google Scholar · View at Scopus