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Network Coding for Two-Way Relaying Networks Over Rayleigh Fading Channels Wei Li, Jie Li, Senior Member, IEEE, and Pingyi Fan, Senior Member, IEEE
Abstract—Wireless network coding is a useful technology that can increase the total throughput of wireless networks. There are, however, few works focusing on wireless network coding over fading channels, which is an important characteristic of many real wireless channels and may result in performance degradation. To investigate the fading channel’s impact on network coding, based on the constant transmission power scheme and the channel inversion-transmission scheme, we analyze network throughput over Rayleigh fading channels. It is shown that, when the difference between average channel gains over two broadcasting channels is very large, the throughput of network coding greatly decreases, and the advantage of network coding almost disappears. To address this issue and to maximize the throughput of network coding over fading channels, we formulate the fading compensation for network coding as optimization problems and present the optimal transmission data rate and transmission power level of the relay node. Furthermore, to consider the realization problem of network coding over fading channels, including unbalanced traffic load and asynchronization of packet arrivals, we present two opportunistic optimal network coding (OONC) schemes. Performance evaluation has shown that the proposed opportunistic schemes perform well in various scenarios. Index Terms—Network coding, optimal data rate, Rayleigh fading channels.
I. I NTRODUCTION
W
IRELESS networks are widely employed worldwide, such as cellular networks, wireless local area networks, wireless sensor networks, etc. Due to the open-air-interface nature of wireless channels, wireless networks face many challenges. First, since channel resources may be shared by the whole network, effective channel resource allocation becomes a critical problem. Second, the radio spectrum available for wireless services is extremely scarce while demands for these services are rapidly growing. Spectral efficiency is therefore of Manuscript received November 3, 2009; revised March 21, 2010 and May 24, 2010; accepted May 31, 2010. Date of publication June 28, 2010; date of current version November 12, 2010. This work was supported in part by the National Natural Science Foundation of China/Research Grant Council Joint Research Scheme 60831160524, by the Tsinghua University Initiative Scientific Research Program, by the Grand-in-Aid for Scientific Research of the Japan Society for Promotion of Science, and by the open research fund of the National Mobile Communications Research Laboratory, Southeast University, China. The review of this paper was coordinated by Prof. B. Hamdaoui. W. Li is with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). J. Li is with the Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba Science City 305-8573, Japan (e-mail:
[email protected]). P. Fan is with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China, and also with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail:
[email protected]). Digital Object Identifier 10.1109/TVT.2010.2053947
primary concern in the design of future wireless communication systems [1]. Third, energy saving is more important in wireless networks than in wireline networks. Most wireless terminals use batteries, and their energy is limited. To prolong the network lifetime, saving energy is necessary. Fourth, wireless links are subject to severe multipath fading due to randomly delayed reflection, scattering, and diffraction. Fading leads to severe degradation in the signal-to-noise ratios (SNRs) of wireless channels. Hence, fading compensation is typically required. Recently, network coding has attracted much attention in wireless communications. Network coding was first proposed by Ahlswede et al. [2] in 2000. Its principle is that the relay node can receive packets from all the input links, encode them into one packet first, and then forward the encoded packet. It has been proven that, in wireline networks, by employing network coding, a source node can send packets at the theoretical upper bound of transmission rate, i.e., the max-flow of a network. Li et al. [3] showed that linear network coding is sufficient to achieve the capacity in theory, and this work has greatly simplified the process of seeking a feasible code. Subsequently, much work has been conducted in developing both theoretical frameworks and engineering practices of network coding. Koetter and Medard [4] proposed an algebraic approach to network coding on its solvability in multicast networks, by which the problems boil down to a set of matrix equations. Performance evaluation of network coding in terms of traffic delay over some given practical graphs has been presented by simulations [5]. Many algorithms for constructing linear codes over finite fields were given by Jaggi et al. [6]. Ho et al. [7], [8] investigated the randomized construction of multicast codes. Chou et al. [9] presented a distributed scheme for practical network coding. Network coding can also be employed in wireless networks (e.g., [10]–[12]). Due to the broadcast nature of wireless channels, wireless networks exhibit significant data redundancy. That is, at each hop, the transmitter delivers the same packet to multiple nodes within its radio range. Network coding can be exploited to reduce redundancy and compress data, which can increase the overall network throughput, improve spectral efficiency, and reduce energy consumption. Some typical work on wireless network coding is given as follows: Zhang et al. [13] investigated the multicast routing problem based on network coding and put forward a practical algorithm to obtain the max-flow multicast routes in wireless ad-hoc networks. Katti et al. [14] proposed a protocol called COPE (which is a wireless network coding protocol), applied COPE in a real 20-node wireless network, and evaluated the performance. The test results indicated that network coding increases network
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LI et al.: NETWORK CODING FOR TWO-WAY RELAYING NETWORKS OVER RAYLEIGH FADING CHANNELS
Fig. 1. Example of the traditional store-and-forward scheme and network coding scheme. (a) Store-and-forward scheme. (b) Network coding scheme.
throughput. Liu and Xue [15] analyzed the rate region, i.e., the sum rate of a two-way relaying network with network coding over additive white Gaussian noise (AWGN) channels. Previous work on wireless network coding, however, was largely based on the condition that the wireless links are reliable and stable, which is similar to wireline networks. As a matter of fact, the wireless medium is fundamentally different from its wireline counterpart. For wireless medium, signal fading is very common due to the time-varying channel characteristic, which results in either a higher bit error rate (BER) or a larger required transmit power. Previous designs of wireless network coding rarely took this characteristic of the wireless medium into account. We note that fading over a single link has been well studied in [16]; however, fading compensation based on network coding is still an open problem. In this paper, we will investigate network coding over fading channels. We will focus on two problems: First, we will investigate the impact of channel fading on the network performance through theoretical analysis. Second, we will investigate the solution of related problems by developing some methods, e.g., adjusting the transmission power level of the relay node according to channel-state information. We first analyze the performance of network coding in a two-way relaying network over Rayleigh fading channels. In a two-way relaying network, two source nodes S1 and S2 want to transmit packets to each other, as shown in Fig. 1. In this network, signal fading greatly degrades the performance of wireless network coding. If network coding is employed, the relay node X will simultaneously transmit encoded packets to both S1 and S2 . However, because the channel conditions of the two links could vary over time, it is not easy to guarantee that the packets sent by X can perfectly be received by S1 and S2 , which degrades the throughput of wireless network coding. In particular, when the difference between the average channel gains of the two channels is very large, network throughput greatly decreases, and the advantages of network coding almost disappear.
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To deal with this problem, a reasonable method is to adjust the transmission power level and transmission data rate of the relay node according to channel state. Recently, we have analyzed the performance of wireless network coding over Rayleigh fading channels based on the constant transmission power scheme and obtained its optimal transmission data rate [17]. In this paper, we extend our previous work and more detailedly analyze the outage capacity of network coding, based on two typical transmission schemes, i.e., the constant transmission power scheme and the channel-inversion transmission scheme. To increase the network throughput, we formulate the fading compensation for network coding over Rayleigh fading channels as two optimization problems and then obtain the optimal transmission data rate and power level of the relay node. Numerical and simulation results show that network throughput increases by employing the proposed optimal transmission data rate and power level. Furthermore, based on the performance analysis, we consider selecting a relay node and obtain the optimal assignment location of the relay node, which can further improve the system performance. In addition, we will also consider the problem of applying network coding in a practical wireless network in the fading environment. In most previous work on network coding, global synchronization of packet arrivals is assumed throughout a network. However, in practical wireless networks, strict synchronization is difficult to satisfy. Asynchronization of packet arrivals may degrade network performance [19]. To deal with the problem of asynchronization and unbalanced traffic load, we propose two novel opportunistic optimal network coding (OONC) schemes. Simulation results indicates that our developed OONC schemes perform well in various scenarios. The rest of this paper is organized as follows: In Section II, we outline the channel and network models. Then, we analyze the optimal transmission data rate based on network coding over Rayleigh fading channels in Section III. In Section IV, we show some numerical results and analyze the selection of relay nodes. The OONC schemes are proposed in Section V. In Section VI, we evaluate the performance of the proposed schemes by simulations. Finally, we summarize our main results and give concluding remarks in Section VII. II. P RELIMINARIES AND S YSTEM D ESCRIPTION Considering a two-way relaying network, as shown in Fig. 1, there are two source nodes S1 and S2 , and a relay node X. Nodes S1 and S2 want to transmit packets to each other. It is assumed that all the three nodes in the wireless network share a common frequency band. To reduce the wireless interference, more than one node is not allowed to transmit packets at the same time. Otherwise, a collision will occur, and receivers cannot correctly decode the signal. All the nodes are operating in the half-duplex mode, i.e., a node cannot simultaneously transmit and receive packets. Note that, although the two-way relaying network is simple, it is a fundamental building block of a wireless network, and operations of the relay node in a twoway relaying network are similar to that in a generic wireless network. In this paper, based on a two-way relaying network, we will investigate the impact of channel fading on the network
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coding performance. The obtained results can be extended in generic wireless networks. A. Channel Model As a reasonable fading model for radio signals in heavily built-up urban environments, Rayleigh fading is popularly employed [20]. Over Rayleigh fading channels, the received power Pc follows an exponential distribution. Its probability density function (pdf) is given by fPc (ϕ) =
1 −ϕ/ϕ ·e ϕ
(1)
where ϕ denotes the average received power [20]. Let g(t), g(t) ≥ 0, denote the instantaneous channel power gain of an arbitrary channel. In fact, channel gain g(t) represents the power attenuation coefficient over the channel. It is independent of the channel input, and its value is equal to the ratio of the received power level to the transmitted power level. In this paper, let gi (t) denote the channel gain of link (X, Si ), i = 1, 2. Over Rayleigh fading channels, channel gain g(t) follows an exponential distribution, and its expected value is denoted as g. In addition, because the transmission power of a transmitter is limited, let Ps denote the average transmit signal power. To simplify notations, let γ(t) = (Ps g(t)/N0 W ) denote the normalized fading gain at the receiver, where N0 denotes the power spectral density of additive Gaussian white noise, and W denotes the received signal bandwidth. Assuming that all the channels are with AWGN, then N0 is a constant, and Ps /(N0 W ) is a constant. The distribution of g(t) determines the distribution of γ(t), and vice versa. Consequently, γ(t) follows an exponential distribution, and its pdf is given by fγ (γ) =
1 −γ/γ ·e γ
(2)
where γ is the expected value of γ(t). For simplicity, γ(t) is denoted as γ without confusions. In this paper, block fading is assumed. Block fading is a model to treat time-selective fading in a tractable manner. In such a model, the channel gain over a fading channel is constant when each packet is being transmitted but independently varies from one packet to its next one [16]. Over a Rayleigh fading channel, the value of the channel gain g(t) is a variable. The receiver cannot correctly decode all received signals due to low SNR. In this paper, we use the outage probability to characterize the probability of unsuccessful decoding. That is, if the received SNR falls below the minimum required SNR for the current data rate, the transmission fails. In this case, the system is said in outage [16]. The outage probability is Pout = Pr(γ < γ0 )
(3)
where γ0 is the minimum required SNR for the current transmission data rate. That is to say, in this paper, we assume that, if the value of the received SNR is larger than a threshold for the current data rate, the receiver can correctly decode the
received signal; otherwise, the received signal cannot correctly be decoded, and the transmission fails. In fact, it is reasonable, because Tse et al. showed that outage probability is a tight upper bound of the bit error probability in wireless fading channels [21]. Then, the average data rate received correctly is C(Pout ) = (1 − Pout ) · R
(4)
where R is the maximum data rate corresponding to outage probability Pout . In fact, the outage probability characterizes the probability of data loss or, equivalently, the probability of deep fading. The capacity with outage probability Pout is correctly defined as the maximum data rate received, as given by Cout = max(1 − Pout ) · R. Pout
(5)
Its basic premise is that, by allowing the system to lose some data in the event of deep fading, a higher data rate can be maintained than the case in which all data must correctly be received, regardless of the fading state, like the case for Shannon capacity. B. Network Coding Network coding is a useful technology that can effectively increase the throughput of wireless networks. The procedure of network coding is shown in Fig. 1(b). In the two-way relaying network, nodes S1 and S2 want to send packets to each other. At stage 1, node S1 sends a packet a to relay node X. At stage 2, node S2 sends a packet b to relay node X. At stage 3, relay node X encodes packets a and b into a new packet a ⊕ b and broadcasts the encoded packet a ⊕ b to both node S1 and S2 . Stage 3 is called coding stage, and the relay node X is called coding node. Then, node S1 can obtain packet b by decoding the packet a ⊕ b with packet a. Node S2 can receive packet a in the same way. This procedure requires three transmissions (stages) if there is no data loss. As a comparison, a traditional relay protocol, referring to the store-and-forward scheme, requires four transmissions (stages). The procedure of the store-and-forward scheme is shown in Fig. 1(a). At stage 1, node S1 sends a packet a to relay node X. At stage 2, relay node X forwards packet a to node S2 . At stage 3, node S2 sends a packet b to relay node X. At stage 4, the relay node X forwards packet b to node S1 . This procedure requires four transmissions (stages) if there is no data loss. Thus, compared with the store-and-forward scheme, by employing network coding, the throughput can indeed increase by 33%. Consequently, spectral efficiency is improved, and energy consumption for each packet may be reduced. III. O PTIMAL T RANSMISSION -S CHEME A NALYSIS As we observe, the performance analysis in Section II-B on wireless network coding were based on reliable and stable wireless links, i.e., the packet sent by the relay node can perfectly be received by all the receivers. However, this is not
LI et al.: NETWORK CODING FOR TWO-WAY RELAYING NETWORKS OVER RAYLEIGH FADING CHANNELS
always true. For wireless links, signal fading is very common, usually resulting in a high BER, which degrades the performance of wireless network coding. For example, in Fig. 1(b), only when both S1 and S2 receive the packets successfully sent by X are the transmission successful for network coding scheme and the advantage of network coding apparent. If only one or none of S1 and S2 correctly receives the packet sent by node X, it is somewhat similar to the store-and-forward scheme. Unfortunately, due to the fading characteristic of wireless channels, the channel gains of links (X, S1 ) and (X, S2 ) are variable, and the channels are not always reliable. That is, it is not easy to guarantee that the packets sent by X can perfectly be received by S1 and S2 ; thus, the performance of network coding is degraded. In particular, when the average channel gains of the two broadcasting channels are not equal, the throughput of the two receivers is not equal, which results in great throughput decrease in network-coding throughput. The advantage of network coding is reduced. Thus, improvement of the performance of network coding in fading environments is still an open problem. In the following, based on two typical transmission schemes, i.e., the constant transmission-power scheme and the channel-inversion scheme, we investigate this problem and analyze how to adjust the transmission power level and transmission data rate of the relay node to increase network throughput. A. Constant Transmission Power Scheme In this part, we consider the case in which both the transmitter and receiver know the distribution of channel gain g(t), but the value of g(t) is only known at the receiver at time t. Equivalently, the instantaneous received SNR is only known at the receiver. As assumed in Section II, the outage probability is adopted to characterize the probability of unsuccessful decoding, i.e., only if the received SNR is larger than a threshold for the data rate can the received signal correctly be decoded. Since the transmitter has no knowledge of the instantaneous channel gain, it is difficult to adjust the transmission power and data rate according to the variety of g(t) to guarantee that the received SNR is larger than the threshold. Therefore, a reasonable scheme is to fix a transmission data rate and a power level independent of the instantaneous channel gain. This scheme refers to the CP (constant transmission power) scheme. Here, the value of transmission data rate R is a design parameter based on the outage probability. The objective is to find the optimal value of data rate R, at which the outage capacity achieves, i.e., the total throughput is maximized. For the CP scheme, if the store-and-forward scheme is employed, i.e., if there are only one transmitter and one receiver in each transmission, as shown in Fig. 1(a), the transmitter fixes a threshold of SNR, i.e., a minimum received SNR γ0 , and transmits at data rate R = W log2 (1 + γ0 ). Then γ0 = 2R/W − 1.
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the received SNR is smaller than γ0 , the receiver declares an outage. The probability of outage is γ0 Pout = Pr(γ < γ0 ) =
fγ (γ)dγ = 1 − e−γ0 /γ .
(7)
0
Consequently, the average data rate correctly received is C(R) = (1 − Pout ) · R = R · e−γ0 /γ .
(8)
Then, the optimization problem can be formulated as Maximize : C(R) = R · e−γ0 /γ Subject to : R > 0 γ0 = 2R/W − 1.
(9)
Here, (9) is called the single-link constant power (SLCP) outage capacity problem. If network coding is employed, the problem becomes more complicated. As shown in Fig. 1(b), at stage 1 or stage 2, there are only one transmitter and one receiver in each transmission, which is similar to the store-and-forward scheme. The transmitter can adjust its transmit power level and data rate according to the SLCP scheme (9) at stages 1 and 2. However, at the coding stage (stage 3), the relay node X broadcasts encoded packets to both S1 and S2 , which is different from the store-and-forward scheme. Thus, in the following part of this section, we only consider the coding stage and analyze the outage capacity at the coding stage. That is, the outage capacity for network coding in this paper is defined as the broadcasting outage capacity of the two relay channels over which the relay node broadcasts encoded packets. At the coding stage, the outage probability of node Si is Pout,i = 1 − e−γ0 /γi
(10)
where γ0 denotes the threshold SNR corresponding to data rate R at the coding stage, and γi denotes the value of the average fading gain of link (X, Si ), i = 1, 2. At the coding stage, there are four cases when the relay node broadcasts an encoded packet. 1) Both nodes S1 and S2 correctly receive the packet. The total throughput is 2R. 2) Only node S1 correctly receives the packet. The total throughput is R. 3) Only node S2 correctly receives the packet. The total throughput is R. 4) Neither node S1 nor node S2 correctly receives the packet. The total throughput is 0. Therefore, the average throughput at stage 3 can be given by C(R) = 2R · (1−Pout,1 )(1−Pout,2 )+R · (1−Pout,1 )Pout,2 + R · Pout,1 (1−Pout,2 )
(6)
A packet is assumed to be correctly received when the instantaneous received SNR is greater than or equal to γ0 . When
= R(e−γ0 /γ1 +e−γ0 /γ2 ).
(11)
Comparing (8) and (11), there is only one term in (8), which means that only one channel is considered in each transmission
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for the store-and-forward scheme. However, there are two terms in (11), which means that two channels are considered at the coding stage for the network-coding scheme. Then, the objective of finding the optimal value of data rate R to maximize the total throughput can be formulated as the following optimization problem: Maximize : C(R) = R(e−γ0 /γ1 + e−γ0 /γ2 ) Subject to : R > 0 γ0 = 2R/W − 1.
(12)
Problem (12) is called the network-coding constant power (NCCP) outage capacity problem. In fact, the solution of problem (12) can be obtained by computer search. In this case, we can obtain the optimal data rate Ropt,nccp and the optimal SNR threshold γo,nccp . The NCCP outage capacity can be expressed as Cout,nccp = Ropt,nccp · (e−γo,nccp /γ1 + e−γo,nccp /γ2 ).
(13)
where γ0 is based on the outage probability Pout = Pr(γ < γ0 ). Since the maximal average transmission power is Ps , the value of σ can be given by 1 = σ
∞
1 fγ (γ)dγ. γ
(18)
γ0
The outage capacity with a given cutoff fading gain γ0 is given by C(γ0 ) = W log2 (1 + σ) Pr(γ ≥ γ0 ).
(19)
The corresponding problem of maximizing the total throughput is formulated as
B. Channel-Inversion Scheme In this section, we consider the case in which both the transmitter and the receiver can obtain the value of channel gain g(t) by some feedback protocols. In this case, the transmitter can adjust the transmission power to ensure that the received packets can correctly be decoded as the value of channel gain varies. Then, a suboptimal transmitter adaptation scheme, called the “channel-inversion (CI)” scheme, can be adopted [18]. For the channel inversion scheme, the transmitter adapts the transmission power to maintain a constant received power level, i.e., it inverts the channel fading. The channel then appears similarly as a time-invariant AWGN channel. The transmitter can send packets at a constant data rate R = W log2 (1 + σ)
(14)
where σ denotes the required constant received SNR. In a wireless network, with the traditional store-and-forward scheme [i.e., there are only one transmitter and one receiver for each transmission, as shown in Fig. 1(a)], the CI scheme is formulated as follows: The transmission power is given by P (γ) =
can be maintained. Such a scheme is called the “truncated CI” scheme [18]. It only compensates for fading above a certain cutoff fading gain γ0 . That is, the transmission power is formulated as σ · Ps , γ ≥ γ0 (17) P (γ) = γ 0, γ < γ0
σ Ps γ
(15)
where Ps is the maximal average transmission power. To keep the transmission power constraint, σ is selected as σ = (1/E(1/γ)), where E(1/γ) denotes the expected value of 1/γ. The channel capacity with channel inversion can be given by 1 C = W log2 1 + . (16) E(1/γ) On the other hand, for Rayleigh fading channels, the channel inversion cannot be realized due to very deep fading, i.e., g(t) = 0 [18]. To deal with this problem, the node is allowed not to transmit packets in particularly deep fading states, referring to outage states. In this case, a higher constant data rate
Maximize : Subject to :
C(γ0 ) = W log2 (1 + σ) Pr(γ ≥ γ0 ) γ0 > 0 ∞ 1 1 = fγ (γ)dγ. (20) σ γ γ0
The problem (20) is called the single-link channel-inversion (SLCI) outage capacity problem. Although the truncated CI scheme based on the store-andforward scheme has been well studied in [16], the problem becomes more complicated if network coding is employed, which is investigated in this paper. As shown in Fig. 1(b), stages 1 and 2 for network coding are similar to the store-andforward scheme, and the transmitter can adjust its power level and transmission data rate according to the SLCI problem (20) at stage 1 or stage 2. However, the coding stage (stage 3) is different from the store-and-forward scheme, at which the relay node X broadcasts encoded packets to both S1 and S2 . Thus, in the following part of this section, we only consider stage 3 (coding stage). That is, the outage capacity for network coding in this paper is defined as the broadcasting outage capacity of the two relay channels over which the relay node transmits encoded packets. At the coding stage, the relay node needs to broadcast packets to both S1 and S2 . Since the truncated CI scheme is adopted, only the links whose instantaneous fading gains are larger than a cutoff fading gain γ0 will be considered. The corresponding transmission power is ⎧ σ Ps , γ1 ≥ γ0 , γ2 ≥ γ0 ⎪ 1 ,γ2 } ⎪ ⎨ min{γ σ γ1 ≥ γ0 , γ2 < γ0 (21) P (γ1 , γ2 ) = γ1 Ps , σ ⎪ ⎪ P , γ1 < γ0 , γ2 ≥ γ0 ⎩ γ2 s 0, γ1 < γ0 , γ2 < γ0 where γ1 and γ2 denote the instantaneous fading gains of links (X, S1 ) and (X, S2 ), respectively. As the preceding equation
LI et al.: NETWORK CODING FOR TWO-WAY RELAYING NETWORKS OVER RAYLEIGH FADING CHANNELS
shows, there are four cases when the relay node broadcasts packets to nodes S1 and S2 . 1) If the fading gains of both links (X, S1 ) and (X, S2 ) are larger than the cutoff fading gain γ0 , the relay node needs to transmit the encoded packets to both S1 and S2 . The total throughput is 2R. 2) Only the fading gain of link (X, S1 ) is larger than γ0 . The relay node transmits packets to node S1 . The total throughput is R. 3) Only the fading gain of link (X, S2 ) is larger than γ0 . The relay node transmits packets to node S2 . The total throughput is R. 4) Neither link (X, S1 ) nor link (X, S2 ) is good enough. The relay node will not send packets. The total throughput is 0. It needs to note that, for the CI scheme, if X determines to transmit a packet to a node, it will adjust the transmission power to guarantee that the received SNR is larger than a threshold, so that the receiver can correctly decode the received packet. Then, the outage capacity with a cutoff fading gain γ0 can be given by C(γ0 ) = 2R · Pr(γ1 ≥ γ0 , γ2 ≥ γ0 )+R · Pr(γ1 ≥ γ0 , γ2 < γ0 ) + R · Pr(γ1 < γ0 , γ2 ≥ γ0 ) = R(e−γ0 /γ1 +e−γ0 /γ2 ) = W log2 (1+σ)(e−γ0 /γ1 +e−γ0 /γ2 )
(22)
where γ1 and γ2 denote the average fading gains of links (X, S1 ) and (X, S2 ), respectively. In addition, the maximal average transmission power is Ps ; hence, the value of constant received SNR σ should satisfy the following constraint: (23) P (γ1 , γ2 )fγ1 (γ1 )fγ2 (γ2 )dγ1 dγ2 ≤ Ps where fγ1 (γ1 ) and fγ2 (γ2 ) denote the pdf of γ1 and γ2 , respectively. By using (2) and (21), (23) can be rewritten as ∞ γ2 γ0 γ0
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Substituting (25) into (24), then σ must satisfy the following condition: 1 1 ≥ E1 σ γ1
γ0 γ1
1 + E1 γ2
∞ −
γ0
γ0 γ2
e−γ2 /γ2 1 E1 γ2 γ1
∞ − γ0
γ2 γ1
e−γ1 /γ1 1 E1 γ1 γ2
dγ2
γ1 γ2
dγ1 .
(26)
In this part, our objective is to choose the best transmission power level to maximize the total throughput. Thus, we have the following optimization problem: Maximize : C(γ0 ) = W log2 (1+σ)(e−γ0 /γ1 +e−γ0 /γ2 ) Subject to : γ0 > 0 ∞ −γ2 /γ2 γ0 γ2 1 e 1 1 ≥ E1 E1 − dγ2 σ γ1 γ1 γ2 γ1 γ1 +
1 E1 γ2
γ0
∞ −γ1 /γ1 γ0 γ1 e 1 E1 − dγ1 . γ2 γ1 γ2 γ2
(27)
γ0
The problem (27) is called the network-coding channelinversion (NCCI) outage capacity problem. Its near-optimal solution can be obtained by computer search. By solving the problem (27), the optimal value of cutoff fading gain γo,ncci and optimal data rate Ropt,ncci can be obtained. The NCCI outage capacity can be expressed as Cout,ncci = Ropt,ncci (e−γ0,ncci /γ1 + e−γ0,ncci /γ2 ).
(28)
Accordingly, the corresponding received SNR σopt,ncci can also be obtained. Using (21), the optimal transmission power level is obtained as well. IV. N UMERICAL R ESULTS AND A NALYSIS
σ fγ (γ1 )fγ2 (γ2 )dγ1 dγ2 γ1 1
∞ γ1
+ γ0 γ0 ∞ γ0
+ γ0 0 ∞ γ0
+ γ0 0
A. Numerical Results
σ fγ (γ1 )fγ2 (γ2 )dγ2 dγ1 γ2 1 σ fγ (γ1 )fγ2 (γ2 )dγ2 dγ2 γ1 1 σ fγ (γ1 )fγ2 (γ2 )dγ1 dγ1 ≤ 1. γ2 1
(24)
For simplicity, let E1 (z) denote the exponential integral function of order 1, with the form ∞ E1 (z) = z
e−t dt, t
z ≥ 0.
(25)
Letting the signal bandwidth W = 1 MHz, we will present some numerical results. Fig. 2 shows the outage capacity for NCCP problem (12) and NCCI problem (27) with different values of average fading gain. To evaluate the effect of the channel gains of two broadcasting channels on the network coding outage capacity, let the outage capacity of a single link be the performance reference, which is also shown in Fig. 2. Here, the outage capacity for network coding is the broadcasting outage capacity of the two broadcasting channels over which the relay node broadcasts the encoded packets. The single-link outage capacities are the SLCP outage capacity (9) and SLCI outage capacity (20) of link (X, S1 ). In this figure, the outage capacity with the CI scheme is larger than the corresponding outage capacity with the CP scheme. This is because, compared with the CP scheme, the transmitter in the CI scheme can obtain more channel information, i.e., the value of channel gain. The transmitter in the CI scheme can
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Fig. 3.
Fig. 2. Average fading gain versus outage capacity.
adjust its transmission power level according to channel status. Hence, the outage capacity of the CI scheme is larger than that of the CP scheme. In addition, when γ1 , which is the average fading gain of link (X, S1 ), is fixed, the NCCP and NCCI outage capacity will increase as the value of γ2 increases. Compared with the performance reference, i.e., the single-link outage capacity, if the average fading gains of the two links are equal, the NCCP outage capacity is exactly twice as much as the SLCP outage capacity, and the NCCI outage capacity is a little smaller than the doubled SLCI outage capacity, which means that both link (X, S1 ) and link (X, S2 ) are sufficiently utilized, and the advantage of network coding is very apparent. However, if γ1 γ2 , the NCCP outage capacity is approximately equal to the SLCP outage capacity, and the NCCI outage capacity is approximately equal to the SLCI outage capacity, which means that the advantage of network coding is reduced. The reason is that, if γ1 is much larger than γ2 , the throughput of node S1 will be much greater than node S2 . Consequently, the total throughput is approximately equal to node S1 ’s throughput. In a word, the advantage of network coding cannot be exploited apparently in the scenario that γ1 γ2 . The preceding results give us a hint that suitable selection of relay node is an important issue to network performance. Along this line, we will consider how to select a relay node in the next section. B. Selection of Relay Nodes In Section III, we have analyzed how to choose the optimal transmission power level to maximize the throughput, if the relay node is chosen. However, in some scenarios, there are several nodes that can be served as relay nodes in a wireless network, and only one relay node is enough in the network. In this case, selecting a better relay node to further improve the network performance is also an important issue. To the NCCP problem, we analyze how to select a relay node in the aspects of capacity. Assuming that the average channel gain of link (X, Si ) is gi = β · d−α i , where β is a constant
Nodes’ locations.
coefficient, di is the length of link (X, Si ), i = 1, 2, and α is the path-loss (attenuation) factor usually satisfying 2 ≤ α ≤ 4, we will analyze the relationship between the NCCP outage capacity and the location of the relay node. Theorem 1: Assuming that the average channel gain of link (X, Si ) is gi = β · d−α i , i = 1, 2, the NCCP outage capacity is maximized, if nodes X, S1 , and S2 are on a straight line and d1 = d2 , where di denotes the distance between the relay node X and receiver Si . Proof: As shown in Fig. 3, there are two candidate coding nodes X and X . First, it is better to select a relay node on the straight line of two source nodes, because shorter distances between the nodes mean larger average channel gains. Second, we analyze how the location of X affects the outage capacity. Because gi = β · d−α i , i = 1, 2, and d2 = d − d1 , (11) can be written as
−α −α (29) C(γ0 ) = R e−γ0 /(δd1 ) + e−γ0 /(δ(d−d1 ) ) where δ is a constant. By solving ∂C(γ0 ) =0 ∂d1
(30)
we get d1 = d/2. In this case, d1 = d2 = d/2. In summary, the NCCP outage capacity is maximized, if the relay node X, S1 , and S2 are on a straight line, and d1 = d2 . For the NCCI problem, a similar conclusion can also be obtained. The detailed analysis to the NCCI problem is omitted here. V. O PPORTUNISTIC O PTIMAL N ETWORK C ODING S CHEME To apply network coding in a practical network, there are still some problems to be solved, e.g., the synchronization issue and the unbalanced traffic load. In most previous work on network coding, global synchronization is assumed throughout the network. However, as some researchers have already noticed, global synchronization is actually too strict in practical networks, and the absence of synchronization can greatly affect the performance of network coding in wireline networks [5], [9], [19]. As a matter of fact, synchronization is more critical in wireless fading channels than in wireline channels. For example, as shown in Fig. 1(b), at stage 3, if network coding is employed, the following condition that there are at least one packet sent to S1 and one sent to S2 in node X’s buffer should
LI et al.: NETWORK CODING FOR TWO-WAY RELAYING NETWORKS OVER RAYLEIGH FADING CHANNELS
be satisfied. Due to high BER and relatively high collision probability, the preceding condition may sometimes not be satisfied in wireless fading scenarios. In this case, node X stops the transmission, receives packets again, and waits for the next transmission, resulting in a waste of time slots. Unbalanced traffic load can result in a similar problem. To mitigate the impact of unbalanced traffic load and asychronization in wireless fading channels, we propose two OONC schemes, i.e., the OONC-CP scheme and the OONC-CI scheme, which combine the network coding and store-and-forward scheme. Compared with the existing opportunistic network coding schemes, the advantage of the proposed OONC schemes is that physical-layer information is considered in OONC schemes. In existing schemes, e.g., in [15] and [19], the coding node selects the network-coding scheme or the store-and-forward scheme just according to medium-access layer information, i.e., the buffer status. However, in this paper, our emphasis is fading channels; thus, in the proposed OONC schemes, the coding node decides which action to take, i.e., network coding or forwarding, based on not only buffer status but on also channel state as well. In addition, the transmission scheme of the physical layer is considered in OONC schemes, i.e., how to adjust the transmission data rate and transmission power level of relay nodes according to channel state, while it is not considered in existing schemes. In the following, we will explain the OONC schemes. Based on the CP scheme, the OONC-CP scheme is described as follows: For the relay node X, its procedure is given as follows: Step 1) Node X receives packets and checks the buffer. If there are packets in its buffer, it begins to contend for the channel. Go to step 2). Step 2) If the relay node X has occupied the channel, it checks its buffer. If there are some packets sent to S1 and some packets sent to S2 , go to step 3); otherwise, go to step 4). Step 3) The NCCP scheme is employed. Node X chooses one packet sent to S1 and one packet sent to S2 , encodes them to one encoded packet, and then broadcasts the encoded packet. The transmission data rate is determined by (12). Go to step 5). Step 4) The Store-and-forward scheme is employed. Node X selects a packet and sends it to its destination. The transmission data rate is determined by (9). Go to step 5). Step 5) Prepare to receive packets. Go to step 1). In addition, based on the CI scheme, the OONC-CI scheme is described as follows: For the relay node X, its procedure is given as follows: Step 1) Node X receives packets and checks the buffer. If there are packets in its buffer, it begins to contend for the channel. Go to step 2). Step 2) If the relay node X has occupied the channel, it checks its buffer. If there are some packets sent to S1 and some packets sent to S2 , go to step 3); otherwise, go to step 4).
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Step 3) The NCCI scheme is employed. Node X checks channel state information, selects receivers, and adjusts its transmission power according to (21). Then, node X chooses one packet sent to S1 and one packet sent to S2 , encodes them to one encoded packet, and then transmits the encoded packet. The optimal cutoff fading gain and transmission data rate are determined by (27). Go to step 5). Step 4) The Store-and-forward scheme is employed. Node X selects a packet and sends it to its destination. The cutoff fading gain and transmission data rate are determined by (20). Go to step 5). Step 5) Prepare to receive packets. Go to step 1). The principle of the OONC schemes is that relay node X needs to make two decisions to determine how to transmit data packets. First, X checks its buffer. If there are packets sent to two nodes S1 and S2 , respectively, network coding is employed; otherwise, the store-and-forward scheme is employed. Second, the relay node selects receivers and determines transmission power level according to channel-state information. In fact, this is also the second selection between network coding and forwarding. Because if the relay node decides to transmit packets to only one receiver in the second decision according to channel-state information, the final action of the relay node will be forwarding in spite of which action is selected in the first decision. For example, at step 3) of the OONC-CI scheme, if the NCCI scheme is employed, node X needs to check the channel state. As (21) shows, only if the instantaneous fading gains of both links (X, S1 ) and (X, S2 ) are larger than the cutoff fading gain γ0 is network coding indeed employed, i.e., node X transmits encoded packets to both S1 and S2 . In other cases, node X transmits packets to one node or does not transmit packets, which is similar to the store-and-forward scheme. In addition, to maximize the total throughput, the transmission data rate and power level are determined by (9), (12), (20), and (27), respectively. Some more details of the OONC-CP scheme and OONC-CI scheme are also given as follows: First, in wireless networks, if two nodes are close to each other and simultaneously transmit packets, a collision occurs, and it may result in the failure of decoding. In the proposed schemes, to avoid packet collisions, it requires that, when a node wants to send a packet, it needs to contend for the channel first. Only if a node, e.g., node X, has occupied the channel can it transmit packets, which means that other nodes within the transmission range will keep quiet when node X is transmitting packets. In this case, collisions are avoided. Then, the problem is how to contend for the channel. In this paper, the CSMA/CA protocol can be employed to deal with this problem in a wireless network [23]. In the CSMA/CA protocol, a node requiring to send data initiates the process by sending a request-to-send (RTS) packet. Then, the destination node replies with a clearto-send (CTS) packet. After receiving the CTS packet, the source node can begin to transmit data. If the source node does not receive the CTS packet due to collisions or low SNR, it retransmits an RTS packet. Any other node that receives the RTS or CTS packet but is neither source node nor destination
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Fig. 4. Example of a large wireless network.
node should refrain from sending data for a given duration. In this case, when the source node is transmitting data packets, other nodes within the ranges of the source node and destination node will keep silent. Collisions are avoided. Second, for the OONC-CI scheme, it requires that the relay node X can obtain perfect CSI, i.e., the value of gi (t), i = 1, 2, which is the channel power gain of link (X, Si ). Assuming that the value of gi (t), i = 1, 2, varies not very fast, node X can obtain the value of channel gain by exchanging RTS/CTS packets with destination nodes in the proposed schemes. Because the CSMA/CA protocol is employed, if node X wants to send a data packet to a destination node, e.g., node S1 , X should send an RTS packet to S1 and wait to receive a CTS packet. When S1 replies with a CTS packet, it can add the value of transmitted power level in the CTS packet. Then, by receiving the CTS packet, X can estimate the received power level and obtain the transmitted power level from the CTS packet. By comparing the two values, X obtains the value of instantaneous channel gain g1 (t). As slow fading is assumed in this paper, after receiving the CTS packet, X can transmit a data packet to S1 according to the obtained value of g1 (t). This procedure can be performed for each data transmission. Third, in the proposed schemes, relay node X can take two actions, i.e., forwarding or network coding. To indicate what action node X has taken, we can add 1 bit in the packet overhead, which is denoted as “ACTIN.” ACT IN = 1 means that network coding is employed, and ACT IN = 0 means that forwarding is employed. Then, when node S1 or S2 receives a packet, it decodes the packet and checks the value of the bit “ACTIN.” If ACT IN = 1, a transmission finishes. If ACT IN = 1, the receiver needs to recover the original packet according to network coding protocol. Fourth, in the proposed schemes, if the received signal is not correctly decoded, the transmitter needs to retransmit the data packet. In particular, for the OONC-CP scheme, the transmitter
cannot adjust the transmission power level according to the channel state; thus, perhaps many packets cannot correctly be decoded due to low SNR. Thus, retransmission is particularly required if the OONC-CP scheme is employed. In addition, the OONC schemes cannot only be applied in a two-way relaying network but can be expanded to a generic wireless network as well. In a large wireless network, if two nodes transmit packets to each other, every relay node on the transmission path needs to relay packets from the two source nodes. Then, every relay node on the transmission path can be treated as the relay node X in a two-way relaying network, and the transmission path can be separated as several two-way relaying networks. In this case, the proposed schemes can be applied at the relay nodes. For example, there are seven nodes in Fig. 4. Node 1 wants to send packets a, c, e, etc., to node 7, and node 7 wants to send packets b, d, f , h, etc., to node 1. Fig. 4 shows the transmission procedure. In this figure, the whole network can be separated as several two-way relaying networks. For instance, one of two-way relaying networks is composed of nodes 5, 6, and 7, in which node 6 is the relay node. The proposed schemes can be employed at node 6. At steps 2) and 6), node 6 can transmit packets. By checking its buffer, only at step 6) can node 6 employ the network coding scheme. At step 2), node 6 just forwards packets. Node 6 also needs to adjust its transmission data rate and power level based on the proposed schemes. VI. P ERFORMANCE E VALUATION In this section, we evaluate the performance of the proposed schemes by simulations. The performance comparison between the proposed schemes and the existing store-andforward scheme is also conducted. In the simulations, we consider a two-way relaying network over Rayleigh fading channels, as shown in Fig. 1. In the network, there is only one
LI et al.: NETWORK CODING FOR TWO-WAY RELAYING NETWORKS OVER RAYLEIGH FADING CHANNELS
Fig. 5.
Total throughput in simplified scenarios for the NCCP scheme.
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Fig. 7. Total throughput at different data rates for the OONC-CP scheme.
retical results very well. If packets are not transmitted at the optimal data rate, i.e., Ropt,nccp or Ropt,ncci , the throughput will decrease, which indicates that our proposed data rates Ropt,nccp and Ropt,ncci are the optimal data rates for the NCCP scheme and the NCCI scheme, respectively. In addition, both the average fading gains of links (X, S1 ) and (X, S2 ) will affect the throughput. As the value of γ1 or γ2 decreases, the total throughput will decrease. B. Performance of OONC Schemes
Fig. 6.
Total throughput in simplified scenarios for the NCCI scheme.
shared frequency band, and the bandwidth is 1.0 MHz. If not specifically given, the packet length is 500 bits, and the heavy traffic load is assumed, which means that S1 and S2 always have packets to send. In addition, every result is based on ten simulations. The confidential intervals are marked in figures, and the confidential level is 95%. A. NCCP and NCCI Outage Capacity First, we validate the NCCP outage capacity (12) and NCCI outage capacity (27) by simulations. In this part, we consider a simplified scenario. That is, we omit the procedure that S1 or S2 transmits packets to the relay node X, and let X always broadcast encoded packets to S1 and S2 , i.e., only stage 3 in Fig. 1(b) is considered. There are 10 000 transmissions in every simulation. Fig. 5 shows the average throughput under the simplified scenarios for the NCCP scheme. Fig. 6 shows the average throughput under the simplified scenarios for the NCCI scheme. Compared with Fig. 2, the simulation results match the theo-
In this part, we evaluate the performance of the OONC schemes by simulations. We consider an actual two-way relaying network. It is a distributed network, and there are contentions and collisions among nodes. To deal with them, the CSMA/CA protocol is employed in our simulations. Some parameters are illustrated. 1) Transmitting a RTS/CTS/ACK packet takes 50 μs. 2) The minimum time interval of two transmissions is 50 μs. 3) The shortest and the longest periods of the sensing channel for each transmission are 100 and 250 μs, respectively. 4) The simulation period is 120 s. As a comparison, the performances of the classical networkcoding scheme (store-and-forward is not exploited) and storeand-forward scheme are also presented. First, we show the simulation results of the CP schemes. Fig. 7 shows the total throughput with different values of the average fading gains and different data rates for the OONC-CP scheme. In this figure, the total throughput at the optimal data rate Ropt,nccp is larger than that at nonoptimal data rate. Figs. 5 and 7 validate that Ropt,nccp is the optimal data rate under both simplified and actual situations. In Fig. 8, we compare the throughput of the OONC-CP, network coding (NCCP), and store-and-forward (SLCP) schemes under balanced traffic load and unbalanced traffic load. Here, balanced traffic load means that the average traffic sent by S1 and S2 are equal. Unbalanced traffic load means that the average traffic sent by S2 is equal to half of the average traffic
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Fig. 8. Total throughput under balanced load and unbalanced load for the CP schemes (γ2 = γ1 ).
Fig. 9. Effect of packet length on throughput for the CP schemes when γ2 = γ1 (CPL: constant packet length; VPL: variable packet length).
sent by S1 . Under balanced load, the throughput of the OONCCP or NCCP scheme is almost twice as much as the throughput of the SLCP scheme. Under unbalanced load, the throughput of all schemes decreases, but the throughput of OONC-CP is much larger than the throughput of the NCCP or SLCP scheme. The reason is that, for the network coding scheme, only after packets from both S1 and S2 arrive can the relay node X transmit encoded packets. Under unbalanced load, the packet from the link with larger traffic load needs to wait for the packet from the link with smaller traffic load, which results in a waste of time. The store-and-forward scheme can mitigate the effect of unbalanced load, but its throughput is smaller than the network coding scheme. The OONC-CP scheme takes the advantages of both the network coding and store-and-forward schemes. Fig. 8 indicates that the OONC scheme performs well under both balanced load and unbalanced load. We investigate the effect of packet length on the network throughput to the CP scheme shown in Fig. 9. In the simulations, CPL means that the packet length is 500 bits, and VPL
Fig. 10.
Total throughput at different data rates for the OONC-CI scheme.
means that the packet length follows a uniform distribution and that the average value is 500 bits. We observe that the network throughput is not sensitive to the conditions of constant packet length or variable packet length. That is to say, the OONC is suitable for various situations. Then, the simulation results of the CI schemes are shown as follows: Fig. 10 shows the total throughput as a function of different values of the average fading gains and different data rates for the OONC-CI scheme. In this figure, the total throughput at optimal data rate is larger than the total throughput at nonoptimal data rate. Figs. 6 and 10 validate that Ropt,ncci is the optimal data rate under both simplified and actual situations. In addition, compared with Fig. 7, the throughput of the OONCCI scheme is larger than that of the OONC-CP scheme. This is because, compared with the OONC-CP scheme, the transmitter in the OONC-CI scheme can obtain the value of instantaneous channel gain, which can be used to adjust transmission power level. In Fig. 11, we compare the throughput of the OONC-CI, network coding (NCCI), and store-and-forward (SLCI) schemes under balanced traffic load and unbalanced traffic load. Similar to Fig. 8, the OONC-CI scheme performs well under both the balanced load and the unbalanced load. Fig. 12 shows the effect of packet length on network throughput to the CI schemes. In this figure, the network throughput is not sensitive to the conditions of constant packet length or variable packet length. The OONC-CI is suitable for various situations. VII. C ONCLUSION In this paper, we have investigated the performance of wireless network coding over Rayleigh fading channels. We have found that signal fading greatly degrades the performance of wireless network coding. In particular, when the difference between the average channel gains of the two relay channels is very large, the advantage of network coding almost disappears. To increase the throughput for wireless network coding over Rayleigh fading channels, we have formulated the fading
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Fig. 11. Total throughput for balanced load and unbalanced load for the CI schemes (γ2 = γ1 ).
Fig. 12. Effect of packet length on throughput for the CI schemes when γ2 = γ1 (CPL: constant packet length; VPL: variable packet length).
compensation as two optimization problems, i.e., NCCP and NCCI problems. By solving the optimization problems, the optimal transmission data rate and optimal transmission power level are presented. The simulations and numerical results have shown that, if the relay node transmits packets at the optimal transmission data rate and optimal transmission power, the network throughput will increase. We have also considered the effect of the location of the relay node on the network throughput over fading channels and proven that, when the relay node and two source nodes are in a straight line and the relay node is exactly at the middle of the two source nodes, the network throughput can be maximized. In addition, to consider the realization problem of network coding including asynchronization and unbalanced traffic load in fading channels, two OONC schemes, i.e., the OONC-CP and OONC-CI schemes, have been designed, which combine the network coding and store-and-forward schemes. Performance evaluation has shown that the OONC schemes perform well under various situations.
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Wei Li received the B.S. degree, in 2004, from Tsinghua University, Beijing, China, where he is currently working toward the Ph.D. degree with the Department of Electronic Engineering. From January 2006 to March 2006, he visited NICT Japan as a Researcher. From November 2008 to October 2009, he visited the University of Tsukuba, Tsukuba, Japan, as a Visiting Foreign Research Fellow. His research interests include network information theory, network coding, and wireless ad hoc networks.
Jie Li (SM’04) is currently a Professor with the Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba Science City, Japan. He has served on the editorial boards of the IPSJ Journal, Wiley Wireless Communications and Mobile Computing, etc. His research interests are mobile distributed multimedia computing and networking, operating systems, network security, and modeling and performance evaluation of information systems. Prof. Li is a Senior Member of the Association for Computing Machinery and a Member of Information Processing Society of Japan (IPSJ). He has served as secretary for the Study Group on System Evaluation of IPSJ and on the editorial board of the IEEE TRANSACTIONS ON V EHICULAR T ECHNOLOGY. He has also served on the Steering Committees of the SIG of System EVAluation (EVA) of IPSJ, the SIG of Database System of IPSJ, and the SIG of MoBiLe computing and ubiquitous communications of IPSJ. He is also on the program committees for several international conferences, such as the IEEE ICDCS, IEEE INFOCOM, IEEE GLOBECOM, and IEEE MASS.
Pingyi Fan (M’04–SM’09) received the B.S. degree from Hebei University, Hebei, China, in 1985, the M.S. degree from Nankai University, Tianjin, China, in 1990, and the Ph.D. degree from Tsinghua University, Beijing, China, in 1994. In 2002, he was promoted to Full Professor with Tsinghua University. From August 1997 to March 1998, he visited Hong Kong University of Science and Technology, Kowloon, Hong Kong, as a Research Associate. From May 1998 to October 1999, he visited the University of Delaware, Newark, as a Research Fellow. In March 2005, he visited NICT Japan as a Visiting Professor. From 2005 to 2009, he visited Hong Kong University of Science and Technology several times. He is the founding editor-in-chief of the International Journal of Wireless Communications and Networking. In addition, he is currently serving as Editor for the Wiley Journal of Wireless Communication and Mobile Computing, the Inderscience International Journal of Ad Hoc and Ubiquitous Computing, and the Inderscience International Journal of Autonomous and Adaptive Communications Systems. From 2007 to 2009, he served as Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. His research interests include beyond third-generation technology in wireless communications such as multiple-input multiple-output, orthogonal frequency-division multiplexing, multicarrier code-division multiple access, space time coding, low-density parity-check design, network coding, network information theory, and cross-layer design. Dr. Fan is an overseas member of the Institute of Electronics, Information, and Communication Engineers. He has organized many international conferences, including the 2010 IEEE International Conference on Wireless Communications, Networking and Information Security as Technical Program Committee (TPC) Co-Chair; the IEEE International Communications Conference as TPC Member; and Globecom from 2007 to 2010. He is also a Reviewer of more than 22 international journals, including 14 IEEE journals and three European Association for Signal Processing journals.
