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COOPERATIVE WIRELESS NETWORKS BASED ON PHYSICAL LAYER NETWORK CODING SHENGLI FU, UNIVERSITY OF NORTH TEXAS KEJIE LU, UNIVERSITY OF PUERTO RICO AT MAYAGÜEZ TAO ZHANG, NEW YORK INSTITUTE OF TECHNOLOGY YI QIAN, UNIVERSITY OF NEBRASKA-LINCOLN HSIAO-HWA CHEN, NATIONAL CHENG KUNG UNIVERSITY
xa(t)+xb(t) Ri-1
R1
(t+1)+xb(t) Ri-1
Ri xa(t+1)+xb(t+
Ri-1
Ri
The authors develop a generic wireless network design framework based on physical layer network coding as a novel cooperation technique. In this framework, several transmitters in a cooperative network may transmit signals simultaneously to the same receiver to improve the overall performance. 86
ABSTRACT Designing a wireless network is always challenging because of the harsh environment of wireless channels. While significant progress has been made over the last decade, most of the techniques were developed and optimized based on the point-to-point communication model. Recently, the cooperative communication model has attracted a lot of attention due to the fact that it may achieve significantly better performance than the traditional wireless network models. In this article we develop a generic wireless network design framework based on physical layer network coding as a novel cooperation technique. In this framework several transmitters in a cooperative network may transmit signals simultaneously to the same receiver to improve overall performance. The topics addressed in this article include network capacity, modulation, channel coding, and security issues from a viewpoint fundamentally different from the traditional communication models.
INTRODUCTION In the last 20 years, we have witnessed great progress in wireless networking technologies. The data rate for the first generation cellular system was 10 kb/s for Advanced Mobile Phone System (AMPS) and 8 kb/s for European Total Access Cellular System (ETACS) in the 1980s. In contrast, the latest Third Generation Partnership Project (3GPP) and Long Term Evolution (LTE) standard can provide up to 326.4 Mb/s downlink and 86.4 Mb/s uplink data rates. To increase the throughput of wireless networks, different techniques have been exploited, including advanced coding schemes (e.g., turbo codes and low density parity check [LDPC] codes), multiple-input multiple-output (MIMO) systems, and orthogonal frequency-division multiplexing (OFDM) systems. Despite those technological breakthroughs, new applications (e.g., real-time multimedia services) continuously bring chal-
1536-1284/10/$25.00 © 2010 IEEE
lenges to the next-generation wireless networks, such as scarce frequency resources, fast fading channels, and user competition to access the networks. To further improve network throughput, cooperative communication is one of the most promising techniques. The motivation to employ users’ cooperation is that most of the current techniques were developed and optimized based on the point-to-point communication model, which may not be effective when applied directly to a multinode scenario. Based on how users share their resources, various cooperative communication schemes can in general be grouped into three categories: frequency, antenna, and relay node. Cognitive radio is a typical collaboration system in the frequency (sometimes also in the time) domain, where different users may temporarily share their resources with others to improve the efficiency of spectrum utilization. The feasibility of cognitive radio comes from the fact that some frequency bands assigned to primary users are only partially occupied or largely unoccupied most of the time. These unused frequency bands can be exploited by secondary users, resulting in a significant improvement in spectrum utilization. Another type of cooperative communication is achieved through antenna sharing to obtain spatial diversity even if each node in a network has only one antenna. In this system the collaboration protocol works in two phases. In the first phase the source broadcasts the information to the relay nodes. In the second phase the relay nodes forward the received information to the destination in a collaborative way, or a virtual MIMO system is formed to increase the channel capacity. In [1] theoretical analysis was provided to compare the performance of different relay strategies for cooperative communication. In this article we investigate cooperative communication through physical layer network coding (PLNC), which can be defined as a way to share relay nodes. While the antenna of the relay node is also shared in this scheme, there is
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a fundamental change in terms of the functions of the relay node, which is one of the key characteristic features of network coding [2]. In traditional network systems, relay nodes only copy and forward the received information from a single source at one time to their neighbors. However, in a network coding system, the relay nodes first use an arithmetic function to combine information received previously and then forward the result of the function to the next receivers. In this manner the throughput of the whole network can be improved since less information exchange is needed. While the original network coding schemes were normally implemented in the data link layer or other higher layers, the information can also be manipulated over the physical layer [3], which in fact can work naturally in a wireless network because of the broadcast nature of signals. In this case the relay node tries to detect combined signals from different source nodes at the same time over the same channel. In a traditional system, if there are more than one signal appearing over the same channel, all of them mutually interfere with one another. But in a network coding system, the interest of relay nodes is just the combined signal, instead of the individual signals. In [3] the authors discussed PLNC from the viewpoint of information theory. In [4] a similar scheme, called analog network coding, was implemented by using software defined radio. In this article we discuss the impact of PLNC on the throughput of networks, the symbol error performance with different modulation techniques, and the security capabilities enabled by PLNC. In the rest of this article we first review the background of network coding and then introduce the system model for PLNC. We also discuss the impact of PLNC on channel capacity and network throughput, as well as the modulation techniques that work in a very different way from that of traditional point-to-point communication systems. A novel channel coding scheme is also presented to enable asynchronous transmissions with PLNC. Then we discuss the security issues, followed by conclusions and future directions.
PHYSICAL LAYER NETWORK CODING Network coding was first investigated by Ahlswede et al. [2] in 2000. While the classical coding techniques such as source coding and channel coding are applicable to communication system terminals, network coding is implemented at the intermediate nodes of a network. Before the proposal of network coding, the functionalities of intermediate (or relay) nodes were limited to copying received information from the previous nodes and forwarding the information to the next nodes. In a network coding system, messages from multiple sources will be manipulated first and then forwarded by the relay nodes, leading to throughput improvement within the whole network. In fact, [2] has shown that network coding can achieve the optimal capacity defined by the max-flow min-cut theorem. As indicated by its name, physical layer network coding is different from traditional network
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xa Alice
xa + xb
xb Relay
xa + xb
Time slot 1 Time slot 2 Bob
Figure 1. Physical layer network coding for the Alice-Relay-Bob model. coding in terms of the layers over which the manipulation of multiple information flows occur. In [2] the relay nodes applied the XOR operation for received data, which was implemented over the data link layer (or the other higher layers). In comparison, in the PLNC scheme [3, 4] the information is processed over the physical layer. To demonstrate this difference, let us first discuss a simple “Alice-RelayBob” model [4], and then present a more generic system. As shown in Fig. 1, the goal of this threenode system is to exchange information between nodes A (Alice) and B (Bob) with the help of node R (Relay). In a traditional network four time slots are required to complete the transmission: binary message xa is transmitted from A to R and then to B in the first two time slots. Similarly, node B transmits binary message x b to R and then to A with another two time slots. With the help of network coding, only three time slots are needed for the exchange: node A transmits x a to the relay node in the first time slot and B sends x b to R in the second slot. In the third time slot, node R broadcasts xr = xa ⊕ xb to A and B where ⊕ is the XOR operation at the bit level. Since node A has the a priori information of x a, message x b can be decoded from the received signal of x r. Similarly, node B can decode xa with the a priori information of xb, to complete the two-way information exchange. This example clearly shows that the information has been processed at the relay node before forwarding, which in turn increases the system throughput. It is worth noting that the XOR operation discussed in [2] was later generalized to any algebraic operations [5]. The linear combination of the received information offers greater flexibility for the design of a network coding scheme in a practical system. Further improvement can be achieved through the new PLNC scheme as shown in Fig. 1. To implement the same function, only two time slots are needed: • Time slot 1: Nodes A and B send information simultaneously to relay node R, the former with message xa and the latter with xb. • Time slot 2: Node R broadcasts received information to both nodes A and B. Obviously, the reduction of time slots comes from the simultaneous transmission of nodes A and B during the first time slot. In a traditional system, if there are more than one transmission over the same frequency band, the signals are interweaved with the other signals, and the receiver cannot decode any of them. In other words, the signal from one link introduces high interference with the other links. However, in a PLNC system, these mixed signals are similar to the output of a relay node after XOR in the network coding system. The superposition nature of
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Time slot
Traditional
Network coding
PLNC
1
xa A→R
xa A→R
xa xb A → R, B → R
2
xa R→B
xb B→ R
R
3
xb B→ R
R
4
xb R→ A
xa+ xb → A and B
xa⊕xb → A and B
Table 1. Comparison of transmission schemes. physical signals actually provides the information combination instead of taking explicit summation over the network layer or other upper layers. A summary of the three schemes is given in Table 1.
RELAY STRATEGIES One of the most important issues for the scheme shown in Fig. 1 is the relay strategies for the intermediate node. In other words, how does relay node R broadcast received messages to nodes A and B in the second time slot? Basically, there are two types of relay mechanisms: amplify-and-forward (AF) and decode-and-forward (DF). In the AF mode, no attempt is made to decode the received information. The received signals from both directions are normalized and then transmitted in the next time slot. In the DF mode, relay nodes first decode the received message and then forward the information to their neighbors. It should be noted that in PLNC the information received by relay nodes is mixed signals from the two directions in the same frequency band. While detecting the individual signals is difficult, the interest in our scheme is the summation of the two signals, and there is no need to decode each of them. More discussions and comparisons between the AF and DF modes are out of the scope of this article. We focus on the characteristics of mixed signals as the unique part of PLNC.
THE SYSTEM MODEL FOR ONE-DIMENSIONAL NETWORKS The three-node PLNC model shown above can be generalized to an n-node system. For analysis convenience, we constrain the network topology to one dimension only (i.e., two end nodes, A and B), and n – 2 relay nodes are evenly distributed along a one-dimensional line. Figure 2 illustrates the topology and transmission protocols for the one-dimensional wireless network system. Similar to the three-node case, nodes A and B exchange message xa(t) and xb(t) through the n – 2 relay nodes. To conduct the analysis, we follow a well-known protocol model introduced in [6]. In this model a transmission from node i to j is successful if and only if the distance between them is less than r, and all the other transmitting nodes are (1 + Δ)r away from node j, where parameter is used to specify the effect of interference range and Δ > 0. In the system shown in Fig. 2, we assume an equal distance r between two adjacent nodes, meaning that the signal transmitted from one node can
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only be successfully received by its two nearest neighbors on the left and right sides. The transmission protocol for the system shown in Fig. 2 is based on a time-division multiple access (TDMA) scheme, in which the time axis is divided into equal length time slots, and the nodes start transmitting signals only at the beginning of a new time slot. To schedule the transmissions, we further divide time slots into odd (solid line) and even (dashed line) segments. The nodes are also divided into odd (empty circle) and even (filled circle) groups. In our protocol, the transmissions are scheduled in an alternative way: all odd numbered nodes broadcast their messages at odd numbered time slots, and all even numbered nodes transmit at even numbered slots. When a node receives the signals from both sides, the relay node forwards the mixed information through either AF or DF. It is noted that the message is always a combination of the signals from two directions. In Fig. 2 the message without noise error is shown above the transmitting nodes, and the directions of transmission are shown by the arrows of lines. The symbol x a (t) denotes the tth information from left to right (node A to B), and x b (t) denotes the tth information from right to left (node B to A). For example, suppose in the odd time slot m – 1, node Ri stores xa(t) + x b(t) and broadcasts this message to nodes Ri+1 and Ri–1. In the following even time slot m, node R i receives x a(t + 1) + xb(t) from its left node Ri–1 and xa(t) + xb(t + 1) from Ri+1. Since node Ri has the information of xa(t) + xb(t), it can decode xa(t + 1) + xb(t + 1) from these received signals. In the following odd time m + 1, xa(t + 1) + xb(t + 1) is transmitted to both Ri–1 and Ri+1. Generally, we can use the following equation to explain the process: {xa(k + 1) + xb(l)} = {xa(k + 1) + xb(l – 1)} + {xa(k) + xb(l)} – {xa(k) + xb(l – 1)}, where xa(k) and xb(l) represent the kth message from node A (left to right) and lth message from node B (right to left), respectively. The “Alice-Relay-Bob” system thus is only a special case of the general model with n = 3. Since nodes A and B are at the edge of the network, they only transmit their own messages in the odd time slots, but node R transmits the summation of xa and xb in the even time slots.
THE IMPACT ON CAPACITY OF WIRELESS NETWORKS The impact of PLNC on capacity can be discussed from two aspects. We first study the impact on channel capacity, which is defined as the maximal rate at which information can be reliably transmitted over the channel from the source to the sink. The “Alice-Relay-Bob” model shown in Fig. 1 is used for this discussion. We also discuss the impact on network capacity, that is, the asymptotic throughput per source-to-destination pair over a large-scale wireless network with n nodes. As there are multiple pairs within the network, the network capacity actually describes the average achievable throughput for
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xa(t+2)+xb(t-1)
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xa(t+2)+xb(t) Time slot
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Ri+1
xa(t+1)+xb(t+1) Ri-1
Ri
Odd time slot Even time slot
Ri+2
Ri+3
xa(t)+xb(t+2) Ri+1
Even node
Ri+2
Ri+3
Odd node
Figure 2. PLNC transmission in one-dimensional networks. a given network. As an example, we also present some results on the capacity for the general onedimension-model shown in Fig. 2.
CHANNEL CAPACITY OF THE ALICE-RELAY-BOB MODEL It is interesting to note that there are two types of channels in the “Alice-Relay-Bob” system at different time slots. The channel for the first time slot is similar to a multiple access channel but differs substantially in the decoded signals. In a traditional multiple access channel, multiple transmitters send information through the same channel, and the receiver(s) try to detect every bit of the information correctly. In the PLNC model, two transmitters (A and B) also send their information (x a and x b , respectively) to relay node R through the same channel. However, the interest of receiver R is the summation signal of xa + xb, not the individual information x a and x b as in the multiple access system. In other words, in a multiple access system, the decoding is successful only if both xa and xb are detected correctly. For the PLNC system, detection is successful as long as the decoding of xa + x b is correct, even with a wrong detection of x a and xb. To compare the capacity between the multiple access channel and PLNC model, let us consider an additive white Gaussian noise channel. The received signal at node R is represented by Y = Xa + Xb + Z where Z is the Gaussian noise. The capacity of multiple access channel is defined by max
p ( xa ) p ( xb )
I ( Xa , Xb ; Y ),
the maximum mutual information between (Xa, Xb) and XZ. Here p(xa), p(xb), and p(xa + xb) are the probability mass functions of random variables Xa, Xb, and Xa + Xb. However, the capacity for the PLNC system is defined as max I ( Xa + Xb ; Y ),
p ( xa + xb )
IEEE Wireless Communications • December 2010
the maximum mutual information between Xa + Xb and XZ. In [7] the capacity of the PLNC system is defined as computational capacity. Furthermore, the authors generalized the function of x a + x b to any functions with an arbitrary number of source nodes, that is, f(x1, x2, ⋅⋅⋅, xn) where f(⋅) is a fixed many-to-one function. The computation capacity for a class of linear functions f(⋅) was also derived in [7]. Therefore, the “Alice-Relay-Bob” system is just a special case of a computation multiple access channel with two independent source nodes and a linear computational function (“XOR”). It was shown in [7] that when Alice and Bob experience the same channels to the Relay node, the computation rate of the “Alice-Relay-Bob” channel is twice that of the separated transmissions (i.e., Alice and Bob transmit information flows in different time slots). The other type of channel occurs in the second time slot, when relay node R transmits information to both nodes A and B. This is a typical broadcast channel involving one sender and two receivers. The capacity region of the broadcast channel is then defined by the closure of the achievable rates R a and R b for nodes A and B, respectively. However, the broadcast channel in the PLNC system has two special properties, which may lead to new designs of coding/decoding strategy. First, the decoding interest at node A (B) is to recover the message of x b (x a) based on the both signals from relay node R and the side information on xa (xb). For the traditional broadcast channel, there is no such side information for detection. Second, the channels for multiple access (A to R) and broadcast (R to A) are symmetric in some cases. By taking advantage of these features, the system performance can be improved through deliberate design of source and channel coding schemes. Some recent work [8] discussed the capacity region of the broadcast channel for the DF PLNC system. Another way to analyze the “Alice-RelayBob” system is the two-way communication channel first studied by Shannon in 1961. In his
In PLNC the received information by relay nodes is mixed signals from the two directions in the same frequency band. While detecting the individual signals is difficult, the interest to our scheme is the summation of the two signals and there is no need to decode each of them.
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The throughput capacity for a large-scale network is defined as the asymptotic average capacity of all the links in a large-scale network. In other words, the throughput capacity describes the average capacity when the number of nodes goes to infinity.
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model, there is no relay node auxiliary for the transmission. The two terminals try to send information directly to the other through the same channel simultaneously. Both inner bound and outer bound were derived in that work. Following this framework, the “Alice-Relay-Bob” system can be converted into a two-way model by replacing the relay node and the two channels (A ↔ R, B ↔ R) with a virtual channel between A and B.
THROUGHPUT CAPACITY OF LARGE-SCALE NETWORKS The throughput capacity for a large-scale network is defined as the asymptotic average capacity of all the links in a large-scale network. In other words, the throughput capacity describes the average capacity when the number of nodes goes to infinity. In [6] Gupta and Kumar derived the throughput bounds for an arbitrary network and random networks. These bounds were derived based on two channel models: the protocol model and the physical model. In the protocol model successful transmission means that the distance between the transmitter and the receiver is less than a predefined transmission range, and at the same time, all other transmitters are located beyond a certain threshold. In the physical model a transmission is successful if the signal-to-interference-and-noise ratio (SINR) exceeds a given threshold. In both models the transmission data rate is fixed. Let us use the physical model to address the impact of PLNC on throughput capacity. In this model a transmission from node i to j is successful if and only if the distance between them is less than r, and all the other transmitting nodes are (1 + )r away from node j, where parameter is used to specify the effect of interference range and > 0. If the data rate for every transmission is fixed at W b/s, the capacity can be derived as [6]
λ F (n ) =
2W . (1 + Δ )n
One interesting observation from this result is that as the number of users (n) increases to infinity, the average throughput for all nodes (λ F ) is actually reduced to zero, which is an important scaling property for a flow-based network. The effect of network coding on the throughput capacity was derived in [9], in which the authors showed that network coding provides no order improvement but brings in a constant factor benefit on throughput. The throughput with the original network coding is given as follows:
λ NC (n ) =
2W . Δ⎞ ⎛ + n 1 ⎜⎝ ⎟ 2⎠
Comparing λ NC and λ F , we can see that the throughput decreases with the increase of n. However, λ NC is always greater than λ F as the denominator is (1 + Δ/2)n instead of (1 + Δ)n. The impact of PLNC on the throughput for a wireless network was studied for the one-dimen-
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sional model shown in Fig. 2 in [10]. Letting λPN be the throughput for a PLNC wireless network, we have derived the capacity as
λPN =
2αW n
and
λPN =
2αW Δ⎞ ⎛ ⎜⎝ 1 + ⎟⎠ n 2
for Δ ≥ 2. Here we use α to represent the impact of PLNC on the data rate. According to the study given in [10], the value of α is quite close to one in most cases. We will further discuss factor α in the next section. Comparing
λPN =
2αW n
with
λ F (n ) =
2W (1 + Δ )n
and
λ NC (n ) =
2W , Δ⎞ ⎛ + n 1 ⎜⎝ ⎟ 2⎠
we can see that PLNC can substantially improve the throughput capacity by eliminating the impact of Δ when Δ < 2.
MODULATION AND DEMODULATION The performance of mixed signal detection is critical to the successful operation of the PLNC scheme. This section investigates issues in the modulation and demodulation techniques for the new scheme, especially the symbol error rate (SER) in terms of signal-to-noise ratio (SNR). Since the “Alice-Relay-Bob” model is a fundamental block of the proposed scheme shown in Fig. 2, we focus on the analysis of this system. Also, we only discuss the performance in the first time slot when the DF relay scheme is used, which is fundamentally different from the traditional point-to-point communications.
ASSUMPTIONS There are several practical issues for the implementation of PLNC. In the “Alice-Relay-Bob” model nodes A and B have their own oscillators, which may lead to carrier and phase offsets. To facilitate the analysis, we assume that perfect synchronization is available. Therefore, global synchronization is required within this threenode network.
THE EFFECT OF SNRS We present the analysis for binary phase shift keying (BPSK), but the analysis can be extended to any other quadrature modulation techniques (i.e., 8-PSK, 16-quadrature amplitude modulation [QAM]). For the convenience of analysis, we assume an additive white Gaussian noise (AWGN) channel, and focus on the impact of the
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BPSK constellation from the transmitter (a)
Constellation of received combination signal (b)
Figure 3. Received signal at relay node for BPSK with a) the same constellation; b) orthogonal constellations.
attenuation factor and Gaussian noise. To avoid confusion, hereafter we use ρ to indicate the signal power at the receiver. Furthermore, we consider a generic model in which two signals have different power levels and ρ1 ≥ ρ2 regardless of the sender. This is reasonable because the relay node does not need to decode the content of individual messages. Instead, the relay only needs to decode the combination of the two signals. Assume that the power levels are known to the receiver at the relay node. Let x a and xb be the transmitted BPSK symbols from nodes A and B, respectively. Then the received signal y at relay node R can be expressed by ——
——
y = √ ρ1 xa + √ ρ2 xb + N,
(1)
where N represents Gaussian noise with zero mean and variance σ2. Again, it is important to note that the combination of the two signals is to be decoded instead of individual signals. Therefore, it does not matter where the source nodes of A and B are. We first consider that A and B use the same BPSK constellation (±1) to modulate the signals. Therefore, the received constellation can be shown in Fig. 3a. To—— simplify the notation, in —— Fig. 3a we have r+ = √ ρ1 and r – = √ ρ2, respectively. As shown in Fig. 3a, there are four points in the constellation (as illustrated by small empty circles), since r+ ≥ r –. As a special case of r+ = r – = 1 the four received signals converge into three nodes at constellation points: –2, 0, and 2. The table in Fig. 3b shows the constellation mapping of transmitted signals and received summation signals with the same SNR: ρ1 = ρ2. a (b) denotes that bit a is mapped to constellation point b. For example, when nodes A and B send bits 1 and 0, respectively, the BPSK symbols are 1 and –1, respectively. The corresponding received constellation point is 0, which is mapped to bit 1. This is exactly the XOR operation discussed in the original network coding, but realized on the physical layer.
IEEE Wireless Communications • December 2010
Maximum likelihood (ML) criterion is used to decode the mixed signal at relay node R. The decision thresholds ±r+ are shown by the dashed lines in Fig. 3a. In particular, we have ⎧ 0, Y < −r + ⎪⎪ Y = ⎨ 1, − r + ≤ Y < r + . ⎪ Y ≥ r+ ⎪⎩ 0,
In the “Alice-RelayBob” model, nodes A and B have their own oscillators, which may lead to carrier and phase offsets. To facilitate the analysis, we assume that a perfect synchronization is available. Therefore, a global synchronization is required within this three-node network.
(2)
Based on the decision regions shown in Eq. 2, in [11] we derived the SER performance for BPSK and QPSK schemes. The theoretical and simulation results are shown in Fig. 4, where SNR = ρ1/(2σ2), which is the SNR for the stronger signal at the receiver of the relay node. Relay node R receives two signals xa and xb from nodes A and B, respectively. The interest of the Relay node is the summation of xa and xb. In Fig. 4 an error occurs when there is a detection error on xa + x b. It is noted that the decision threshold of r+ is not optimal [3]. However, it is a good approximation because its performance is very close to that of the optimal threshold derived in the analysis [11]. As we can see from Fig. 4, our analysis is consistent with the simulation results for the schemes with different arrival power levels. It is noted that in Fig. 4 the SNR difference means the difference between ρ 1 and ρ 2 in terms of decibels (dB). For example, “Diff 1dB” denotes that ρ 1 – ρ 2 = 1 dB. From Fig. 4, we can also observe that, given the same SNR at the receiver, the performance of PLNC with the same arrival power (“Same SNR”) is very close to that of BPSK. Let P SSNR and P BPSK be the SER for “Same SNR” and BPSK, respectively. As shown in [11], we have P SSNR ≤ 1.5 P BPSK , given the same SNR. For example, if a certain SNR can lead to 10 –5 SER with BPSK, then on average 99,999 symbols are received successfully of 100,000 symbols. With the same SNR, the scheme with PLNC can correctly deliver 99,998.5 symbols on the average. Clearly, the parameter α, which is used in the network throughput
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straightforward since the transmissions of source nodes A and B are separated, and each transmission is equivalent to a conventional point-topoint communication process. In [13] the authors studied a three-phase network coding scheme with channel coding used at the source nodes, and proposed several joint network coding and channel decoding schemes. The performance of the Repeat Accumulate (RA) codes was also studied. However, the proposed scheme was based on the assumption that the transmissions of two source nodes are perfectly synchronized. Such perfect synchronization is difficult to achieve, and the cost could be prohibitively high in real applications. In this section, we first discuss the effect of synchronization errors and then propose a new channel coding scheme to support asynchronous PLNC.
100
10-1
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10-2
10-3 BPSK Sim BPSK Theory Same SNR Sim Same SNR: Theory Diff SNR: 1 dB Sim Diff SNR: 1 dB Theory Diff SNR: 2 dB Sim Diff SNR: 2 dB Theory Orth BPSK Sim Orth BPSK Theory
10-4
10-5 0
0
1
2
3
4
5 SNR (dB)
6
7
8
9
10
Figure 4. SER comparison for BPSK constellations.
2αW n from earlier, is asymptotically close to one with the increase of SNR.
λPN =
EFFECT OF CONSTELLATIONS The curve of “Orth BPSK” in Fig. 4 also shows the performance when nodes A and B use orthogonal constellation points: one is (±1) and the other is(±j). We assume the same SNR for nodes A and B. The constellation of the summation signal at relay node R and the mapping table are shown in Fig. 3b. Both simulation and theoretical results shown in Fig. 4 indicate that the same constellation scheme outperforms the orthogonal constellation. An intuitive explanation is that for the case of the same constellation, the error probability of 0 (dash circle with 0 in Fig. 4) is lower than that of the orthogonal scheme. Some recent work [12] discussed the effect of constellation with consideration of both phases (multiple access channel and broadcast channel in Fig. 1). When QPSK is used in the “Alice-Relay-Bob” system, the relay node first maps the received signals (the summation of two QPSK symbols) to a point in the QPSK constellation and then broadcasts to A and B. However, [12] showed that when Alice and Bob experience different channel fading effects, the mapping over an irregular 5-ary constellation gives better performance than that of QPSK in terms of — throughput.—— The 5-ary—— constellation is (0, –3/√ —— —— — 55 ), (–16/√ 165, –3/√ 55 ),—— (16/√—— 165, –3/√ 55 ), —— —— (–8/√165, 5/√ 55 ), and (8/√165, 5/√ 55 ).
CHANNEL CODING FOR ASYNCHRONOUS PLNC In a wireless system channel coding is commonly used to improve link performance. How to incorporate channel coding with network coding is an important research topic. In the traditional network coding schemes with three time slots, it is
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THE EFFECT OF IMPERFECT SYNCHRONIZATION Figure 5a illustrates the effect of imperfect synchronization on channel coding of the PLNC system. In this example a 1/2 linear convolutional code is used at A and B. For the ith information bit Ia(i) (Ib(i)), the convolutional encoder at A (B) generates two coded bits, s a1(i) and s a0(i) (sb1(i) and sb0(i)), which are then modulated into symbols xa1(i) and xa0(i) ((xb1(i), and xb0(i)), where x a0 (i), x a1 (i), x b0 (i), and x b1 (i) are in {1, –1} for BPSK modulation. Assume that each data packet consists of L information bits. As shown in Fig. 5, the 2L symbols are transmitted sequentially xa0(1), xa1(1), xa0(2), xa1(2), ⋅⋅⋅, xa0(t), xa1(t), ..., xa0(L), xa1(L) for node A. It was shown in [14] that the summation of two linear convolution codes is also a linear convolution code. Therefore, in the case of perfect synchronization, the received signal at the relay node is xa0(t) + xb0(t) or xa1(1) + xb1(t) for a zero noise scenario. A Viterbi decoding procedure can be carried out to detect the summation. However, the mismatch in synchronization between two transmitters A and B may destroy the trellis structure, and the Viterbi algorithm becomes invalid for signal detection. In Fig. 5a we show two transmissions with only one symbol difference. It is clearly seen from the figure that the symbols generated from the tth trellis transition of the encoder at A (xa0(t), xa1(t)) are entangled with the symbols generated from both the tth trellis transition (xb0(t)) and the (t – 1)th trellis transition (xb1(t – 1)) of the encoder at B. The maximum likelihood (ML) decoding in this case becomes extremely complicated.
CHANNEL CODING TO SUPPORT ASYNCHRONOUS PLNC To enable asynchronous PLNC with channel coding, in [14] we proposed a new channel coding design by re-organizing the transmission sequence. The design is shown in Fig. 5b. Instead of transmitting xa0(t) and xa1(t) alternatively, node A sends all L symbols of x a0 (t) first, and then sends all L symbols of xa1(t). Between these two blocks, we insert two zeros. Node B follows the same way to generate the transmitted symbols.
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When the synchronization mismatch is less than two symbols (one symbol error is shown in Fig. 5b), the received signal is either xa0(t) + xb0(t – 1) or x a1(t) + x b1(t – 1), which is the summation of symbols from A and symbols from B with onesymbol shift. As long as the convolutional trellis structure is mainteined, we can apply the Viterbi algorithm for the decoding. Inserting zeros between blocks can be seen as a zero padding operation in an OFDM system, which is used to remove the interblock interference. The number of zeros used directly determines the tolerance of synchronization errors. When D max zeros (0s) are used, the maximum number for synchronization errors is Dmax symbols (D max = 2 for Fig. 5b). It should be noted that the increasing of D max leads to decreased data rate. For a channel code with the coding rate of R c , the actual achievable rate is R c (1 – Dmax/L).
PRACTICAL PLNC SYSTEM DESIGN To the best of our knowledge, the first PLNC system was reported in [4], in which the authors implemented the “Alice-Relay-Bob” model with software defined radio. The system was built on the Universal Software Radio Peripheral (USRP) with its operating frequency at 2.4 GHz. The open source GNU Radio program was used for the signal processing over the PC. The modulation scheme is minimum-shift key (MSK). A bit rate of 500 kb/s was achieved through this system. To apply the PLNC scheme to a practical system, there are still several challenging issues to be addressed.
TIME SYNCHRONIZATION Time synchronization is a critical factor for implementing cooperative communications. The transmission protocol, as shown in Fig. 2, works based on time slots. The transmission time is divided into time slots with equal length. The transmission alternates between even and odd numbered nodes. Therefore, global synchronization is needed in the network. Also, a central control node is responsible for assigning time slots to every node based on the topology of the network. While a new channel coding scheme for asynchronous PLNC systems was discussed earlier, symbol-level synchronization is still needed for the new design.
CARRIER SYNCHRONIZATION In the “Alice-Relay-Bob” model, we assume that both nodes A and B transmit messages over the same frequency simultaneously. The carrier offset among the three nodes also leads to some performance degradation. Compared to traditional point-to-point communication systems, we understand that there are new challenges to synchronize carriers in the PLNC system. First, both carrier frequency and phase should be synchronized. Furthermore, since there are three nodes involved in cooperative communications, the synchronization procedure becomes much more complicated than the two-node scenario. Second, some well-known techniques such as carrier estimation and noncoherent detection may not be
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χ1a(L) χ0a (L)
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Figure 5. Channel coding design for asynchronous PLNC systems. applied directly to the new model. Modifications and new designs are necessary to tackle those challenges.
POWER CONTROL The importance of power control is justified from two aspects. First, the symbol error rate is minimized when relay node R has the same received SNRs from both nodes A and B. This can also be seen from the simulation results for both BPSK and OFDM. It is to be noted that the channel between A and R is unlikely to be the same as that between B and R. To achieve balanced SNRs at node R, power control is necessary for both transmitters A and B. Second, the security performance is also determined by SNR balance. As discussed earlier, when node R has the same SNR, the information is transparent to the relay node, which provides perfect privacy. At the same time, an eavesdropper is unlikely to have the same SNR, which provides protection from wiretapping. To balance the received SNRs, the reverse channels are required to send power adjustment information from relay node R to A and/or B. Power adjustment can be implemented at the beginning of message transmission and updated according to channel dynamics.
FUTURE WORK AND OPPORTUNITIES As shown above, physical layer network coding works in a fundamentally different way from the traditional point-to-point model. It is worthwhile to re-investigate the theory and design of communication systems taking into account the impact of the PLNC model. Future work and opportunities are described.
SECRECY THROUGH PLNC PLNC can provide secrecy for wireless networks from two aspects: the privacy is maintained while information is forwarded by relay nodes, and information is protected from eavesdroppers. From the “Alice-Relay-Bob” system model and Eq. 1, we can see that when ρ1 = ρ2 and N = 0, the mutual information between received signal y and transmitted signals x1 and x2 is zero. This means that relay node R cannot decode the individual information of x 1 and x 2 , which is very important for privacy in practical cooperative
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Feedback is an important transmission mechanism to improve transmission reliability. The role of feedback is even more critical for the scheme of decodeand-forward than that of amplify-andforward since DF requires retransmission when the relay node cannot decode the received signal.
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communications. Actually, in the general system model shown in Fig. 2, all intermediate nodes cannot detect the individual messages while forwarding the mixed signals to their neighbors. Therefore, PLNC provides a solution to keep messages secret from the relay nodes while the information is transmitted by them. In the case of wiretapping, we assume that eavesdropper Eve (E) observes the signals transmitted from Alice and Bob. When Eve and Relay nodes are located at different positions, it is unlikely that the channel between A and R is the same as the channel between A and E since the transmission is over wireless fading channels. This is also the case for the nodes pairs (B, R) and (E, R). When the system has the same SNRs at relay node R by adjusting the transmission power at A and B, it is unlikely that Eve will have the same SNRs, which may create an obstacle for Eve to decode the mixed signals. As shown in Fig. 4, if SNR = 8 dB, when the received SNRs are the same, the SER is on the order of 10 –4 , but the error is on the order of 10 –2 if there is 2 dB difference between the received SNRs.
PLNC WITH FEEDBACK Feedback is an important transmission mechanism to improve transmission reliability. The role of feedback is even more critical for the scheme of decode-and-forward than that of amplify-and-forward since DF requires retransmission when the relay node cannot decode the received signal. Also, feedback provides the channels for power control and time/frequency synchronization. One unique feature of a PLNC system is that both forward and backward channels are already available, while a traditional communication system needs extra channels for feedback. Therefore, the feedback information can be transmitted along with the message transmission through either the multiple access channel or the broadcast channel. Possible research topics include the trade-off between the message rate and feedback rate, and design of medium access control (MAC) protocol.
ASYMMETRIC PLNC SYSTEM While most of the exiting work has assumed symmetric PLNC systems, there are several asymmetric scenarios in a practical PLNC system. Let us again consider the “Alice-RelayBob” model. The possible asymmetry in this system may include: Alice and Bob have different lengths of information to transmit, the channel between Alice and relay is different from that between Bob and relay, the channel from Alice to relay is different from that from relay to Alice, or Alice and Bob have different quality of service (QoS) requirements. The solutions for these asymmetric problems are not unique, but there is not much research on the comparison among different approaches over a unified platform. For example, when Alice has twice the information of Bob, Alice can transmit with QPSK while Bob can transmit with BPSK modulation. Another approach is that they both use the same modulation, and Alice may exploit the channel exclu-
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sively when Bob completes its transmission. A holistic evaluation is needed on the performance including delay, throughput, and power efficiency.
CONCLUSION Cooperative communication has become increasingly important for wireless networks to meet the stringent throughput requirements. In this article we discuss physical layer network coding, a new cooperation paradigm that allows different users to share relay nodes while forwarding information. The unique characteristics of PLNC ensure that two users can simultaneously transmit information to the same receiver in the same channel. Such a transmission scheme, although meaningless in traditional point-to-point communication models, can significantly improve the throughput capacity in a cooperative network. This has been demonstrated in this article from the viewpoint of information theory by using a one-dimensional random wireless network as an example. In addition, we discuss the new challenges brought in by PLNC, including modulation, channel coding, and the design of a practical PLNC system.
ACKNOWLEDGMENTS This work was supported in part by U.S. NSF grants CNS-0424546, CNS-0709285 and OCI063642, and Taiwan National Science Council research grant NSC98-2219-E-006-011.
REFERENCES [1] W. Su, A. K. Sadek, and K. J. Ray Liu, “Cooperative Communication Protocols in Wireless Networks: Performance Analysis and Optimum Power Allocation,” Wireless Pers. Commun., Springer, vol. 44, no. 2, Jan. 2008, pp. 181–217. [2] R. Ahlswede et al., “Network Information Flow,” IEEE Trans. Info. Theory, vol. 46, no. 4, July 2000, pp. 1204–16. [3] S. Zhang, S. C. Liew, and P. P. Lam, “Physical-Layer Network Coding,” Proc. MobiCom ’06, ACM, 2006, pp. 358–65. [4] S. Katti and D. Katabi, “Embracing Wireless Interference: Analog Network Coding,” Proc. 2007 Conf. App., Tech., Arch. and Prot. for Computer Comm., 2007, pp. 397–408. [5] R. Koetter and M. Medard, “An Algebraic Approach to Network Coding,” IEEE/ACM Trans. Net., vol. 11, no. 5, Oct. 2003, pp. 782–95. [6] P. Gupta and P. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. Info. Theory, vol. 46, no. 2, Mar. 2000, pp. 388–404. [7] B. Nazer and M. Gastpar, “Computation over MultipleAccess Channels,” IEEE Trans. Info. Theory, vol. 53, no. 10, Oct. 2007, pp. 3498–516. [8] T. J. Oechtering et al., “Broadcast Capacity Region of Two-Phase Bidirectional Relaying,” IEEE Trans. Info. Theory, vol. 54, no. 1, Jan. 2008, pp. 454–58. [9] J. Liu, D. Goeckel, and D. Towsley, “Bounds on the Gain of Network Coding and Broadcasting in Wireless Networks,” Proc. INFOCOM 2007, Anchorage, AK, May 6–12, 2007, pp. 724–32. [10] K. Lu et al., “On Capacity of Random Wireless Networks with Physical-Layer Network Coding,” IEEE JSAC, vol. 27, no. 5, June 2009, pp. 763–72. [11] K. Lu et al., “SER Performance Analysis for Physical Layer Network Coding over AWGN Channel,” Proc. IEEE GLOBECOM 2009, Honolulu, HI, Nov. 30–Dec. 4, 2009. [12] T. Koike-Akino, P. Popovski, and V. Tarokh, “Optimized Constellation for Two-Way Wireless Relaying with Physical Network Coding,” IEEE JSAC, vol. 27, no. 5, June 2009. [13] S. Zhang et al., “Joint Design of Network Coding and Channel Decoding for Wireless Networks,” Proc. WCNC 2007, Hong Kong, Mar. 11–15, 2007, pp. 780–85.
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[14] D. Wang, S. Fu, and K. Lu, “Channel Coding Design to Support Asynchronous Physical Layer Network Coding,” Proc. IEEE GLOBECOM ’09, Honolulu, HI, Nov. 30–Dec. 4, 2009.
ADDITIONAL READING [1] D. S. Lun et al., “Minimum-Cost Multicast Over Coded Packet Networks,” IEEE Trans. Info. Theory, vol. 52, no. 6, June 2006, pp. 2608–23.
BIOGRAPHIES SHENGLI FU [S’03, M’05, SM’08] (
[email protected]) received his B.S. and M.S. degrees in telecommunication engineering from Beijing University of Posts and Telecommunications, China, in 1994 and 1997, respectively, his M.S. degree in computer engineering from Wright State University, Dayton, Ohio, in 2002, and his Ph.D. degree in electrical engineering from the University of Delaware, Newark, in 2005. He is currently an assistant professor in the Department of Electrical Engineering, University of North Texas. His research interests include coding and information theory, wireless sensor networks, and joint speech and visual signal processing. K EJIE L U [S’01, M’04, SM’07] (
[email protected]) received B.S. and M.S. degrees in telecommunications engineering from Beijing University of Posts and Telecommunications, in 1994 and 1997, respectively. He received his Ph.D. degree in electrical engineering from the University of Texas at Dallas in 2003. In 2004 and 2005 he was a postdoctoral research associate in the Department of Electrical and Computer Engineering, University of Florida. Since July 2005 he has been an assistant professor in the Department of Electrical and Computer Engineering, University of Puerto Rico at Mayagüez. His research interests include architecture and protocol design for computer and communication networks, performance analysis, network security, and wireless communications. TAO ZHANG [M’05, SM’07] (
[email protected]) received B.S. and M.S. degrees in electric engineering from Wuhan University of Science and Technology, Hubei, China, in 1992 and 1998, respectively. She received her Ph.D. degree in computer science from the University of Texas at Dallas in 2005. In 2005 she joined the faculty at New York Institute
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of Technology at Old Westbury, where she is currently an assistant professor of computer science. She is conducting research in the areas of WDM optical networks and wireless networks, focusing on the design and analysis of network architectures and protocols. Y I Q IAN [M’95, SM’07] (
[email protected]) received a Ph.D. degree in electrical engineering from Clemson University. Currently he is an assistant professor in the Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, located at the Peter Kiewit Institute in Omaha, NE. His research interests include information assurance and network security, computer networks, mobile wireless ad hoc and sensor networks, wireless communications, systems, and networks. He is a veteran of the telecommunications industry, academia, and U.S. government. His previous professional experience included serving as a senior member of scientific staff and a technical advisor at Nortel Networks, an assistant professor at the University of Puerto Rico at Mayaguez, and a senior research staff member at the National Institute of Standards and Technology — a major US federal government research agent. He has a successful track record leading research teams and publishing research results in leading scientific journals and conferences. Several of his recent journal articles on wireless network design and wireless network security are among the most accessed papers in the IEEE Digital Library. He is a member of ACM. H S I A O -H W A C H E N [S’89, M’91, SM’00, F’10] (
[email protected]) is currently a full professor in the Department of Engineering Science, National Cheng Kung University, Taiwan. He obtained his B.Sc. and M.Sc. degrees from Zhejiang University, China, and a Ph.D. degree from the University of Oulu, Finland, in 1982, 1985, and 1991, respectively. He has authored or co-authored over 250 technical papers in major international journals and conferences, five books, and three book chapters in the areas of communications. He has served as general chair, TPC chair, and symposium chair for many international conferences. He has served or is serving as an Editor or/and Guest Editor for numerous technical journals. He is the founding Editorin-Chief of Wiley's Security and Communication Networks Journal (www.interscience.wiley.com/journal/security). He was the recipient of the best paper award at IEEE WCNC 2008.
The unique features of PLNC ensure that two users can simultaneously transmit information to the same receiver in the same channel. Such a transmission scheme, although meaningless in traditional point-to-point communication models, can significantly improve the throughput capacity in a cooperative network.
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