Practical Cross-Layer Design based on EGC and ARQ for DF-Cooperative Sensor Networks

Qiuna Yan and Dian-Wu Yue

College of Information Science and Technology Dalian Maritime University, Dalian, Liaoning 116026, China

qiu7589@yahoo.com.cn, dianwuyue@yahoo.com

Abstract

In this paper, the detect scheme based on equal gain combining (EGC) at the destination node is first investigated for a cooperative wireless sensor network with decode-and-forward (DF) relaying protocol. It is shown by simulation that the EGC scheme is a good practical solution by comparing with the traditional maximal-ratio combining (MRC) scheme and the cooperative-MRC scheme. Then the combination of EGC at physical and automatic repeat request (ARQ) at data link layer is analyzed further, and a practical cross-layer design scheme based on EGC and truncated ARQ is finally presented. 1. Introduction

Recently, the concept of cooperation in wireless communications has been attracting much interest due to its potential in improving the efficiency of wireless networks [1]–[3]. In cooperative communications, users can cooperate to relay each other’s information signals, and hence achieving spatial diversity. Cooperative diversity techniques can dramatically improve the reliability of signal transmission from each user.

In general, relaying transmission strategies can be divided into two main categories: amplify-and-forward (AF) and decode-and-forward (DF). In AF protocol, a relay just amplifies the signal received from the source and retransmits to the destination or the next node. On the other hand, with the DF protocol, the relay decodes the signal and remodulates the decoded information before transmitting to the next node. For these two protocols, outage and error performance have been extensively investigated [4]–[7]. In addition, the DF protocol can be combined with coding techniques and thus forming the so-called coded cooperation [8], which has been further developed in [9].

The uncoded DF protocol is relatively simple and particularly attractive for wireless sensor networks due to the fact that the relays do not rely on any error correction or error detection codes and thus the

network can have a severe energy limitation. Unlike coded DF relaying, however, the relays in uncoded DF may forward erroneous information, and with a conventional combining scheme such as the maximal ratio combining (MRC), the error propagation degrades the end-to-end (e2e) detection performance.

In order to mitigate error propagation, the authors in [10] present the so called cooperative-MRC scheme that can approximate the optimal maximum likelihood (ML) detection scheme. This scheme is shown to achieve the full diversity order at the expense of increased signaling overhead to convey the first hop (source-relay link) signal-to-noise ratio (SNR) information to the destination. For sensor networks, however, this requirement involving much signaling overhead is difficult to fulfill.

It is well known that in wireless communications there are three popular combining methods: MRC, EGC, and selection combining (SC). Among these them, MRC and SC have been deeply investigated and developed in cooperative relay networks [11]. However, the simplest EGC has been seldom considered so far in the literature.

On the other hand, in addition to diversity combining, ARQ error control technique is also a simple and effective means to overcome the channel fading. In order to greatly improve the system reliable performance, there have been several papers exploring the cross-layer approach [12] which combines ARQ at the data link layer and cooperative diversity at the physical layer [13]-[14]. In practice, among all protocols involving ARQ, truncated ARQ is quite popular for sensor networks.

To this end, for the special cooperative sensor networks operating in fading environments, our objective in this paper is to propose a practical cross-layer design scheme based on the simple EGC and truncated ARQ through comprehensively analysis of reliable performance and implement complexity. 2. System Model

Consider a cooperative wireless sensor network

2011 Third International Conference on Communications and Mobile Computing

978-0-7695-4357-4/11 $26.00 © 2011 IEEE

DOI 10.1109/CMC.2011.42

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with nodes, including one source node, one destination node and sensors as relay nodes. Each node is equipped with only one antenna and works in a half-duplex mode (i.e., it cannot receive and transmit signals simultaneously). For simplicity, we first assume that there is no direct link from the source to destination. All channel links are assumed to be quasi-static and mutually independent, which means that the channels are constant within one transmission duration, but vary independently over different transmission durations. Furthermore, it is assumed that each sensor relay knows the channel state information (CSI) of its source-relay link.

Information transmission over a wireless sensor network is accomplished in two phases. In the first phase, signals are broadcasted by the source to the sensor relays. In the second phase, each relay first detects the received signal and retransmits it by the DF protocol, then the destination combines all these signals from these R relay nodes based on some combining scheme (e.g. MRC), and makes a final decision. The involved details are as follows:

In the first phase, source broadcasts a modulated signal s to all the relays. The received signal at the i -th relay is expressed as

i s i ir E f s v= + 1, ,i R= ⋅⋅ ⋅ (1) In the above expression, s has unit power (thus sE is the transmit power), if is the channel gain between the source and the i -th relay which has a Rayleigh distribution with the second moment (1)

iN , and iv is the complex additive white Gaussian noise (AWGN) with zero mean and unit variance.

In the second phase, with the DF protocol, the i -th relay detects the symbol s based on the received signal

ir , and then forwards the detected result is to the destination. Therefore the received signal at the destination from the i -th relay can be written as

i i i i iy E g s ω= + (2) where iE is the transmit power of the i -th relay, ig is the channel gain between the i th relay and the destination, which follows a Rayleigh distribution with second moment (2)

iN , and iω denotes the AWGN at the destination with zero mean and unit variance. Moreover, is also has unit average energy.

It is assumed now that all the random variables 1{ }R

i if = , 1{ }Ri ig = , 1{ }R

i iv = 和 1{ }Ri iω = are

independent of each other. Furthermore, for simplicity of analysis, we assume that

(1) (1) (1)1 RN N N= ⋅⋅ ⋅ = = (3) (2) (2) (2)1 RN N N= ⋅⋅ ⋅ = = (4)

And

1 1T

R sE

E E E ER

= ⋅⋅ ⋅ = = = =+

(5)

where TE denotes the total power consumed by the network. 3. Combining Schemes A. Traditional-MRC

Traditionally, there are three popular combining methods: MRC, EGC, and SC. For multiple fading direct links without relays, all of them can achieve full diversity order. Among them MRC is the most popular as having the highest coding gain [15].

For the cooperative network, by weighting each signal from these R fading links, the combiner at the destination node outputs

1

R

i ii

y yω=

=∑ (6)

Regarding MRC, the i -th weighting value is equal to *

i igω = (7) where *( )⋅ denotes conjugation.

It should be noticed that in order to employ the MRC strategy the destination requires to know all the channel gains { | | , 1,2,..., }i

i ig g e i Rθ−= = , or to know all the channel envelopes {| |, 1,2,..., }ig i R= and all channel phases { , 1,2,..., }i i Rθ = . Typically, a channel phase is estimated by using a carrier synchronization loop before coherent detection.

However, because some of the relays may forward erroneous information, the traditional-MRC scheme does not get full diversity performance [10].

B. Cooperative-MRC

Recently, authors in [10] modified the traditional-MRC scheme, and presented the cooperative-MRC scheme. The novel combining scheme can achieve full diversity order, and obtain almost the same performance as the optimal ML detection.

For the i -th relay link, the instantaneous SNRs of the source node to the relay (the first hop) and the relay to the destination (the second hop) are given respectively by

2(1)i if Eγ = (8)

2(2)i ig Eγ = (9)

Hence, for any given modulation, the individual BER at the destination for this link with two hops should be

(2) (1) (1) (2)( ) (1 ( )) ( ) (1 ( )) ( )b b b b bP i P i P i P i P i= − + − (10)

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where (1) ( )bP i and (2) ( )bP i are the BERs involving the first hop and the second hop, respectively. And they are functions with respect to (1)

iγ and (2)iγ , respectively.

If we review the two hop link as a direct link, then the corresponding equivalent output SNR is expressed as [10]

1 2{ ( ( ))}bi

Q P iγα

−

= (11)

where ( )Q x is just the well-known Q -function, andα is a constant that depends on the given modulation (e.g.,

2α = for BPSK). With cooperative-MRC, the weight value in the

combiner for the i -link is modified as *

(2)i

i ii

gγω

γ= (12)

However, in order to employ the cooperative-MRC technique, the destination needs to get all values of if and ig , 1,2,...,i R= . This means that the use of the cooperative-MRC requires a great amount of signaling overhead. For sensor networks with power constraint, it will be difficult to fulfill.

C. Equal gain combining

Even the network can carry on the channel estimation, it is very possible that the estimated results is not exact, which influences the system performance in reverse order. Therefore, the simple EGC scheme is of our particular interests because it has good BER performance at the low-medium SNR region at much lower implement complexity.

Regarding EGC, all weight values for these relay links are given by

*

, 1,2,...,iii

i

ge i R

gθω −= = = (13)

Note that the EGC scheme does not require to know that if and ig , 1,2,...,i R= . This means that EGC requires minimum amount of channel information compared to the traditional-MRC and the cooperative-MRC.

D. Simulation comparison

In all the simulation curves of Figures 1-3, SNR denotes the total power TE since the variance of AWGN is set to one, and only BPSK modulation is used for simplicity. We also assume that (1) (2) 1N N N= = = .

In this subsection, we observe only the BER performance for three different combining schemes. Figure 1 plots three BER curves which correspond to the network employing cooperative-MRC, EGC and

traditional-MRC, respectively. As can be seen, the one with cooperative- MRC is the best, but its implement complexity is the highest. The one with traditional-MRC is the worst, but its implement complexity is higher than the one with EGC.

The EGC is simple and easy to implement. Since it has the BER performance close to that with cooperative-MRC, thus it is a very good choice for the cooperative sensor network.

0 5 10 15

10−3

10−2

10−1

BE

R

SNR (dB)

Coopperative Maximal−Ratio CombiningEqual−Gain CombiningMaximal−Ratio Combining

Fig. 1. BER performance comparison for different combining schemes.

4. Combination of simple EGC and truncated ARQ A. Truncated ARQ

ARQ protocol at link layer is an effective means to overcome the channel fading, where cyclic redundancy check (CRC) is usually used for error check and retransmissions are requested if the data packet is received erroneously. In practice, the maximum number of retransmissions is limited so as to minimize the delay and buffer size and such variant ARQ is called truncated ARQ protocol.

Below we are going to consider and propose a practical cross-layer design which combines simple EGC at the physical layer and truncated ARQ at the data link layer. In order to apply the ARQ error-control technique, now we must modify the system protocol for the cooperative network.

Firstly, the source node must encode an information sequence in to a data packet before broadcasting. Next, all relay nodes work just like the uncoded DF case, and are not allowed to carry on error check since sensors are low complexity and low-energy devices. At the destination, EGC is first used to recover the data packet, and then CRC is used to check if the packet

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includes error bits. If the packet has error bits, the destination will request retransmissions through a feedback link. There exist two different retransmission strategies: retransmission by both source and relays, and retransmission by only relays. B. Retransmission by both source and relays

For this retransmission strategy, the source rebroadcasts the requested data packet to these sensor relay nodes, and then these relay nodes detect and forward it again based on DF protocol. C. Retransmission by only relays

For this retransmission strategy, the source keeps silent, and only these relay nodes forward again the requested data packet to the destination. D. Simulation comparison

We now observe the BER performance for the combination of EGC with the above-mentioned two truncated ARQ schemes. In the following simulation, we set that the maximum number of retransmissions is equal to 1. We call the scheme involving retransmission by both source and relays as EGC-ARQ Scheme 1, and the scheme involving retransmission by only relays as EGC-ARQ Scheme 2.

Figure 2 plots the BER curves with the two EGC-ARQ schemes, and also plots the BER curve of the EGC system without ARQ for comparison. For the cooperative network employing EGC-ARQ Scheme 1, a complete information processing averagely consumes the total power equal to

1 . 2T b T TP E P E E= + ≤ (14) where bP denotes the BER at the destination before ARQ processing. For EGC-ARQ Scheme 2, the average total power becomes

2 . 21

TT b T

E RP E P E

R= + <

+. (15)

In order to do justice, we set that for the network without ARQ the average total consumed power is 2 TE per a complete information processing.

It can be seen from Figure 2 that the performance with EGC-ARQ Scheme 1 is obviously better than the others. The EGC-ARQ Scheme 2 has BER performance close to that of the system without ARQ. Therefore we recommend EGC-ARQ Scheme 1 for the practical use.

Figure 3 plots the BER curves with EGC-ARQ Scheme 1 for different numbers of the relay nodes 4,6,8R = . As expected, the BER performance becomes better as R increases at medium SNR region. However, at low SNR region the three BER curves are very close each other.

0 5 10 15

10−4

10−3

10−2

10−1

BE

R

SNR (dB)

EGC−ARQ Scheme 1EGC−ARQ Scheme 2EGC without ARQ

Fig. 2. BER performance comparison for different ARQ schemes.

0 5 10 1510

−5

10−4

10−3

10−2

10−1

BE

R

SNR(dB)

EGC−ARQ Scheme 1: R=8EGC−ARQ Scheme 1: R=6EGC−ARQ Scheme 1: R=4

Fig. 3. BER performance comparison for different numbers

of relay nodes.

5. Conclusions

It is widely known that both of EGC and ARQ are simple and effective means to overcome the channel fading. In this paper, we have investigated the cross-layer approach which combines EGC and truncated ARQ for DF-cooperative sensor networks, and presented EGC-ARQ Scheme 1 as a nice practical solution. Although we analyzed only the case of simple two-hop cooperation, extension of our investigation to the multi-hop cooperation is quite straightforward.

Acknowledgements

This work was supported by the Research Fund for

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