IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 2, FEBRUARY 2012 379
Topology-Aware Modulation and Error-CorrectionCoding for Cooperative Networks
Zhe Yang, Student Member IEEE, Lin Cai, Senior Member IEEE, Yuanqian Luo, Student Member IEEE, andJianping Pan, Senior Member IEEE
Abstract—User cooperation in wireless networks is inherentlya cross-layer optimization problem. We identify a new directionfor cooperative communications: i.e., in addition to the point-to-point communication channel between the transmitter andthe receiver, the communication configuration should take thenetwork topology into account. In this paper, we first proposea network modulation (NM) design that can transmit bits withdifferent SNR requirements in a single symbol transmission. Wethen propose an error-correction coding assisted relay (EAR)scheme that is also configured according to the network topology.We study the performance of NM and EAR in both a three-node collinear network and a two-dimensional cellular network.Extensive simulations have been conducted, which demonstratethe substantial performance gain of the proposed schemes, interms of both a higher network throughput and a lower bit-energy consumption. Comparing between NM and EAR, NM ismore beneficial for the downlink performance and EAR is morebeneficial for the uplink performance. Combining NM and EARleads to a more efficient cooperative network. It is concludedthat the topology-aware physical layer design will be a promisingdirection with many open issues for further study.
Index Terms—Topology Awareness, Network Modulation, Re-lay Communication, Error Correction.
I. INTRODUCTION
FOR THE WIRELESS communications among coopera-tive users at different locations, exploring the spatial di-
versity of wireless media is a promising direction but relativelyunder-explored. Previous approaches to address the spatialdiversity can be classified into two categories. One is to takeadvantage of the spatial diversity gain to improve the physical(PHY)-layer performance, such as improving the spectrumand energy efficiency and reducing the bit error rate [2], [3].The other one is to arrange multi-hop relaying and routingconsidering the network topology to improve the networkperformance, such as network throughput and end-to-enddelay [4]. On the other hand, it is well known that, given theshared medium of a wireless channel, isolating communicationand networking designs may lead to performance degradation.However, existing cross-layer solutions mainly focus on howto use the PHY-layer information to enhance the networkprotocol design, taking a bottom-up approach.
Manuscript received 15 February 2011; revised 20 July 2011. Part of theresults in Section IV, related to the network modulation (NM), has beenpresented at IEEE Infocom 2011 [1], Shanghai, China.
Z. Yang, L. Cai and Y. Luo are with the Department of Electrical andComputer Engineering, University of Victoria, Victoria, BC, Canada (e-mail:{zyang@ece., cai@, yqluo@ece.}uvic.ca).
J. Pan is with the Department of Computer Science, University of Victoria,Victoria, BC, Canada (e-mail: [emailprotected]).
Digital Object Identifier 10.1109/JSAC.2012.120217.
We investigate the cross-layer design for user-cooperativewireless networks in a new direction. Specifically, we proposeto enhance the PHY-layer modulation and error-correctioncoding designs considering the network topology, aimed toimprove both the PHY-layer spectrum and energy efficiency,which can lead to a better network performance in terms of ahigher network throughput and a lower bit-energy consump-tion.
The main contributions of this paper are threefold. First, wepropose a network topology-aware modulation scheme, callednetwork modulation (NM). Different from the traditional mod-ulation schemes that are optimized for point-to-point trans-missions, we design and select the NM schemes consideringthe network topology and the three communication channelsamong the source node, the destination node, and the relaynode that assists the transmission. Second, we propose anerror-correction coding assisted relay (EAR) scheme, wherea strategically located relay can generate and transmit Reed-Solomon (RS) code instead of the original information bits tothe receiver. The configuration of the RS code also dependson the topology and the channels among the three nodes.Third, we further evaluate the performance of the proposedNM and EAR schemes by simulation. Simulation results showthat the NM and EAR schemes can improve the networkperformance substantially for different topologies. For thethree-node collinear topology, if the relay node is closer to thesource node (i.e., the channel quality between the relay nodeand the source node is better than that between the relay nodeand the destination node), NM is more effective to enhancethe performance; if the relay node is closer to the destinationnode, EAR contributes more to the performance gain.
The rest of the paper is organized as follows. In Sec. II,we summarize the related work. In Sec. III, we introduce themotivation and the design of network modulation, and discussits performance and implementation. Two case studies on howto use NM for cooperative networks are also given. The error-correction coding assisted relay scheme is proposed in Sec. IV.The performance study of the proposed NM and EAR schemesby simulation is presented in Sec. V, followed by concludingremarks and further research issues in Sec. VI.
II. RELATED WORK
User-cooperative communication has been an active re-search topic [2], [3], [5], [6]. There are many approaches indifferent layers to improve the system performance. In thispaper, we take a new direction to configure the modulation
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380 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 2, FEBRUARY 2012
and error-correction coding schemes to enhance the networkperformance via user cooperation.
We propose a network modulation scheme inspired bysuper-positioning precoding (SPC) [7], which was designedfor multicast transmissions, and recently how to use SPC forrelay communications has also appeared [8], [9]. However,SPC (or h-mod) requires specialized hardware and sophisti-cated signal processing techniques, so it is not desirable forwireless hand-held devices. In [10], we designed a scalablemodulation (s-mod) scheme that uses software mapping torearrange the constellation of typical QAM schemes to providedifferentiated services for layer-encoded video multicast overwireless networks. Here, we focus on how the software-based modulation remapping can be used to assist relaycommunications to improve the spectrum efficiency.
Using error-correction coding to improve throughput is awell-studied topic [11]–[18]. For instance, in [11], the opti-mal error-correcting code is selected based on time-varyingwireless channel conditions. An adaptive link-level forwarderror correction algorithm was proposed in [12] to adjust theerror-correcting codes according to the predicted packet lossrate. In [19], a partial packet recovery scheme was proposed:instead of retransmitting the corrupted packet, the sender onlyretransmits the bits in a packet that are likely in error andtherefore the retransmitted packet length can be much smallerthan that of the original packet. To overcome the shortcomingof the previous solution in [19] that requires sophisticatedhardware modifications, in [20], the sender retransmits asmaller packet contains error-correcting codes. Our proposedEAR scheme is motivated by [20]. However, in a relay assistedtransmission, the relay node may not have a correct copyof the original packet, which makes the configuration morecomplicated. In addition, the original messages and the error-correcting codes are transmitted through different channels.Therefore, the selection of error-correcting codes needs toconsider the topology and channels among multiple nodes,and its performance gain is topology sensitive.
III. NETWORK MODULATION FOR COOPERATIVE
NETWORKS
A. Wireless channel model
Wireless communication channels suffer from path loss,fading, shadowing, interference and other impairments. Denoteκ the path-loss factor at reference distance d0. It can becalculated using the Friis free-space model: κ = GtxGrxv2
(4π)2d20L
,
where v is the carrier signal wavelength, L is the systemloss factor, and Gtx and Grx are the transmitter and receiverantenna gains, respectively.
Given the transmission power Pt, the received power Pr atd away can be calculated as Pr = Ptκβ( d
d0)−α, where β is
the channel fading and shadowing factor, and α is the path-loss exponent, which is a constant with the value from 2 to 6typically. β is a random variable, depending on the fading andshadowing environment, and can be measured and estimatedusing training sequences. For simplicity, we assume β = 1 forall links in the following calculation.
The received SNR, γ, is given by γ = Pr
N0= γ0( d
d0)−α,
where N0 is the background noise power, and γ0 is thereceived SNR at the reference distance d0.
S D
R
Fig. 1. A three-node topology.
B. Motivation
It is well known that relaying can improve the networkperformance. As shown in Section III-A, the channel qualitydecays quickly, proportional to dα. Thus, using R as a relaycan result in a higher overall throughput than the directtransmission between S and D as shown in Fig. 1.
The transmission from S to R can be overheard by D, butbecause of the lower received SNR, the demodulated bits atD may suffer from a very high BER. If we design a specialmodulation scheme such that D can demodulate some of thereceived bits, and R can demodulate all the bits and furtherrelay those bits that cannot be decoded correctly by D fromS directly, the overall spectrum efficiency can be improved.
In the literature, SPC-aided relay can serve the abovepurpose to improve the efficiency [8]. However, as the SPCreceiver is quite complicated and needs to implement iterativeSuccessive Interference Cancellation (SIC) for demodulation,SPC has been used in the Digital Video Broadcast (DVB)standard, but not fully recommended in portable wirelesssystems yet. Here, we take a software-only approach to re-mapthe typical QAM constellation to transmit bits with differentSNR requirements in a symbol. As the design and selectionof the modulation consider network topology, we call theapproach network modulation.
C. NM schemes
Considering the three-node topology shown in Fig. 1, theSNR of link SR is typically much higher than that of linkSD. Therefore, the NM should maintain the similar BER forbits with different SNR. We can achieve it by selecting theconstellation points of a typical QAM such that the points areclustered, and the Euclidean distances between clusters aremuch longer than that within the same cluster. After selectingthe constellation points, we have the flexibility to assign bitsin each cluster to minimize the BER of each bit.
Using this strategy, we design five NM schemes as shownin Figs. 2 and 3, based on the constellation maps of 16-QAM, 64-QAM, and 256-QAM. Note that the traditionalQAM modulation can be viewed as a special case of NM.Obviously, there are many other possible NM designs andwe do not explore the full space of NM here, which remainsa future research issue. In this paper, we study how to usethese sample NM schemes and the traditional QAM schemesto facilitate user cooperation for performance improvement.
D. BER analysis
To obtain the BER performance of demodulated bits, wefirst need to identify the decision region of each symbol. Theprobability of a symbol is demodulated in error is equivalent tothe probability that the received symbol is outside its decision
YANG et al.: TOPOLOGY-AWARE MODULATION AND ERROR-CORRECTION CODING FOR COOPERATIVE NETWORKS 381
NM_16 NM_64A
NM_256NM_64B
Fig. 2. Sample network modulation schemes.
region. Given the noise following Gaussian distribution, wecan estimate the BER as
pe ≈ 1m
(1 −∫∫
(x,y)∈R
p(x, y)dxdy), (1)
where m is the number of bits per symbol, and R is thedecision region for the tagged symbol. The integral repre-sents the probability that a received signal locates withinthe decision region. Therefore, if we use Gray code, thesymbol error typically causes one bit error and thus the BERcan be approximated by (1). The approximation comes fromthe assumption that there is only one bit in error for eacherroneous symbol, which is acceptable if we use the Graycode for mapping bits to symbols [21].
For NM, the location of the clusters can carry m1 layer-one (L1) bits, and within each cluster, the location of theconstellation points can carry m2 layer-two (L2) bits. We canobtain the Voronoi diagram for 2m1 clusters, which defines thedecision boundaries of L1 symbols, and similarly the decisionboundaries of L2 symbols. Then, we can use (1) to calculatethe BERs for L1 and L2 bits, respectively.
E. Implementation
To implement the NM schemes, assume S and R havingthe knowledge of the channel conditions of SR, SD and RD.If we assume a quasi-static channel, the channel condition ofRD estimated by R can be fed back to S. At the transmitterside, we add a mapping function before modulation. Usingthe example in Fig. 3, S groups five bits and maps themto a six-bit symbol according to the standard constellationmap of 64-QAM. For example, “00000” and “00111” aremapped to “000000” and “001101” in Gray-mapped 64-QAMconstellation, respectively.
Layer−two
01 00
11 10
000000
000 000
001
001001
001
010
010
011
110 111
101
100
100100
100
101
110
111
111
101 011 010
110 110
011 010 011 101
111
(a)Layer−one
(b)
Fig. 3. Decision regions for L1 and L2 symbols for a sample NM scheme.
At the receiver side, we first define the decision regions forL1 and L2 symbols, and then demodulate each symbol to L1and L2 bits directly. This strategy requires a minor modifica-tion to a QAM demodulator (for other options, see [10]).
F. NM-assisted user cooperation
We consider two cases that users can cooperate using NM.The first case is that S needs to transmit to D only, and a relaynode R helps to relay the message to D. The second one isthat S needs to transmit to both R and D, and R also relaysfor D. The downlink transmissions in a cellular network canbe an example of the second case. Next, we study how toconfigure NM for these two cases.1) Case one: If S uses a traditional QAM to deliver mS bits
per symbol duration (b/sym), and let R relay all bits to D withthe data rate of mR b/sym, the throughput from S to D equalsmSmR
mS+mRb/sym. For an NM scheme, S can transmit mS1 L1
bits and mS2 L2 bits to D and R in one symbol duration,respectively. Then the relay node R transmits mR b/sym torelay the L2 bits to D. Thus, the throughput from S to Dequals (mS1+mS2)mR
mR+mS2b/sym.
Denote Ps and Pr the transmission power of source andrelay node respectively, we can formulate the problem to selectthe best NM scheme to maximize the throughput under theBER constraint.Problem 1: (P1)
max Th =(mS1
′ + mS2′)mR
mR + mS2,
s.t. pe,sd(mS1, Ps) ≤ pe,
pe,sr(mS2, Ps) + pe,rd(mR, Pr) ≤ pe.
In (P1), pe,·(m, P ) is the BER given the modulation type mand the transmission power P . As the desired pe,sr , pe,rd <<1, the BER of L2 can be approximated by pe,sr + pe,rd.
As the number of modulation schemes that we can choosefrom is quite limited (in this paper, we consider the fiveproposed NM schemes and four traditional QAM modula-tion schemes), it is feasible to solve the above optimizationproblem by the search Algorithm 1, where the inputs are pe
(the required BER), Ps (the transmission power of S) and Pr
(the transmission power of R), and the outputs are Th (thethroughput) and n (the modulation scheme index).
382 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 2, FEBRUARY 2012
Algorithm 1 NM Configure One ReceiverRequire: (pe, Ps, Pr)
1: set Th = 02: for all NM schemes do3: calculate pe,rd, pe,sr and pe,sd
4: if pe,sr + pe,rd ≤ pe and pe,sd ≤ pe then5: if (mS1+mS2)mR
mR+mS2> Th then
6: Th = (mS1+mS2)mRmR+mS2
7: set n equal to the index of the NM scheme8: end if9: end if
10: end for11: Return: Th, n
As the channel conditions of SR and RD can be different,appropriate transmission power allocation is desirable to fur-ther improve the system performance, i.e. Ps + Pr ≤ Ptotal.Considering that the power control in a practical system isdiscretized with a limited number of values, we set it to be100 in this paper and add a search loop to Algorithm 1 to findthe best power allocation.2) Case two: In this case, S needs to transmit different
messages to R and D, respectively. Without loss of generality,the message lengths to R and D are assumed to be the same.Using NM, S can transmit mS1 bits and mS2 bits to R and Dsimultaneously in one symbol duration. If mS1 > mS2, S cantransmit the remaining message to R using a traditional QAMmodulation. If mS1 < mS2, S and R can use the NM-assistedrelay in Case one to transmit the remaining message to D. Tomaximize the throughput under the BER constraints, we canobtain the optimal NM configurations using Algorithm 2.
Algorithm 2 returns the throughput using the best NMschemes (Th), the NM scheme selected for the two-receivertransmission (n), and that for the one-receiver transmission(n′). To consider power allocation, we can add another loopto find the best power allocation strategy.
IV. ERROR-CORRECTION CODING ASSISTED RELAY
A. Motivation
Still consider the three-node topology in Fig. 1. For thetransmission from S to R, D also receives a copy. Due tothe worse channel condition of SD, the received copy by Dmay contain severe errors. In the existing solutions of relaynetworks, D solely relies on the transmission from R to decodethe message from S; in the traditional cooperative communi-cation systems, D combines two copies of the transmissionsfrom S and R to decode the message [22], [23]. The relayapproach is simpler, but it wastes the erroneous copy from S toD entirely. Another cooperative communication approach canutilize both copies to achieve the spatial diversity gain, but itrequires sophisticated signal processing and, more importantly,transmitting two copies of the same information bits increasesthe cost.
Here, we investigate a new direction for cooperative trans-missions. The transmission takes two steps. In the first step,S transmits a packet to R and D. In the second step, R usesthe received packet to generate a smaller packet that containsthe error-correcting code (ECC) of the original packet. Then,D can use the corrupted copy of the original packet from the
Algorithm 2 NM Configure Two ReceiversRequire: (pe, Ps, Pr)
1: Th = 02: for all NM schemes do3: calculate pe,sr and pe,sd
4: if pe,sr ≤ pe and pe,sd ≤ pe then5: if mS2 ≤ mS1 then6: if mS1
1+(mS1−mS2)/mR> Th then
7: Th = mS11+(mS1−mS2)/mR
8: set n to the index of the NM scheme, and set n′ tothe index of the mR modulation scheme
9: end if10: else11: (Th0, n0) =NM Configure One Receiver(pe, Ps, Pr)
//find the best NM scheme to relay message to D by R12: if mS2
1+(mS2−mS1)/Th0> Th then
13: Th = mS21+(mS2−mS1)/Th0
14: set n to the index of the NM scheme, and set n′ = n0
15: end if16: end if17: end if18: end for19: Return: Th, n, n′
transmission by S and the ECC from the transmission by Rto recover the original packet.
B. Selection of ECC
Error coding is a well developed yet still very active area.Different ECCs have different applicable scenarios consideringthe trade-off of overhead, performance, and implementationcomplexity. In traditional applications, both the message andthe parity bits are transmitted over the same channel and thuswith equal error probability. For EAR, the transmissions fromS and R to D are over independent channels with differentBERs due to the spatial diversity.
Given the special property of EAR, the desirable ECCshould satisfy three requirements. First, it must be a systematiccode, because the relay node needs to receive the originalpacket before it can encode it. Second, it should be scalable,so the code length can be adjusted according to different errorcorrection requirements. Third, the computational cost shouldbe acceptable for current hardware platforms. Consideringthese requirements, we choose the Reed-Solomon (RS) codes,as they satisfy the above requirements and there are manyhigh performance software and/or hardware implementationsreadily available.
C. RS-code configuration
The RS-code is a systematic linear block code and it isorganized into fixed-length blocks. Each block contains bbits and the encoding and decoding operations are in Galoisfield G(2b) [24]. Since modern computing systems are byteoriented, it is straightforward to choose the block size of 8 bitsto be compatible with the mainstream hardware and softwaresystems. Therefore, we use GF(28) consisting of 28−1 blocksto construct the RS-code.
Denote the RS-code by a two-tuple (n, k), where n = 255is the length of encoded blocks and k is the length of messageblocks (in bytes). Their difference, r = n−k, is the length of
YANG et al.: TOPOLOGY-AWARE MODULATION AND ERROR-CORRECTION CODING FOR COOPERATIVE NETWORKS 383
additive parity blocks appended to the k message blocks. RS-code (n, k) can correct up to t = r/2 block errors. RS-codewith longer parity blocks (i.e., larger r) can correct more biterrors at the cost of a higher overhead, so we need to selectthe code length carefully.
Assume that RS-code is employed during all transmissionsfor a fair comparison. Given the BER, the block error rate, PE ,can be calculated as PE = 1 − (1 − BER)b. Different fromthe conventional configuration of RS-code in point-to-pointcommunications, here, we need to consider the BERs of boththe direct transmission and the relayed one. The correspondingblock error rates are denoted as PSD
E and PRDE , respectively,
which can be estimated by R.Given the RS(n, k) code, the probability that D can decode
the k-block message correctly by combining the ECC from Rand the original message from S is
Pc,EAR(r) =
r2∑
i=0
(k
i
)(PSD
E )i(1 − PSD
E )k−i·⎡⎣ r
2−i∑j=0
(r
j
)(PRD
E )j (
1 − PRDE
)r−j
⎤⎦ .
(2)
When wireless channels are worse than the estimation andthe chosen ECC is insufficient to recover the original packet,a failed transmission occurs. We have two choices: (a) totransmit another stronger ECC, or (b) to retransmit the wholepacket. The first scheme may require less channel time but itis difficult to determine how many bits are in error and whichECC code is sufficient. Thus, we let the relay node retransmitthe whole packet if the ECC attempt fails for simplicity.
We denote the maximum retransmission limit by R as Rmax,and the RS-code length for the retransmission by R as rRD .The probability that the packet can be successfully receivedby D by a retransmission is
P (1)c,r =
rRD/2∑i=0
(k + rRD
i
)(PRD
E )i(1 − PRDE )k+rRD−i. (3)
If the previous retransmission fails, the message will be re-transmitted again till reaching the retransmission limit. Hence,the probability that the message can be successfully receivedby retransmissions is
Pc,r =Rmax−1∑
i=0
(1 − P (1)c,r )iP (1)
c,r . (4)
Thus, for each successfully transmitted L(r) = (Pc,EAR+(1−Pc,EAR)Pc,r)k bytes, the expected transmitted data length (inbytes) by R is
U(r) = r + (1 − Pc,EAR)(k + rRD)(Rmax−1∑
i=0
(i + 1)(1 − P (1)c,r )iP 1
c,r + Rmax(1 − P (1)c,r )Rmax
).
(5)Ignoring the feedback delay, given R using the modulationtype with mRD bit/sym, the corresponding channel time isT (r) = U(r)
mRDsymbol duration.
Based on T (r), the expected throughput of the second hop(RD) is Et(r) = L(r)
T (r) (bytes per symbol duration), whichshould be maximized.Discussion: As there are many efficient implementations of
RS codec, the extra computation cost of EAR is moderate.Experimental results in [20] showed that the computation costof RS encoding and decoding is less than 10% of the capacityfor a commodity computer. If using FPGA to implement RScodec, the efficiency is even higher. For example, the decodingrate is up to 496 Mbps on Spartan-II by Xilinx [25].
V. PERFORMANCE EVALUATION AND DISCUSSION
A. Linear Topology
We first use a linear topology, where three nodes S, R,and D, are located on a line segment. The distance betweennode S and node D is fixed at 1 unit with the correspondingreference SNR equal to 12 dB (15.85). α is set to three, so theaverage received SNR at distance x unit equals 15.85 · (x)−3
and the AWGN channel model is considered. The tolerableBER (before error coding) is set to pe = 10−3. Therefore,with direct transmission, node S can transmit to node D atmost 2 b/sym using QPSK. The distance between node R andnode S, x, is varying between 0.05 and 0.95 to evaluate thesystem performance under different channel conditions.1) Single-receiver case: First, we evaluate the performance
of the single-receiver case, i.e., S transmits to D using R as arelay. In Fig. 4(a) and (b), we compare the expected throughputunder the equal power allocation and optimal power allocation,respectively. In these figures, x-axis represents the locationof node R, and y-axis is the expected throughput (i.e., theexpected number of bits received by node D divided by theexpected number of symbol durations). For the direct trans-mission, the throughput is 1.984 b/sym considering packetretransmissions and error-control coding.
As shown in Fig. 4(a) and (b), first, to outperform thedirect transmission, the location of R can be in a widerrange using the NM-assisted relay schemes than that usingthe traditional relay schemes. Second, the proposed NM witha fixed transmission power can outperform the traditional relayschemes (by up to 30% for x = 0.3 or 0.7); if combined withthe EAR scheme, it can achieve an even higher throughput andoutperform the traditional relay scheme by 50% at x = 0.7.The improvement comes from twofold: 1) using the NMscheme, two-layered bits are transmitted simultaneously andonly the L2 bits need to be relayed; and 2) with the EARscheme, the relayed packet contains the RS parity bits, whichis much smaller than the original packet.
Furthermore, compared the results in Fig. 4(a) and (b), thesystem throughput can be further improved by the optimalpower allocation between S and R, and NM/EAR can outper-form the traditional relay by around 50% for x ∈ (0.55, 0.85).The results demonstrate the importance of power allocation.In the following, all the results are obtained with the optimalpower allocation.
The throughput curves in Fig. 4 are in zig-zag patterns.This is because both the number of modulation schemesand the RS code length are limited and cannot be adjustedcontinuously. The throughput curve of the traditional relay
384 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 2, FEBRUARY 2012
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2
2.2
2.4
2.6
2.8
3
Location of node R (x)
Thr
ough
put [
b/sy
m]
NM Scheme with EARNM Scheme without EARTraditional Relay Scheme
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
Location of node R (x)
Thr
ough
put [
b/sy
m]
NM Scheme with EARNM Scheme without EARTraditional Relay Scheme
(a) Equal power allocation (b) Optimal power allocation
Fig. 4. Throughput comparison, the single-receiver case.
scheme is symmetric with respect to x = 0.5, while those ofthe NM-assisted relay schemes are asymmetric. In specific,when x < 0.5, the performance gain is mainly from the NM;when x > 0.5, EAR can achieve a substantial improvement.This is because, with EAR, when R is closer to D, the SNRof link SR is closer to that of SD, so we need a less strong RScode (fewer parity bits) to help D to successfully decode thepackets. When R is very close to S, R has to retransmit all L2bits similar to the traditional relay scheme, so the performancegain of EAR largely disappears.
2) Two-receiver case: Next, let node S transmit differentmessages to nodes D and R. The throughput results are givenin Fig. 5. From the figure, the NM schemes can achieveup to 72% and 91% throughut gains over the traditionalschemes with or without relay, respectively. The preferableregion of the relay (in which the NM-assisted relay schemescan outperform the direct transmission schemes) is wider thanthat for the single-receiver case. This is because that, for thetwo-receiver case, with NM, the data to R can be piggybackedwith the transmission to D, which can achieve a much higherthroughput gain than using R as a relay only.
However, for the two-receiver case, the EAR scheme canonly achieve a marginal gain. This is because, using NM, thepercentage of the data to be relayed by R to D in the two-receiver case is much lower than that in the previous one-receiver case.
Note that these results are sensitive to the received SNR ofSD. If the received SNR of SD changes, the desirable relaylocations and the performance gains of NM and EAR alsochange. Nevertheless, the overall trend will remain the same.
The results with the linear topology not only provideimportant insights of where the performance gain comes fromand for which scenarios the proposed scheme is more useful,but also indicate where the desirable relay nodes should belocated.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
Location of node R (x)
Thr
ough
put [
b/sy
m]
NM Scheme with EARNM Scheme without EARTraditional Relay SchemeDirect Transmission
Fig. 5. Throughput comparison, the two-receiver case.
BS
Fig. 6. Network topology.
YANG et al.: TOPOLOGY-AWARE MODULATION AND ERROR-CORRECTION CODING FOR COOPERATIVE NETWORKS 385
5 10 15 20 25 30 35 40 45 500.95
1
1.05
1.1
1.15
1.2
1.25
1.3
Number of active nodes
Nor
mal
ized
net
wor
k th
roug
hput
NM Scheme with EARNM Scheme without EARTraditional Relay Scheme
5 10 15 20 25 30 35 40 45 500.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
Number of active nodes
Nor
mal
ized
net
wor
k th
roug
hput
NM Scheme with EARNM Scheme without EARTraditional Relay Scheme
(a) uplink (b) downlink
Fig. 7. Network throughput.
B. Network scenario
We further evaluate the performance in a two-dimensionalnetwork, where a base station (BS) serves all the active usersuniformly distributed in the cell as shown in Fig. 6. Forsimplicity, we assume that there is no interference for thedownlink and uplink transmissions, and each node has thesame amount of data to transmit for both the downlink and theuplink. Assume that the BS has the knowledge of the networktopology and channel conditions that are stable during thescheduling period.
First, grouping users into pairs for cooperative transmissioncan be formulated as the following weighted non-bipartitematching problem, which is applicable to both the uplink anddownlink scenarios. Denote the set of the mobile users in thecell by F . Denote by Ri,j the throughput for a pair of usersi and j, and Ri and Rj their (downlink or uplink) individualthroughput with traditional modulations, respectively. The gainof using NM (with or without EAR) for users i and j isGi,j = max(1/Ri +1/Rj −2/Ri,j, 0). The optimal matchingwill maximize the sum of Gi,j for all users.
If the Gi,j for all users in F is known, the state-of-the-art optimal matching algorithm can solve the above matchingproblem with the time complexity of O(N3) [26]. However,obtaining Gi,j for all pairs is nontrivial. Thus, instead of usingthe optimal matching algorithm, we use a simple heuristic al-gorithm called worst-link-first (WLF) matching [27] to groupusers: the BS first sorts the channel qualities of all users; thenit selects an unmatched user j with the worst channel qualityand finds another unmatched user i who is most desirable forj (i.e., the pair can achieve the highest performance gain);it repeats the above procedure till all users are matched. Ifusing relay schemes (with NM and/or EAR) for a pair cannotachieve any throughput gain, the direct transmission schemeswill be used. We also use the optimal power allocation for allschemes and all pairs.1) Network throughput: Network throughput is used to
evaluate the performance of different schemes, which is the
total amount of information transmitted in the whole networkover the total channel time consumed.
To consider different node densities, we vary the number ofactive users from 2 to 50 with the step size of 4. Set the SNRat the cell boundary as 11 dB (which can support QPSK usingthe traditional modulation scheme). For each node density, werepeated the simulation 1, 000 times using different randomlygenerated topologies, and calculated the average results. In thefollowing figures, the network throughputs are normalized tothe one with direct transmission (which adopts the adaptivemodulation scheme) for easy comparison.
The normalized network throughputs for uplink and down-link are shown in Fig. 7(a) and (b), respectively. We note thatthe downlink and uplink throughputs are the same with thetraditional relay schemes. This is because, with the traditionalrelay schemes, the most preferable relay nodes are at thesame or symmetric locations for the downlink and uplinktransmissions. Thus, the same node will serve as the relayfor both uplink and downlink transmissions. However, thethroughput of downlink and uplink may not be the same withNM-assisted relay, since different relay nodes might be chosenfor uplink and downlink transmissions. Thus, with NM, theworkloads of relay nodes can be more balanced, which isdesirable for energy-constrained wireless networks.
From the simulation results, the proposed NM with EARscheme can achieve a 25% throughput gain when the numberof nodes exceeds 50, which is much higher than that of thetraditional relay schemes.2) Bit-energy: In addition to the throughput gain, the
average bit-energy consumption is also reduced by using NMwith EAR. Fig. 8(a) and (b) shows the bit-energy results,which are normalized to the bit-energy of direct transmission.With more than 30 users in the cell, for the uplink case, theNM without and with EAR schemes can reduce the bit-energyby more than 20% and 31%, respectively, when compared withthe direct transmission. For the downlink case, the NM schemewithout and with EAR can reduce the bit-energy consumption
386 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 2, FEBRUARY 2012
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by more than 22% and 28%, respectively. Note that thereis a tradeoff between energy consumption and throughput.How to minimize bit-energy consumption while maintainingcertain throughput using NM and EAR can be formulated asa different optimization problem, which can be an interestingfurther research issue.3) Further discussions: The gain by the NM is more
significant for the downlink transmissions while the gain bythe EAR is more significant for the uplink transmissions,because the uplink scenario is similar to the one-receiver caseand the downlink scenario is similar to the two-receiver casein the linear topology.
For the uplink, a higher node density can lead to a muchhigher gain as the performance of EAR is more sensitive tothe relay location. For the downlink, even when the networkonly has two active users, using NM can achieve around 11%throughput gain on average.
Note that we only consider five NM schemes and theRS(255, ∗) codes in this paper. If more well-designed NMschemes and RS codes are used, it is possible to furtherimprove the network performance.
VI. CONCLUSIONS
In this paper, we have advocated the design and configura-tion of the PHY layer by considering the network topology andchannel conditions among multiple nodes. We have proposedthe network modulation and error-correction coding assistedrelay schemes. The proposed NM is based on the mainstreamQAM modem, and the proposed EAR uses the widely-usedRS codes. Therefore, they are easy to be adopted in practicalwireless systems. Extensive simulation results have demon-strated the substantial performance gains and lower bit-energyconsumption of the proposed schemes.
It is concluded that topology-aware PHY layer design willbe a promising direction with many open issues for furtherstudy. First, in this paper, we group users mainly consid-ering the estimated channel conditions. For heterogeneousapplications, the scheduling of users should consider the
different utility functions for different applications. Second,the admission region of single-hop and multi-hop wirelessnetworks with NM and EAR needs to be redefined in thenew setting. Third, the interactions of NM, EAR and theprotocols of other layers need further investigation. Fourth, inthis work, the receiver demodulates and decodes bits from onetransmission. It is possible to combine various user cooperativediversity techniques with NM/EAR to further improve thesystem performance by fully utilizing the spatial diversitygain. Finally, many new cross-layer optimization problemscan be formulated, e.g., jointly optimize NM/EAR with relayselection/scheduling and routing, as the topology-aware PHYlayer design provides one more dimension of freedom toimprove the network performance.
ACKNOWLEDGMENT
The authors would like to thank the anonymous reviewersfor their valuable comments that improve the quality of thepaper. The authors would also like to thank Dr. T. A. Gulliverat University of Victoria, for his helpful discussions.
REFERENCES
[1] Z. Yang, Y. Luo, and L. Cai. Network modulation: A new dimensionto enhance wireless network performance. In IEEE Infocom’11, 2011.
[2] J.N. Laneman, D.N.C. Tse, and G.W. Wornell. Cooperative diversity inwireless networks: Efficient protocols and outage behavior. IEEE Trans.Inf. Theory, 50(12):3062–3080, Dec. 2004.
[3] V. Mahinthan, L. Cai, J.W. Mark, and X. Shen. Maximizing cooperativediversity energy gain for wireless networks. IEEE Trans. WirelessCommun., 6(7):2530–2539, June 2007.
[4] A.E. Khandani, J. Abounadi, E. Modiano, and L. Zheng. Cooperativerouting in static wireless networks. IEEE Trans. Commun., 55(11):2185–2192, 2007.
[5] H. Shan, W. Zhuang, and Z. Wang. Distributed cooperative MAC formulti-hop wireless networks. IEEE Commun. Mag., 47(2):126–133,2009.
[6] W. Su, A. Sadek, and K.J. Ray Liu. Cooperative communicationprotocols in wireless networks: performance analysis and optimumpower allocation. Wireless Personal Commun., 44(2):181–217, 2008.
[7] T. Cover. Broadcast channels. IEEE Trans. Inf. Theory, 18(1):2–14, Jan.1972.
YANG et al.: TOPOLOGY-AWARE MODULATION AND ERROR-CORRECTION CODING FOR COOPERATIVE NETWORKS 387
[8] M. Butt, R. Zhang, S. Ng, and L. Hanzo. Superposition coding aidedbi-directional relay transmission employing iteratively decoded self-concatenated convolutional codes. In IEEE VTC’10-Spring, May 2010.
[9] P. Popovski and E. De Carvalho. Improving the rates in wireless relaysystems through superposition coding. IEEE Trans. Wireless Commun.,7(12):4831–4836, 2008.
[10] L. Cai, Y. Luo, S. Xiang, and J. Pan. Scalable modulation for scalablewireless videocast. In IEEE INFOCOM-MC’10, Mar. 2010.
[11] M. Elaoud and P. Ramanathan. Adaptive use of error-correctingcodes for real-time communication in wireless networks. In IEEEINFOCOM’98, volume 2, pages 548–555, 1998.
[12] Y. Jin, D.G. Le, and G.W. Bai. Kalman filter-based adaptive link-layerFEC mechanism for wireless sensor networks. Application Research ofComputers, 27(4):1412–1415, 2010.
[13] C.Q. Yang, E. Hossain, and V.K. Bhargava. On adaptive hybrid errorcontrol in wireless networks using Reed-Solomon codes. IEEE Trans.Wireless Commun., 4(3):835–840, 2005.
[14] T. Tran, T. Nguyen, and B. Bose. A joint network-channel codingtechnique for single-hop wireless networks. In IEEE NetCod’08, 2008.
[15] S. Kim, R. Fonseca, and D. Culler. Reliable transfer on wireless sensornetworks. In IEEE SECON’04, pages 449–459, 2004.
[16] M.C. Vuran and I. F. Akyildiz. Cross-layer packet size optimization forwireless terrestrial, underwater, and underground sensor networks. InIEEE INFOCOM’08, pages 226–230, 2008.
[17] K. Cheun and W.E. Stark. Optimal selection of Reed-Solomon code rateand the number of frequency slots in asynchronous FHSS-MA networks.IEEE Trans. Commun., 41(2):307–311, 2002.
[18] C. Li, G. Yue, X. Wang, and M.A. Khojastepour. LDPC code designfor half-duplex cooperative relay. IEEE Trans. Wireless Commun.,7(11):4558–4567, 2008.
[19] K. Jamieson and H. Balakrishnan. PPR: Partial packet recovery forwireless networks. In ACM SIGCOMM’07, Kyoto, Japan, August 2007.
[20] K.C.J. Lin, N. Kushman, and D. Katabi. ZipTx: Harnessing partialpackets in 802.11 networks. In ACM MobiCom’08, pages 351–362,2008.
[21] A. Goldsmith. Wireless Communications. Cambridge University Press,2005.
[22] Y. Luo and L. Cai. Throughput maximization for user cooperativewireless systems with adaptive modulation. In IEEE ICC’10, 2010.
[23] S. Sharma, Y. Shi, Y.T. Hou, H.D. Sherali, and S. Kompella. Cooperativecommunications in multi-hop wireless networks: joint flow routing andrelay node assignment. In IEEE INFOCOM’10, 2010.
[24] S. Lin and D.J. Costello. Error Control Coding. Prentice-HallEnglewood Cliffs, NJ, 1983.
[25] Antolin Agatep. Reed-Solomon solutions with spartan-II FPGAs. WhitePaper: Spartan-II Family, 2000.
[26] H.N. Gabow. An efficient implementation of Edmonds’ algorithm formaximum matching on graphs. Journal of the ACM, 23(2):221–234,April 1976.
[27] V. Mahinthan, L. Cai, J.W. Mark, and X. Shen. Partner selection basedon optimal power allocation in cooperative-diversity systems. IEEETrans. Veh.r Technol., 57(1):511–520, 2008.
Zhe Yang (S’09) received his B.S. degree in In-formation Engineering in 2005 and M.S. degreein Control Theory and Engineering in 2008, bothfrom Xi’an Jiaotong University, Xi’an, China. Heis currently a Ph.D. candidate at the Departmentof Electrical and Computer Engineering, Universityof Victoria, British Columbia, Canada. His currentresearch interests include cross-layer design for co-operative networks, scheduling and resources allo-cation for wireless networks and synchronization.
Lin Cai (S’00-M’06-SM’10) received her M.A.Sc.and PhD degrees (awarded Outstanding Achieve-ment in Graduate Studies) in electrical and com-puter engineering from the University of Waterloo,Waterloo, Canada, in 2002 and 2005, respectively.Since 2005, she has been an Assistant Professor andthen an Associate Professor with the Department ofElectrical & Computer Engineering at the Universityof Victoria. Her research interests span several areasin wireless communications and networking, with afocus on network protocol and architecture design
supporting emerging multimedia traffic over wireless, mobile, ad hoc, andsensor networks. She has been a recipient of the NSERC Discovery Accel-erator Supplement Grant in 2010, and the best paper awards of IEEE ICC2008 and IEEE WCNC 2011. She has served as a TPC symposium co-chairfor IEEE Globecom’10, and the Associate Editor for IEEE Trans. WirelessCommunications, IEEE Trans. Vehicular Technology, EURASIP Journal onWireless Communications and Networking, International Journal of SensorNetworks, and Journal of Communications and Networks (JCN).
Yuanqian Luo (S’09) received his B.S. and M.S.degrees in Electrical Engineering from SoutheastUniversity, Nanjing, China, in 2005 and 2008, re-spectively. He is currently a Ph.D. candidate at theDepartment of Electrical and Computer Engineering,University of Victoria, British Columbia, Canada.His current research interests include cross-layerdesign and optimization for cooperative networks.He has received the best paper award of IEEEWCNC in 2011.
Jianping Pan (S’96-M’98-SM’08) is currently anassociate professor of computer science at theUniversity of Victoria, Victoria, British Columbia,Canada. He received his Bachelor’s and PhD degreesin computer science from Southeast University, Nan-jing, Jiangsu, China, and he did his postdoctoralresearch at the University of Waterloo, Waterloo,Ontario, Canada. He also worked at Fujitsu Labs andNTT Labs. His area of specialization is computernetworks and distributed systems, and his currentresearch interests include protocols for advanced
networking, performance analysis of networked systems, and applied net-work security. He received the IEICE Best Paper Award in 2009 and theTelecommunications Advancement Foundation’s Telesys Award in 2010, andhas been serving on the technical program committees of major computercommunications and networking conferences including IEEE INFOCOM,ICC, Globecom, WCNC and CCNC. He is a senior member of the ACM.
