A Fully Distributed Opportunistic Network Coding Scheme for Cellular Relay Networks

0.24 MB·English

by  Yulong Zou

A Fully Distributed Opportunistic Network Coding
Scheme for Cellular Relay Networks
Yulong Zou, Jia Zhu, and Baoyu Zheng
Inst. of Signal Process. and Transm., Nanjing Univ. Post & Telecomm., Nanjing, P. R. China
Email: Yulong.Zou,Jiazhu2010 @gmail.com,[email protected]
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Abstract—In thispaper, we propose an opportunisticnetwork to destination [5]. To alleviate such an issue, two-way relays
3 coding(ONC)schemeincellularrelaynetworks,whichoperates have been proposed by using a so-called physical network
1 dependingonwhethertherelaydecodessourcemessagessuccess-
coding (PNC) that enables the transmission of two messages
0 fullyornot.Afullydistributedmethodispresentedtoimplement
2 the proposed opportunistic network coding scheme without the in two orthogonal channels [6]. However, the PNC requires
n need of any feedback between two network nodes. We consider complex symbol-level synchronization between distributed
a theuseofproposedONCforcellulardownlinktransmissionsand network nodesforsignal combinationand exact channelstate
J derive its closed-form outage probability expression considering information (CSI) of all network nodes at receiver side for
cochannel interference in a Rayleigh fading environment. Nu-
1 signal decoding, which is challenging in practical systems.
mericalresultsshowthattheproposedONCschemeoutperforms
3 In this paper, we investigate network coding without the
the traditional non-cooperation in terms of outage probability.

We also develop the diversity-multiplexing tradeoff (DMT) of complex symbol-level synchronization between distributed
]
T proposed ONC and show that the ONC scheme obtains the full network nodes and propose an opportunistic network coding
I diversity and an increased multiplexing gain as compared with (ONC) scheme for cellular relay networks. It is worth men-
. the conventional cooperation protocols.
s tioning that, although the proposed ONC is an opportunistic
c IndexTerms—Networkcoding,cellularnetworks,outageprob- scheme that operatesdependingon whetherthe relay decodes
[ ability, diversity-multiplexing tradeoff, cochannel interference.
sourcemessagessuccessfullyornot,itcanbeimplementedin

1 a fully distributed manner without any feedback between two
v I. INTRODUCTION network nodes. This differs from the conventional network
6
Next-generation cellular mobile networks, including Inter- coding approacheswhere the cooperativeusers have to notify
0
nationalMobile Telecommunications- Advancedand Beyond the destination whether or not they succeed in decoding
5
7 (IMT-Advanced and Beyond) [1], are expected to provide a each other’s message so that the destination can perform the
. peak download speed at 100Mbit/s (or higher) for mobile maximal ratio combining (MRC) among different network
1
0 receptions and 1Gbit/s (or higher) for stationary receptions nodesindifferentsituationsofdecodingoutcomes(successful
3 to meet continuously growing demand on mobile multime- or not). In addition, differing from conventional network
1 dia services (e.g., video-on-demand, mobile game/TV, and coding research (e.g., [7]-[9]), we study the ONC design
:
v so on). Although the multiple-input multiple-output (MIMO) anditsdiversity-multiplexingtradeoff(DMT)in cellular relay
i and orthogonal frequency division multiplexing (OFDM) are networks, where cochannel interference should be taken into
X
shown as effective methods to combat wireless fading and account.
r
a increase per-link throughput, they do not inherently mitigate The rest of this paper is organized as follows. In Section
the cochannel interference and fail to benefit cell-edge users II, we first present the system model of a cellular network
significantly[2]. To that end,one promisingsolution is to use with relay and then propose the ONC scheme for cellular
wireless relayswhich assist the transmissionsbetween mobile downlink transmissions. Section III derives a closed-form
users and a base station [3], [4]. outage probability expression of the proposed ONC scheme
Typically, relays are categorized into two broad types [2]: by considering cochannel interference in a Rayleigh fading
full-duplex relay and half-duplex relay, where the full-duplex environment, based on which a DMT analysis is also con-
relay refers to the relay capable of transmitting and receiving ducted.In SectionIV, numericalresults arepresentedto show
radio signals overthe same channel, however,the half-duplex the outageprobabilityand DMT performanceof the proposed
relay means that two channels (in terms of time/frequency) ONCschemeand conventionalcooperationprotocols.Finally,
are required at a relay for transmitting and receiving signals. Section VI provides concluding remarks.
While full-duplex relays are attractive in terms of spectrum
II. PROPOSED OPPORTUNISTICNETWORKCODING
utilization, they are generally considered as impractical due
to the significant difference in the power levels of incoming A. System Model
andoutgoingsignals.Thus,thehalf-duplexrelayconfiguration ConsideracellularrelaynetworkasshowninFig.1,where
is typically used, which, however, reduces the data rate since a base station (BS) is located in the center of a cell and a
two channels are required to forward a message from source relay station (RS) serves the BS. At present, such a cellular
(cid:4)(cid:5)(cid:6)(cid:6)(cid:6)(cid:6)(cid:2)(cid:6)(cid:6)(cid:2)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:7)(cid:2)(cid:8)(cid:7)(cid:3)(cid:9)(cid:6)(cid:10)(cid:5)(cid:11) (cid:4)(cid:5)(cid:6)(cid:6)(cid:6)(cid:6)(cid:2)(cid:6)(cid:6)(cid:3)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:7)(cid:3)(cid:8)(cid:7)(cid:2)(cid:9)(cid:6)(cid:10)(cid:5)(cid:11) (cid:10)(cid:5)(cid:6)(cid:6)(cid:8)(cid:6)(cid:12)(cid:6)(cid:6)(cid:9)(cid:6)(cid:2)(cid:6)(cid:6)(cid:2)(cid:6)(cid:6)(cid:11)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:8)(cid:6)(cid:12)(cid:6)(cid:6)(cid:9)(cid:6)(cid:2)(cid:6)(cid:6)(cid:3)(cid:6)(cid:11)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:7)(cid:2)(cid:9)(cid:6)(cid:7)(cid:3)
(cid:1) (cid:1)(cid:1)(cid:2) (cid:1)(cid:1)(cid:3)
Fig. 2. The encoding structure of proposed ONC for cellular downlink
transmissions considering timedivision multiplexing (TDM).
check(CRC)codeisgenerallyusedasforwarderrordetection
for every data package. Hence, RS can recognize whether or
(cid:1)(cid:25) not it succeeds in decoding b1 or b2 by CRC checking, i.e., a
successfulCRCcheckingimpliesacorrectlydecodedoutcome
(cid:12) (cid:15)(cid:23) and vice versa.
We here consider that both b and b consist of CRC-
(cid:1)(cid:24) 1 2
encoded bits in two different CRC codes, as denoted by
CRC 1 and CRC 2, respectively. Accordingly, in case that
RS only forwards b or b during slot n+2 as shown in
1 2
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:3)(cid:4)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11) Fig. 2, both U1 and U2 are able to recognize through CRC
(cid:16)(cid:14)(cid:7)(cid:7)(cid:17)(cid:9)(cid:8)(cid:18)(cid:10)(cid:6)(cid:8)(cid:14)(cid:9)(cid:5)(cid:11)(cid:8)(cid:9)(cid:19)
checking that either b or b is transmitted, assuming a
1 2
(cid:12)(cid:3)(cid:11)(cid:10)(cid:13)(cid:5)(cid:2)(cid:6)(cid:10)(cid:6)(cid:8)(cid:14)(cid:9)
(cid:16)(cid:14)(cid:18)(cid:20)(cid:10)(cid:9)(cid:9)(cid:3)(cid:11)(cid:5)(cid:21)(cid:9)(cid:6)(cid:3)(cid:4)(cid:22)(cid:3)(cid:4)(cid:3)(cid:9)(cid:18)(cid:3)(cid:5) perfecterrordetection.Inthisway,theproposedONCscheme
can be implemented in a fully distributed manner without
(cid:15)(cid:10)(cid:2)(cid:3)(cid:5)(cid:2)(cid:6)(cid:10)(cid:6)(cid:8)(cid:14)(cid:9)
any feedback information between two nodes. The detailed
illustration of this fully distributed implementation method
Fig.1. Systemmodelofacellular relaynetwork.
will be presented in Section II-D. In addition, it is pointed
outthat, if there are multiplecell-edgeusers, we can pairwise
relayarchitecturehasbeenadoptedinthecommercialwireless themtogeneratemultipleuserpairs,wheredifferentuserpairs
network IEEE 802.16j, where relay stations are allowed to proceedwiththeproposedopportunisticcodingidenticallyand
communicatewithBS anduserterminalsin onedirectionata independentlyof each otherwith differentorthogonalchannel
time(i.e.,eitheruplinkordownlink).Inthispaper,weassume groups.Sincedifferentuserpairscanbedifferentiatedthrough
that the channels are narrowband and modeled as Rayleigh theidentificationoforthogonalchannelgroups,theycanreuse
fading, which correspond to ideal LTE OFDM subchannels. the same set of CRC codesforthe distributedimplementation
Fig. 1 illustrates two cell-edge users (i.e., U1 and U2) that of the ONC scheme.
receivedatafromBSoverdownlinkswiththeassistanceofone As shown in Fig. 2, BS first transmits b to U1 in time
1
relaystation(RS),whereinterferences(receivedatU1,U2and slot n and, at the same time, both U2 and RS overhear this
RS)arefromneighboringcochannelbasestations.Thereasons transmission. Hence, the received signal at U1 in time slot n
forconsideringthetwo-usercooperationaretwofold.First,the can be expressed by
two-usercooperationissimpleforimplementationinpractical
K
cellular systems, which is also shown as an effective means y (n)=√Ph (n)b +(cid:229) √Pg (n)I (n)+z (n), (1)
1 b1 1 ik1 ik 1
toimprovewirelesstransmissionperformance[5].Secondly,a k=1
generalscenariowithmultipleuserscanbetypicallyconverted
wherePistransmitpower,h (n)istheBS-U1channelintime
b1
to the two-usercooperationby designingan additionalgroup-
slotn,K isthenumberoftotalcochannelinterferers,g (n)is
ing and partnerselection protocol. In addition, this paper will ik1
thechannelfromk-thinterferertoU1,I (n)isthetransmitted
focus on the cellular downlink transmission, while a similar ik
symbolofk-thinterfererintimeslotn,andz (n)istheadditive
1
analysis can be applied to the uplink.
white Gaussian noise (AWGN) at U1 with zero mean and
variance N . Notice that subscripts 1, b and i represent U1,
B. Proposed ONC Scheme 0 k
BS and k-th interferer, respectively. We can similarly express
Fig. 2 shows the proposed ONC encoding structure for
the received signals at U2 and RS in time slot n as
cellulardownlinktransmissions, whereBS intendsto transmit
b1 andb2 toU1andU2intimeslotsnandn+1,respectively. y (n)=√Ph (n)b +(cid:229)K √Pg (n)I (n)+z (n), (2)
During time slot n+2, the information to be transmitted 2 b2 1 ik2 ik 2
k=1
(from RS to U1 and U2) dependson whether RS succeeds in
decodingb andb ornot.Specifically,ifRSdecodesbothb and
1 2 1
and b successfully, it transmits an XOR coded version of b K
2 1 (cid:229)
andb2toU1andU2.IfRSsucceedsindecodingb1(orb2)and yr(n)=√Phbr(n)b1+ √Pgikr(n)Iik(n)+zr(n), (3)
failstodecodeb (orb ),ittransmitsb (orb )toU1andU2. k=1
2 1 1 2
Otherwise,anullsequenceistransmittedfromRSintimeslot whereh (n)andh (n)are,respectively,the channelsofBS-
b2 br
n+2. Notice that, in practical systems, a cyclic redundancy U2andBS-Rintimeslotn,g (n)andg (n)arethechannels
ik2 ikr
(cid:23)(cid:4)(cid:24)(cid:4)(cid:3)(cid:3)(cid:2)(cid:3)(cid:10)(cid:20)(cid:2)(cid:11)(cid:18)(cid:20)(cid:14)(cid:15)(cid:16)(cid:10)(cid:17)(cid:22)(cid:24)(cid:21)(cid:11)(cid:22)(cid:21)(cid:24)(cid:2)
(cid:24)(cid:22)(cid:3)(cid:3)(cid:10) (cid:9)(cid:17)(cid:22)(cid:10)(cid:25)(cid:24)(cid:4)(cid:15)(cid:11)(cid:12) (cid:6)(cid:7)(cid:6)(cid:8)(cid:9)(cid:10)
(cid:18)(cid:2)(cid:25)(cid:22)(cid:2)(cid:15)(cid:11)(cid:2) (cid:11)(cid:12)(cid:2)(cid:11)(cid:13)(cid:14)(cid:15)(cid:16)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5) (cid:1)(cid:2)(cid:20)(cid:19)(cid:21)(cid:22)(cid:3)(cid:4)(cid:23)(cid:14)(cid:19)(cid:15) (cid:1)(cid:9) (cid:5)(cid:15)(cid:2)(cid:19)(cid:18) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) (cid:1)(cid:2)(cid:19)(cid:18)(cid:20)(cid:21)(cid:3)(cid:4)(cid:22)(cid:14)(cid:18)(cid:15) (cid:1)(cid:9) (cid:15)(cid:5)(cid:18)(cid:2)(cid:17)
(cid:6)(cid:7)(cid:6)(cid:8)(cid:9)(cid:10) (cid:26)(cid:15)(cid:20)(cid:10)(cid:25)(cid:24)(cid:4)(cid:15)(cid:11)(cid:12) (cid:1) (cid:6)(cid:7)(cid:6)(cid:8)(cid:9)(cid:10)
(cid:11)(cid:12)(cid:2)(cid:11)(cid:13)(cid:14)(cid:15)(cid:16) (cid:1) (cid:1) (cid:1)(cid:2)(cid:19)(cid:18)(cid:20)(cid:21)(cid:3)(cid:4)(cid:22)(cid:14)(cid:18)(cid:15) (cid:26) (cid:11)(cid:12)(cid:2)(cid:11)(cid:13)(cid:14)(cid:15)(cid:16)
(cid:9) (cid:17)
(cid:11)(cid:6)(cid:12)(cid:2)(cid:7)(cid:11)(cid:6)(cid:13)(cid:8)(cid:14)(cid:15)(cid:17)(cid:16)(cid:10) (cid:5)(cid:2)(cid:18) (cid:1)(cid:2)(cid:19)(cid:18)(cid:20)(cid:21)(cid:3)(cid:4)(cid:22)(cid:14)(cid:18)(cid:15) (cid:1)(cid:9) (cid:1)(cid:26) (cid:1)(cid:9) (cid:15)(cid:5)(cid:18)(cid:2)(cid:17) (cid:28)(cid:2)(cid:3)(cid:2)(cid:11)(cid:22)(cid:14)(cid:18)(cid:15) (cid:1)(cid:9)
(cid:1)(cid:2)(cid:20)(cid:19)(cid:21)(cid:22)(cid:3)(cid:4)(cid:23)(cid:14)(cid:19)(cid:15) (cid:1) (cid:15)(cid:19)
(cid:17) (cid:27)(cid:24)(cid:20)(cid:10)(cid:25)(cid:24)(cid:4)(cid:15)(cid:11)(cid:12) (cid:6)(cid:7)(cid:6)(cid:8)(cid:9)(cid:10)
(cid:11)(cid:12)(cid:2)(cid:11)(cid:13)(cid:14)(cid:15)(cid:16)
(cid:24)(cid:22)(cid:3)(cid:3)(cid:10)
(cid:18)(cid:2)(cid:25)(cid:22)(cid:2)(cid:15)(cid:11)(cid:2) (cid:1)(cid:2)(cid:19)(cid:18)(cid:20)(cid:21)(cid:3)(cid:4)(cid:22)(cid:14)(cid:18)(cid:15) (cid:1)(cid:9) (cid:1)(cid:9) (cid:15)(cid:5)(cid:18)(cid:2)(cid:17)
Fig.3. Areceiver structure attherelaystation.
Fig. 4. A parallel decoder structure at U1 in decoding b1. The process at
U2indecoding b2 issimilar.
from k-th interfererto U2 and RS, respectively,and z (n)and
2
z (n) are AWGN with zero mean and variance N at U2 and
r 0
and CRC 2 checking both pass, CRC 1 checking passes and
RS,respectively.Then,duringnextslot n+1,BStransmitsb
2
CRC 2 checking fails, CRC 1 checking fails and CRC 2
to U2 and, meanwhile, both U1 and RS overhear. Thus, the
checking passes, and both CRC 1 and CRC 2 checking fail.
received signal at U2 in time slot n+1 is given by
It is assumed that a failed CRC checking indicates that an
y2(n+1)=√Phb2(n+1)b2+z2(n+1) outage event occurs. Hence, given a data transmission rate R
K (4) over downlink, we can describe events q =1, 2, 3, and 4 as
(cid:229)
+ √Pgik2(n+1)Iik(n+1), (in an information-theoreticsense [5])
k=1
q =1: I (n)>R and I (n+1)>R
where h (n+1) is the BS-U2 channel in time slot n+1, br br
b2 q =2: I (n)>R and I (n+1)<R
g (n+1) is the channel from k-th interferer to U2, and br br
ik2 (7)
z (n+1) is the AWGN at U2 with zero mean and variance q =3: I (n)<R and I (n+1)>R
2 br br
N0. Meanwhile, the received signals at U1 and RS are, q =4: Ibr(n)<R and Ibr(n+1)<R,
respectively, given by
where I (n) and I (n+1) are the mutual information from
br br
y1(n+1)=√Phb1(n+1)b2+z1(n+1) BS to RS in time slots n and n+1, respectively. Following
K (5) Eq. (3) and considering coherent detection, I (n) are given
(cid:229) br
+ √Pgik1(n+1)Iik(k+1), by
k=1 2 h (n)2g
br
I (n)= log (1+ | | ), (8)
and br 3 2 K
(cid:229) g (n)2g +1
yr(n+1)=√Phbr(n+1)b2+zr(n+1) k=1| ikr |
+(cid:229)K √Pgikr(n+1)Iik(n+1). (6) wfrohnerteofg l=ogP/(N)0isisdsuiegntoalt-htoe-nfaocitsethraattitohr(eSeNtRim)eansldotfsacatroeru23seidn
k=1 2 ·
fortransmittingtwoinformationsymbolsb andb .Similarly,
whereh (n+1)andh (n+1)are,respectively,thechannels 1 2
b1 br fromEq.(6),we canobtain I (n+1)with coherentdetection
of BS-U1 and BS-R in time slot n+1, g (n+1) and br
ik1 as
gikr(n+1) are the channels from k-th interferer to U2 and 2 hbr(n+1)2g
RS, respectively, and z1(n+1) and zr(n+1) are AWGN at Ibr(n+1)= 3log2(1+ K | | ). (9)
U2 and RS, respectively. (cid:229) |gikr(n+1)|2g +1
k=1
C. Decoding Structure at a Relay Station Meanwhile, given q =1, 2, 3, and 4, the received signal at
In what follows, we present a decoder design of the pro- U1 in time slot n+2 is given by Eq. (10) at the top of the
posedONCattherelaystation.AsshowninFig.3,ifCRC 1 following page, where h (n+2)is the R-U1 channel in time
r1
and CRC 2 checking both pass, b1⊕b2 will be transmitted slotn+2,gik1(n+2)isthechannelfromk-thinterferertoU2,
at RS in time slot n+2. If RS fails in both CRC 1 and z (n+2) is the AWGN at U2 with zero mean and variance
1
CRC 2 checking, a null sequence will be transmitted. One N , and b represents a null sequence transmitted at RS.
0
can see from Fig. 3 that, if RS succeeds in CRC 1 checking
D. Decoding Structure at User Terminals
(or, CRC 2 checking) and fails to pass CRC 2 checking (or,
CRC 1 checking), it transmits b (or, b ) in time slot n+2. In this subsection, we present the decoding process of
1 2
For notational convenience, let q =1, 2, 3, and 4, respec- proposed ONC scheme at user terminals. We focus on the
tively, denote the above-mentioned four cases, i.e., CRC 1 details of the decoder structure at U1 in decoding b , and
1
K
√Ph (n+2)(b b )+ (cid:229) √Pg (n+2)I (k+2)+z (n+2), q =1
r1 1⊕ 2 ik1 ik 1
 k=1
K
y1(n+2)=√√PPhhrr11((nn++22))bb12++k(cid:229)(cid:229)=K1√√PPggiikk11((nn++22))IIiikk((kk++22))++zz11((nn++22)),, qq ==23 (10)
k=1
K
√Phr1(n+2)b+k(cid:229)=1√Pgik1(n+2)Iik(k+2)+z1(n+2), q =4
a similar design can be applied to U2 in decoding b . As Given q =2 (i.e., RS decodes b , but fails to decode b ), U1
2 1 2
shown in Fig. 4, we utilize three parallel branches at U1 in would possibly succeeds in decoding b either from the first
1
decoding b , where the first branch is to decode the direct branch or third branch as shown in Fig. 4. Hence, in given
1
transmission of b from BS to U1, the second branch is to case q =2, the conditional mutual information from BS to
1
combine the transmissions from BS (i.e., b ) and RS (e.g., U1 is obtained as
2
b b )to U1,andthe thirdbranchisused todemodulatethe
p1os⊕sib2le transmission of b1 from RS. Typically, the branch Ib1(q =2)=max{Ib1(n),Ir1(n+2)}. (15)
that passes CRC 1 checkingis selected as the decoderoutput Finally, either event q =3 or q =4 occurs, U1 can rely on
at U1. Moreover, if more than one branch succeed in CRC the first branch only to decode b . Thus, given case q =3 or
1
checking,wecanchooseoneofthesuccessfulbranchesasthe q =4, the corresponding conditional information from BS to
output.OnecanobservefromFig.4that,intheproposedONC U1 is given by
scheme, signal transmissions from different network nodes at
I (q =3)=I (q =4)=I (n), (16)
different slots are demodulated separately at receiver without b1 b1 b1
thesignalcombinationbetweendifferenttransmissions,which whereI (n)isgivenbyEq.(12).Now,wecompletethesignal
b1
canavoidthecomplexsymbol-levelsynchronizationissueand modelingforthe decodingprocessof proposedONC scheme.
shows the advantage of the proposed opportunistic network
codingoverconventionalPNC[6].Also,Fig.4showsthatU1 III. PERFORMANCE ANALYSIS OFPROPOSED ONC
can decode b locally withoutany feedbackinformationfrom SCHEME OVERRAYLEIGHFADINGCHANNELS
1
RS, implying that the proposed ONC scheme is implemented In this section, we focus on the performance analysis of
in a fullydistributedmanner.Asshownin Fig.4, given q =1 the transmission from BS to U1 and the BS-U2 transmission
(i.e., RS decodes both b and b ), U1 would possibly recover has similar performance results. We first examine outage
1 2
b eitherfrom the first branchor second branch.Thus, in this probabilityof theONC scheme,followedbya DMT analysis.
1
case, the conditional mutual information from BS to U1 is As is known [5], an outage event occurs when the channel
given by capacityfallsbelowapredefineddatarateR.Hence,anoutage
probability of the ONC scheme is given by
I (q =1)=max I (n),min[I (n+1),I (n+2)] , (11)
b1 b1 b1 r1
{ } Pout =Pr[I <R]
ONC b1
where Ib1(n), Ib1(n+1), and Ir1(n+2) are the mutual infor- = (cid:229) Pr(q =k)Pr[I (q =k)<R]. (17)
mation from BS to U1 in time slot n, from BS to U1 in time b1
k=1,2,3,4
slot n+1, and from RS to U1 in time slot n+2, respectively.
FollowingEqs.(1)and(5),we,respectively,obtainthemutual Using Eqs. (7) - (9), we can obtain term Pr(q =1) as
information Ib1(n) and Ib1(n+1) as Pr(q =1)=Pr[I (n)>R]Pr[I (n+1)>R]
br br
Ib1(n)= 23log2(1+k(cid:229)=K1||ghibk11((nn))||22gg +1), (12) =. Pr[k(cid:229)=K|1h|bgri(knr()n|2)|2 >23R/2−1] (18)
and Pr[ |hbr(n+1)|2 >23R/2 1],
Ib1(n+1)= 23log2(1+ (cid:229)K |ghb1((nn++11))|22gg +1). (13) × k(cid:229)=K1|gikr(n+1)|2 −
| ik1 | where the second equation is obtained by ignoring the noise.
k=1
This is valid when the interference becomes a dominant con-
Similarly,onecaneasilyobtainthemutualinformationI (n+
r1
cern, e.g., in interference-limited systems. Note that random
2) from Eq. (10) as
variables h (n)2, h (n+1)2, g (n)2, and g (n+1)2
2 hr1(n+2)2g follow exp|obnrenti|al d|isbtrribution|s a|ndikrare |indepen|deiknrt of eac|h
Ir1(n+2)= 3log2(1+ K | | ). (14) other.Thus,wecanfurtherobtainPr(q =1)asEq.(19)atthe
(cid:229) g (n+2)2g +1
k=1| ik1 | top of this page, where s b2r=E(|hbr(n)|2)=E(|hbr(n+1)|2),
(cid:229)K l br-ikr (cid:213)K l b−r-1ikr 2, l = =l
Pr(q =1)= k=1l br-likr+(23R/2−12)Kj=1,j6=kl b−r-1ikr−l b−r-1ijr! br-i1r6 ···6 br-iKr (19)
br-ikr , l = =l
(cid:18)l br-ikr+(23R/2−1)(cid:19) br-i1r ··· br-iKr
s 2 =E(h (n)2)=E(h (n+1)2),andl =s 2/s 2 is
ikr | ikr | | ikr | br-ikr br ikr 100
viewedas the signal-to-interferenceratio(SIR) of the channel
R = 1bit/s/Hz
gain from BS to RS to that from k-th interferer to RS. We
can similarly determine terms Pr(q = 2), Pr(q = 3), and
Pr(q =4) in closed-form. Besides, following Eqs. (11) - (14)
a(1n7d)iagsnoring noise, we obtain term Pr[Ib1(q =1)<R] in Eq. bility10−1
a
b
o
pr R = 0.5bit/s/Hz
e
g
Pr[I (q =1)<R]=Pr[ |hb1(n)|2 <23R/2 1] Outa
b1
K −
(cid:229) |gik1(n)|2 10−2
k=1 non−cooperative (Analyt.)
h (n)2 non−cooperative (Simul.)
Pr[ | b1 | <23R/2 1] proposed ONC (Analyt.)
− K − proposed ONC (Simul.)
(cid:229) g (n)2
| ik1 | 5 10 15 20 25 30
k=1 (20) SIR (dB)
h (n+1)2
Pr[ | b1 | >23R/2 1]
× K − Fig.5. Outageprobabilityversussignal-to-interferenceratio(SIR)ofthenon-
k(cid:229)=1h|gi(kn1(+n+2)12)|2 clor1o-pike1ra=tiolnrb-aiknbd=plro1pr-oiksre=d Ol1Nb-Cikbs=chlem21e-isk1w=ithl2rK-ik=r.7 and lb1-ik1=lbr-ikr=
Pr[ | r1 | >23R/2 1],
× K −
(cid:229) g (n+2)2
| ik1 | Meanwhile, the multiplexing gain r is defined as
k=1
R(l )
r= lim b1-i11 . (22)
wherePr[k(cid:229)=K|1h|bg1ik(n1)(|n2)|2 <23R/2−1],Pr[k(cid:229)=K|1h|bg1ik(n1(+n1+)1|2)|2 >23R/2−1], Following the generalilzbe1-di11D→M¥ lTogd(elfib1n-ii1ti1o)n as given by Eqs.
and Pr[ |hr1(n+2)|2 >23R/2 1] can be easily determined in (21) and (22), we can obtain the DMT performance of pro-
k(cid:229)=K1|gik1(n+2)|2 − posed ONC scheme as
closed-form.Similarlyto Eq.(20),we can also obtainclosed-
form solutions to Pr[I (q =2)<R], Pr[I (q =3)<R] and dONC+3r=2. (23)
b1 b1
Pr[Ib1(q = 4)<R]. So far, we have completed the closed- One can observefrom Eq. (23)that a diversity gain dONC=2
form outage probability analysis for proposed ONC scheme, is achieved as r 0 and, on the other hand, a maximum
based on which the DMT will be developed in the following. multiplexing gain→of two-third (i.e., r=2/3) can be achieved
Note that the traditional diversity gain is defined as d = as the diversity gain approaches to zero.
lim logPe(SNR) [12] whereSNR is SNR and P represents
−bitSNeRrr→or¥ raltoeg,SwNRhich is not applicable here since tehe interfer- IV. NUMERICALRESULTS
ence, rather than AWGN noise, becomes a dominant concern Fig. 5 shows the outage probability versus the signal-to-
indeterminingthetransmissionperformance,asshowninEqs. interference radio (SIR) of the non-cooperationand proposed
(18) and (20). Therefore, we present a generalized diversity ONC schemes for different data rates, where the simulation
gain as an asymptotic ratio of the outage performanceto SIR results are also given. It is shown from Fig. 5 that the
l =s 2 /s 2 with l ¥ , where s 2 =E(h 2) is simulation results match analytical results very well. One can
b1-i11 b1 i11 b1-i11→ i11 | i11|
the average gain of the channel from the 1st interferer to U1. observefromFig.5thatinlowSIRregions,theproposedONC
Accordingly, the diversity gain of proposed ONC scheme is scheme performs worse than the non-cooperation in terms of
given by outageprobabilityforboth R=0.5bit/s/HzandR=1bit/s/Hz.
Thisisbecausethatahalf-duplexrelayconstraintisconsidered
log(PoutONC) forthe ONC scheme, whichsacrifices the spectrumefficiency
d = lim . (21)
ONC −lb1-i11→¥ log(l b1-i11) (also known as multiplexing gain) to achieve the diversity
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constraintandtheoutageprobabilityperformanceoftheONC
scheme becomes better than that of the non-cooperation.
Fig. 6 compares the DMT performance of the non-
cooperation,conventionalcooperationprotocols,andproposed
ONC scheme. As shown in Fig. 6, as the multiplexing gain
approaches zero, the non-cooperation achieves a diversity
gain of only one; however the conventional cooperation and
proposed ONC schemes obtain the full diversity gain of two,
showing the advantage of cooperation over non-cooperation.
On the other hand, one can also see from Fig. 6 that as the
diversity gain decreases to zero, the conventionalcooperation
schemes achieve a maximum multiplexing gain of one-half.
In contrast, the proposed ONC scheme obtains a maximum
multiplexing gain of two-third, which is better than the con-
ventional cooperation.
V. CONCLUSION
In this paper, we investigated opportunisticnetwork coding
for cellular relay networks and proposed a fully distributed
ONC scheme. We derived a closed-form outage probability
expressionoftheproposedONCschemeoverRayleighfading
channels.Numericaloutageprobabilityresultsshowedthatthe
ONC scheme performs better than the non-cooperation. We
also studied the DMT performanceof proposedONC scheme
and showed that the proposed ONC strictly outperforms the
conventionalcooperation in terms of DMT performance.
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