Peng, Y., Armour, SMD, & McGeehan, JP (2007). An investigation of dynamic subcarrier allocation ...

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Peng, Y., Armour, SMD., & McGeehan, JP. (2007). An investigation of

dynamic subcarrier allocation in MIMO–OFDMA systems. IEEE
Transactions on Vehicular Technology, 56(5, part 2), 2990 - 3005.
https://doi.org/10.1109/TVT.2007.899951
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2990 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.56,NO.5,SEPTEMBER2007
An Investigation of Dynamic Subcarrier Allocation in
MIMO–OFDMA Systems
YingPeng,Member,IEEE,SimonM.D.Armour,andJosephP.McGeehan
Abstract—In this paper, orthogonal frequency-division Ck,s,m(cid:1) Matrix to record the location of allocated
multiple-access(OFDMA)systemswithdynamicdeterministic(as subcarriers for user k, subcarrier (within the
opposed to pseudorandom) allocation of subcarriers to users to subchannel)s,andspatialchannelm(cid:1).
exploitmultiuserdiversityareinvestigated.Previouslypublished
k User.
work on dynamic multiuser subcarrrier allocation for OFDMA (cid:1)
systems with single-input–single-output (SISO) channels are k Useroritsduplication.
surveyed. A near-optimal low-complexity algorithm for SISO K Numberofallusers.
(cid:1)
systems,whichisstructurallysimilartothealgorithmbyRheeand K Number of S times duplication of K users,
Cioffi, is extended to the case of multiple-input–multiple-output K(cid:1) =S×K.
(MIMO) systems in this paper. The optimality and adaptability
h Channelresponseforuserk,subcarriernfor
of this algorithm are analyzed by formulating an assignment k,n
problem and comparing with one optimal and two extended acertainchannel.
suboptimal strategies proposed based on previous work. Con- hk,n,m(cid:1) Channelresponseforuserk,subcarriern,and
sideration of a MIMO channel creates further issues for the channelm(cid:1).
subcarrier-allocationprocess.Inparticular,methodswherebyan |h | Channeltransfer-functionamplitude.
appropriate subcarrier allocation may be exploited to minimize k,n
the effects of correlation in MIMO channels are of considerable |hk,n,m(cid:1)| Relativechannelgaininamplitude.
interest. Several novel variants of the algorithm (referred to as |huser,sub|2 Channel gain of a certain user for the
“schemes”) are proposed and evaluated for MIMO systems allocated subcarrier in a certain simula-
employing both space-time block coding (STBC) and spatial tiontime.
multiplexing (SM) in both uncorrelated and correlated fading H Channel gain matrix, H ={|h |2},k =1,
channels. Simulation results identify the most suitable schemes k,n
2,...,K,n=1,2,...,N .
for bothSTBCandSMand, inparticular, show thatsubstantial sub
improvements in performance (in terms of bit-error rate) L Alternativesubcarrierinschemes4and5.
in correlated channels can be achieved by means of suitable m Certainspatialsubchannel.
subcarrier allocation. In uncorrelated channels, the best scheme m(cid:1) Spatialsubchannelindexm(cid:1) ={1,...,M(cid:1)}.
can offer approximately 7-dB gain over the conventional MIMO
M True number of spatial subchannels (M =
channel; in highly correlated channels, even more substantial
T ×R ).
improvements(>11-dBgainforSTBC,>20-dBgainforSM)in x x
performancecanalsobeachieved,demonstratingtheabilityofa M(cid:1) Effective number of spatial subchannels con-
well-designed subcarrier-allocation scheme to mitigate the sideredbytheallocationalgorithm.
debilitatingeffectsofcorrelationonMIMOsystems. n Certainsubcarrier.
IndexTerms—Multipleinputmultipleoutput(MIMO),orthog- Nsub Numberofalluseablesubcarriers.
onal frequency-division multiple access (OFDMA), single input N M(cid:1) by N matrix, where each row is a
Sub
single output (SISO), space-time block coding (STBC), spatial vector containing the indexes of the useable
multiplexing(SM),subcarrierallocation.
subcarriersforthecorrespondingspatialsub-
NOMENCLATURE P Tchoatanlnelp(eir.ec.e,iNvemd(cid:1) =ch{a1n,n2e,l3,g..a.in,,NSPub}). =
total (cid:2) (cid:2) total
0cm(cid:1),NSub MAlalotrcixatioofnz-emroasppoifnsgizmeamtri(cid:1)xbeyleNmSeunbt.foruserk Popt MaKkximuNnmsubtoctka,lnp|herkc,nei|v2e.dchannelgain.
k,n total
andsubcarriern. P Nsub×Nsub Total perceived channel gain for L times
total
c(cid:1) Allocation-mappingmatrixelementforauser duplication of K users PNsub×Nsub =
k,n (cid:1) (cid:2) (cid:2) total
oritsduplicationkandsubcarriern. Nnsub (cid:1)Nk=su1bc(cid:1)k,n|h(cid:1)k,n|2.
P Normalizedpowerperuserandpersubcarrier.
norm
P Averagereceivedpower.
ManuscriptreceivedJanuary25,2006;revisedJune25,2006,September18, k
2006,andSeptember21,2006.ThisworkwassupportedbyKyoceraR&D.The q Number of near-adjacent subcarriers avoided
reviewofthispaperwascoordinatedbyProf.X.-G.Xia. in scheme 5 process. The value of ten was
The authors are with Centre for Communications Research, Electrical
chosen on the basis of some crude optimiza-
and Electronic Engineering Department, University of Bristol, BS8 1UB
Bristol, U.K. (e-mail: [email protected]; [email protected]; tion via a trial-and-error approach and is not
[email protected]). necessarilyoptimal.
Colorversionsofoneormoreofthefiguresinthispaperareavailableonline
R Numberofreceiveantennas.
athttp://ieeexplore.ieee.org. x
DigitalObjectIdentifier10.1109/TVT.2007.899951 s Subcarrierindex.
0018-9545/$25.00©2007IEEE
PENGetal.:INVESTIGATIONOFDYNAMICSUBCARRIERALLOCATIONINMIMO–OFDMASYSTEMS 2991
S Number of subcarriers per user in this paper, gain and achieve an optimal solution. However, simulation
the case of equal numbers of subcarriers per resultsshowthattheDSAalgorithmin[3]achieves perceived
subchannel,S =N /K. channel gains within a fraction of a decibel of the optimal
sub
T Numberoftransmitantennas. solution[11].
x
Thecorenoveltyofthispaperliesinthefactthatitconsiders
anotheropportunitytoexploitdiversityinadditiontotheuplink
I. INTRODUCTION
andmultiuserdiversitygainsdescribedbefore.Thisopportunity
ORTHOGONAL frequency-division multiple access is specific to multiple-input–multiple-output (MIMO) systems
(OFDMA), which is also referred to as multiuser- wherein the flexibility of subcarrier allocation facilitates an
OFDM, is an extension of the orthogonal frequency-division opportunitytomitigatethedebilitatingeffectsofcorrelationin
multiplexing (OFDM) and is a highly regarded candidate thechannel.
modulationandmultiple-accessmethodforafourth-generation Considering MIMO systems, the DSA algorithm [3] is ini-
physical layer (4G PHY). It has recently been chosen for the tially extended to three candidate schemes (schemes 1, 2,
IEEE 802.16 and Digital Video Broadcasting-return channel and3)—allMIMOcompatible—andperformanceisevaluated
terrestrial (RCT) standards [4], [5] and received significant in uncorrelated channels. The schemes inherit the low com-
research interest. Similarly to OFDMA, various combinations plexity of the algorithm in SISO and get much benefit from
of direct-sequence code-division multiple access [6] and spatialdiversityandmultiuserdiversityinuncorrelatedchannel
OFDM—e.g., multicarrier code-division multiple-access scenarios.
[7]—are also highly regarded. In practice, there is little However, as is well known, MIMO-system capacity mostly
difference between the schemes in their robustness against dependsonthespatial-correlationpropertiesoftheradiochan-
noise and intercell interference [8]. However, OFDMA can nel.Anobviouswaytoachievedecorrelationbetweenasetof
often outperform the others for high system loads due to its antenna elements is to place them far away from each other.
lower complexity and ability to maintain orthogonality on However,inmostcases,thenatureoftheequipmentwilllimit
frequency-selectivefadingchannels. the antenna spacing. The nature of the environment may also
OFDMA makes use of OFDM modulation while allowing limit the effectiveness of this method, for example, due to the
multiple access by separating symbols in frequency and op- keyholeeffect[12].Twofurtheradaptive-multiusersubcarrier-
tionally in time as well. In a certain time slot, all or some allocationalgorithms,whichareextendedfrom[3](schemes4
of the active subcarriers can be used by a given terminal. and5),areproposedinthispaper.Theseschemesaredesigned
OFDMA, therefore, concentrates uplink transmit power into specifically to combat the debilitating effects of correlation
a “subchannel,” which consists of 1-Nth of the whole band- while still seeking a maximal or near-maximal allocation of
width (where N is the number of terminals), resulting in a channelenergy.Theeffectivenessofthesemethodsisevaluated
10log N-dBgain. inbothuncorrelatedandcorrelatedchannels.
10
Furthermoretothisuplinkgain,thereisalsotheopportunity This paper is organized as follows. Section II describes the
to exploit the advantages of multiuser diversity to mitigate system model used in this paper. Section III summarizes the
channel fading. This is the focus of the algorithms proposed DSA algorithm for the SISO–OFDMA system and confirms
in [1]–[3]. In a frequency-selective channel, subcarriers will its near-optimality by analyzing its performance in compar-
perceive a large variation in channel gain, and the perceived ison with optimal and alternative suboptimal solutions. The
channelwillbedifferentforeachuser.Ifadeterministicrather extendedschemesforuncorrelatedandcorrelatedscenariosare
than random allocation of subcarriers is employed, multiuser proposedinSectionsIVandV,respectively.SectionVIintro-
diversitycanbeexploited.Inthisway,themajorityofsubcar- ducesthesimulationenvironmentandparameters.SectionVII
riers allocated to each user perceive gain (relative to the mean includesallsimulationresultsandperformanceanalysis.Con-
forallfrequencies)ratherthanattenuationintheradiochannel. clusionsareprovidedinSectionVIII.
Such a deterministic allocation algorithm will be referred to,
here,asadynamic-subcarrier-allocation(DSA)algorithm.
II. SYSTEMMODEL
DSA algorithms have been proposed previously in [1]–[3]
for the case where the channel on a per-link basis is single The OFDMA system considered here consists of one base
input single output (SISO). Reference [3] is of particular rele- station (BS) and multiple mobile stations (MSs), all of which
vanceinsofarasitisalow-complexityadaptive-multiuserDSA possesseithertwoorfourantennas.Inthispaper,thedownlink
algorithm in which the per-subcarrier channel gain of each is considered for the sake of simplicity. However, the DSA
user is used as the metric to allocate the subcarriers and algorithm and the diversity gains, which it achieves, are, in
ensure a fair allocation for all users insofar as they all receive principle, equally applicable to the uplink (which will enjoy
approximately equal gain from the DSA while not adversely further benefits of OFDMA uplink gain as discussed before).
affecting overall system capacity. However, while achieving The BS is considered to communicate simultaneously with
significant gain, this algorithm might not reach the optimal multiple MSs, each of which is allocated a single subchannel
solution(intermsofachievingthetotalmaximumchannelgain consisting of a given number of OFDMA subcarriers (equal
forusers).TheHungarianmethod[9]andsort–swapalgorithm numbersofsubcarrierspersubchannelandasinglesubchannel
[10]areintroducedandextendedtosolvethisallocationprob- per MS is assumed for simplicity in this paper, but this is not
lem as an assignment problem in maximizing total channel essentialtothefunctionalityoftheDSAalgorithm).
2992 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.56,NO.5,SEPTEMBER2007
Fig.1. Systemmodel.DSA-OFDMAinSISOsystem.
The BS takes the downlink data for all MSs and applies Three graphs of the system model of SISO and MIMO
independent bit-level-error control coding, symbol mapping, cases are shown in Figs. 1 and 2(a) and (b) to indicate the
and serial to parallel conversion. In the case of SISO, a whole previously mentioned process. The later two can also
DSA-mapping process allocates the parallel data symbols to be extended to higher dimension MIMO system. Note that all
appropriatesubcarriersasindicatedbytheDSAalgorithm.On connections to the channel estimator and the control channel
theotherhand,inthecaseofMIMO,eachusersignalissubject betweentheDSAalgorithmandthereceiverareshowndashed,
toeitherspace-timeblockcoding(STBC)orspatialmultiplex- since neither channel estimation nor the communication of
ing (SM) at the BS. The resultant 2 or 4 (depending on the control information is considered explicitly in this paper. In
number of transmit elements) coded/multiplexed user-symbol [15], the impact of nonideal channel estimation is considered
streams are assigned to appropriate subcarriers, as indicated in detail in the context of the DSA algorithm, and it is shown
by the DSA algorithm. Subsequently, the symbols are OFDM thattheproposedalgorithmisinsensitivetochannel-estimation
modulatedviainversefastFouriertransform(FFT),andaguard errors.Theexchangeofcontrolinformationhasreceivedfairly
interval(GI)isinsertedbetweensymbolstoavoidintersymbol limitedattentionintheopenliterature[26],[27].
interference. The corresponding block diagrams are shown in
Figs.1and2.
The signal received by the MSs takes the form of the BS III. DSAINSISO–OFDMA
signal,convolvedwiththechanneltransfer-functionmatrixand
The SISO–DSA algorithm presented in [3] is considered
additionallysubjecttoadditivewhiteGaussiannoise.Symbols
as a starting point here. Although structurally similar to the
sentbytheBStootherMSs(users)maybediscardedafterthe
algorithm in [2] (both exhibit relatively low complexity), this
FFTintheMSreceiver.
algorithmconsidersthechannelgainofeachuserasthemetric
After extracting the GI and applying a FFT process at each
to allocate the subcarriers and ensures a “fair” allocation for
MS receiver, the subcarriers assigned to a given MSs sub-
all users by allocating an equal number of subcarriers to all
channelareextractedaccordingtotheallocationofsubcarriers
users.Inordertoinvestigatetheoptimizationprobabilityofthis
determined by the DSA algorithm (the method by which this
algorithm, the classic assignment problem based on channel
allocationiscommunicatedtotheMSisnotconsideredinthis
gain as the metric is first defined and some relative solutions
paper). Then, for an STBC system, a combining scheme [13]
suchasanextendedHungarianmethod,“optimalchannelsub-
(proposedbyAlamouti)isapplied.IntheSMcase,aminimum
carrier allocation (OCSA),” suboptimal solutions, “maximum
mean-squared error (MMSE) receiver is used to balance
gain sort–swap (MGSS),” “DSA” algorithm, and improved
multistream-interference mitigation with noise enhancement
“DSA”algorithm“DSA-swap”arepresentedandcompared.
andminimizethetotalerror[14].Finally,thesignals,byzero-
forcingprocess(inthecaseofSISO)orthecombined(STBC)
or demultiplexed (by MMSE in SM) signals, are subject to
A. AssignmentProblemforOptimumSolution
forwarderrorcorrection(FEC).Inthispaper,convolutionalen-
coding, channel-state information (CSI)-enhanced soft Viterbi AssuminginanOFDMAsystem,provisionofQoSanddata
decoding, and block interleaving are assumed as a standard rate requests have been fixed, the number of subcarriers is
case, but the DSA algorithm is, again, independent of such specified by the request of submitted data rate for each user
issues. k. h is the channel response for user k, subcarrier n for a
k,n
PENGetal.:INVESTIGATIONOFDYNAMICSUBCARRIERALLOCATIONINMIMO–OFDMASYSTEMS 2993
Fig.2. (a)STBC2×2OFDMAsystemmodel.(b)SM2×2OFDMAsystemmodel.
certain channel. |h | manifests the relative channel transfer- subjectto
k,n
function amplitude. The channel gain matrix H ={|h |2}, (cid:4)
k,n
1, subcarriernisassignedtouserk
k =1,2,...,K,n=1,2,...,Nsub (K is the number of all ck,n = 0, otherwise (2)
users, and Nsub is the number of all useable subcarriers) (cid:3)
isassumedtobeknownintheBSforsubcarrierallocation.The c =1 (3)
k,n
totalperceivedchannelgainP forallusersisconsideredin
total (cid:3)k
ordertoprovidegoodsubchannelsforallusers.
c =S (4)
k,n
Then,theallocationproblemcannowbeformulatedas
n
where c is the allocation-mapping matrix element for user
k,n
(cid:3)K N(cid:3)sub k andsubcarriern.Nsub isthenumberofuseablesubcarriers,
MaximizeP = c |h |2 (1) andK isthenumberofusers(andthenumberofsubchannels
total k,n k,n
k n as well in this case). S is the number of subcarriers per user.
2994 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.56,NO.5,SEPTEMBER2007
In this paper (the case of equal numbers of subcarriers per basic processing rules based on a reformulated channel-gain
subchannel),S =N /K. matrix instead of a cost matrix to achieve the allocation-
sub
The maximum total perceived channel power is indicated mappingmatrix[9],[16]:1)Alwaysfindthemaximumelement
byPopt . in each row and column of the channel-gain matrix instead
total
of the minimum element in the cost matrix, and 2) always
makelocationswiththeirmaximumelementrecorded(suchas
B. OptimalandSuboptimalSolutions
locatingzerostodifferentiateotherelements).
1) OCSA—Extended Hungarian Method: An optimal so- ThisissimilartotheHungarianmethodasakindofexhaus-
lution to the above assignment problem can be obtained by tivesearchwhichmakesuseofcomputationtocheckallpairs
an extended Hungarian method. In order to realize OCSA of “job” and “individual” one by one and compares the total
by extending the Hungarian method, the practical problem gain for the maximum value. When the size of the channel-
has to be reformulated. The manipulation of the new matrix gainmatrixincreases(duetomoreusersand/orsubcarriers),the
C ∈RNsub×Nsub isconsidered[16].TherelativegainmatrixH computational time and complexity becomes extremely high.
shouldbechangedfromsizeofK×N toK(cid:1) ×N ,where Thus,inthispaper,theoptimalsolutionisshownasareference
sub sub
eachuser’sentryisduplicatedforS times(S isthenumberof upper bound of the system performance and is not suggested
subcarriersallocatedperuser),i.e.,K(cid:1) =S×K.Consequently, foruseinpractice.
thesizeofthisnewgainmatrixbecomesN ×N tomatch 2) MGSS—Suboptimal Solution: Due to the unfeasible
sub sub
theextendedHungarianmethod. complexity of OCSA, a lower complexity suboptimal solution
Theoptimizationproblemisreformulatedas must be considered. Thus, the algorithm previously proposed
in [10] is extended to attempt to achieve maximum perceived
N(cid:3)subN(cid:3)sub
MaximizePNsub×Nsub = c(cid:1) |h(cid:1) |2 (5) channel gain. It is named MGSS and sorts subcarrier pairs
total k,n k,n by metric of total perceived channel gain and swaps subcar-
n (cid:1)
k=1
rier allocations between users to exploit the maximum gain.
subjectto The iteration is applied to make the most of the sort–swap
(cid:5)
process to achieve a near-optimal solution. In addition, the
1, subcarriernisassignedto
c(cid:1) = userkatitssubcarrierl (6) iterative swap process is used again to improve the DSA
(cid:3) k,n 0, otherwise algorithm in Section III-D. Note that the channel-gain matrix,
which is applied in this solution, is H with original and de-
c(cid:1) =1 (7)
k,n creased (relative to OCSA) size of K×N [the allocation
(cid:1) sub
(cid:3)k problem is formulated the same as (1)], and the process in
c(cid:1) =1 (8) [10] is inverted to give the following rules: 1) The elements
k,n
n of initial channel-gain matrix and processed-gain matrix are
where PNsub×Nsub is the total perceived channel gain for S always sorted in descending order (from highest to lowest),
total (cid:1) and 2) the subcarriers replacement occurs when the sum of
times duplication of K users, and k is the user or its dupli-
(cid:1) minimum values of all gain-increase-factor per user [10] is
cation index k =1,2,...,S,S+1,...,2S,...,N . As the
sub negative.
allocation-mappingmatrixelementforthisuseroritsduplica-
Due to reasonable and low-complexity initial process, the
(cid:1)
tion k and subcarrier n, c(cid:1)k,n is determined, it can be easily iteration of sort and swap decreases, consequently result-
returnedtoc ,andPopt canbeobtained. ing in the lower complexity and better practicability relative
k,n total
As is well known, the Hungarian method [9] aims to min- toOCSA.
imize the cost for the assignment problem. The reciprocal of
thechannelgaincanbeusedtomeetthismethodexactly,butit
C. DSAAlgorithm
mightreasonablybeexpectedthattheoptimalallocationcannot
beachieved.Hence,itisnecessarytoinvertthemethodsothat In this section, an algorithmic definition of the proposed
themaximumperceivedchannelgaincanbedetermined. (SISO) DSA scheme is provided. The allocation problem is
The subcarrier allocation by the Hungarian method is re- formulated the same as (1)–(4), and in this solution, the
ferred to [9] and [16], in which the assignment problem is channel-gain matrix follows the original size. This algorithm
the inverse (5) to achieve the minimum cost for assignment isdefinedherefortheSISOcase.ThevariousMIMOschemes
of all the jobs among the individuals, such as each individual arediscussedlater(anddetailedintheAppendices).
withexactlyonejobandeachjobdonebyexactlyoneperson. In the following, P represents the average received power
k
Reference[16]usesacostmatrixofRbyR(Risthenumberof foruserk,K isthetotalnumberofusers,N isanM(cid:1)byN
Sub
both individuals and jobs) and then searches for the minimum matrix, where each row is a vector containing the indexes of
value of the rows and columns by subtracting each element in theuseablesubcarriersforthecorrespondingspatialsubchannel
therowsandcolumns fromtheminimumvalue andminimum (i.e.,thechannelthatexistsbetweenanyonetransmitelement-
linesdrawnoverallzerosintheprocessedcostmatrix. receive element pair in a MIMO system). The possibility of
In the case of this paper, “job” can be simulated as “sub- multiplespatialsubchannelsisaccommodatedinthealgorithm
carrier allocation” and “individual” as “user.” The inversion atthisstage(whenconsideringtheSISOcase)inordertomake
is a modification of the aforementioned method, following the algorithmic definition generic to both SISO and MIMO
PENGetal.:INVESTIGATIONOFDYNAMICSUBCARRIERALLOCATIONINMIMO–OFDMASYSTEMS 2995
cases. That is, Nm(cid:1) ={1,2,3,...,NSub}, where NSub is the
totalnumberofuseablesubcarriers.m(cid:1) ={1,...,M(cid:1)},where
M(cid:1) is the effective number of spatial subchannels considered
by the allocation algorithm. hk,n,m(cid:1) is the channel response
for user k (|hk,n,m(cid:1)| manifests the relative channel gain in
amplitude), with subcarrier n and channel m(cid:1). Ck,s,m(cid:1) is a
matrix to record the location of allocated subcarriers for user
k,subcarrier(withinthesubchannel)s,andspatialchannelm(cid:1).
0m(cid:1),NSub isamatrixofzerosofsizem(cid:1)byNSub.
I.Initialization
SetP =0forallusersk =1,...,K
k
Set Ck,s,m(cid:1) =0 for all users k =1,...,K and spatial
subchannelsm(cid:1) ={1,2,...,M(cid:1)} Fig. 3. Comparison of CCDF of total channel gain with conventional
Sets=1 OFDMAandDSAsolutions.
II.Mainprocess
buttheproposedalgorithmisrelativelyinsensitivetochannel-
WhileN (cid:7)=0m(cid:1),NSub estimationerrors,sinceonlythemagnitudeofthechannelgain
{(a)Makeashortlistaccordingtotheusersthathaveless
isusedforthemetrictoallocatesubcarriers[15].
power.1 Finduserksatisfying
P ≤P , forall i, 1≤i≤k. D. DSA-Swap:Improved“DSA”Algorithm
k i
One possible method to improve the DSA algorithm men-
(b)Fortheuserkobtainedin(a),findsubcarriern tioned in Section III-C is to subsequently apply the sort–swap
satisfying method. The solution of the “DSA” algorithm is used as an
|hk,n,m(cid:1)|≥|hk,j,m(cid:1)|, forall j ∈N. initial solution and, subsequently, the swap-iteration process
(defined in Section III-B2) can be applied to try to further
improvetheallocation.Thesimulationresultsshowthatabetter
(c) Update Pk, N, and Ck,s,m(cid:1) with the n from (b) performance can be achieved than the initial DSA algorithm
accordingto
solution and that this method can even reach the performance
oftheoptimalsolutionafterenough(aboutthreetofivetimes)
(cid:3)M
Pk =Pk+ |hk,n,m(cid:1)|2 iterations.
However, it can be shown in Section III-E that the initial
m=1
DSA algorithm is a near-optimal solution for achieving max-
Nm(cid:1),n =Nm(cid:1),n−n imum perceived channel gain. In the following sections, this
Ck,s,m(cid:1) =n algorithm is called directly “DSA algorithm” and extended to
MIMO–OFDMA.
s=s+1.
(d)Gotothenextuserintheshortlistobtainedin(a)until E. ComparisonofAlgorithmPerformance
allusersareallocatedinanothersubcarrier}.
The algorithms described above can be compared via soft-
waresimulation.Inthissection,thechannelmodel“E”(defined
Thus, the algorithm operates by ranking users in order of
inSectionVI)isused.
current allocated (mean) channel gain from lowest to highest.
Inordertosimplify(1)andnormalizepowerperuserandper
Subsequently, additional subcarriers are allocated to users in
subcarrier
rankorderallowingthosewiththelowestallocatedgaintohave
thenext“choice”ofsubcarrier.Theoperationsinthealgorithm,
P (dB)
norm
thus, largely consist of sorting, comparing, and performing (cid:6) (cid:7)
simplearithmetic. 1 1 (cid:3)16 (cid:3)48
=10log × × |h |2 (dB) (9)
As well as achieving high multiuser diversity gains (as 10 16 48 user,sub
detailed in the simulation results section), this algorithm has user=1sub=1
meritsincomparisontoothersincludingafairallocationofre- where |h |2 is the channel gain of a certain user for the
user,sub
sourcestousersandinherentcompatibilitywithlink-adaptation allocatedsubcarrier(1–48istheallocatedsubcarrierindexper
schemes. userandnottheindexinthereal768subcarriersequence)ina
The algorithm is considered in this paper for the case of certainsimulationtime.
idealCSI.CSIisimportant,bothforDSAandforequalization, The total perceived channel gains offered for 16 users by
differentalgorithmsarecompared.Thishasbeendonefor2000
independent identically distributed (i.i.d.) quasi-static random
1Forthefirstiteration(whennosubcarriershavebeenallocatedand,hence,
allusershaveequalpower).Thelistmaybeentirelyarbitrary. channelinstances.
2996 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.56,NO.5,SEPTEMBER2007
Fig.4. Examplechannelresponseandsubcarrierallocation. Fig. 6. Comparison of CCDF of total channel gain for all suboptimal
solutions.
The result of DSA-swap is slightly better than that of MGSS.
Careshouldbetakentonotethescaleonthepower-gainaxis,
whileDSAandOCSAlookfarapartonthisgraph,sinceDSA
actually achieves approximately 97.54% of the power gain of
OCSA. Hence, the DSA algorithm (without swapping) can be
considered a low-complexity near-optimal solution. MGSS is
alsoworthyofinterestbecauseitalsooffersalow-complexity
near-optimalsubcarrierallocation.DSA-swapisoflessinterest,
sinceitoffersminimalimprovementsoverDSAandMGSSin
returnforincreasedcomplexity(itisessentiallyaconcatenation
ofthetwo).
Fig. 6 presents the CCDF of all 2000 random channels for
DSA,DSA-Swap,andMGSS(OCSAcannotbeshownbecause
of high complexity in simulation). This shows that the similar
Fig.5. Comparisonofallsolutions:OCSA,DSA,DSA-swap,andMGSS.
performanceofthesealgorithmsisconsistentacrosstheentire
Complementary cumulative distribution functions (CCDFs) statisticalsample.
ofchannelgainachievedbyDSAand“conventional”OFDMA Having established that all the above algorithms achieve
(pseudorandomsubcarrierallocation)arecomparedinFig.3.It near-optimal performance, the DSA algorithm is identified as
canbeseenthatDSAoutperformstherandom-allocationstrat- thealgorithmofprimaryinterestduetoonefurtherfeature—it
egy by up to 6 dB and results in significantly lower variation is readily extendable to the MIMO case and is particularly
aroundthemean. amenabletoenhancementstocombatthedebilitatingeffectsof
Theseeffectscanbejustifiedbyconsideringtheexampleof correlation in the radio channel, as discussed in the following
an instantaneous wideband-channel response in the frequency sections.
domain for a single user and the corresponding subcarrier
allocation achieved by DSA, as shown in Fig. 4. This serves IV. DSASCHEMESINMIMO–OFDMA
to illustrate the multiuser diversity benefit, which the DSA
Three“schemes”toextendtheDSAalgorithmtoMISO(2Tx
algorithmisabletoachieve.Itcanbeseenthatthesubcarriers
1Rx)andMIMO(2Tx2Rxand4Tx4Rx)systemsareinitially
allocated in this instance have consistently high gain (all are
proposed. These schemes are designed to transmit a certain
higher than the mean for the channel over all subcarriers) and
user’s symbols on the subcarriers, which are allocated by the
a much flatter response than the actual channel. These factors
metricfromperceivedspatialsubchannelgain.Thereisnomore
lead to the change in channel statistics illustrated in Fig. 3
than one user per subcarrier per spatial subchannel. Scheme 1
and the bit-error rate (BER) performance gains demonstrated
considerssubcarrierallocationforeachspatialsubchannelsep-
and discussed in Section VII. It can be intuitively seen how
arately; schemes 2 and 3 allocate subcarriers jointly for all
analternativeuserperceivinganuncorrelatedchannelresponse
spatialsubchannels.Thesethreeschemesareextensionsofthe
couldderivesimilarbenefitfromadifferentsetofsubcarriers.
core algorithm detailed in Section III-C and are detailed in
It can also be seen that a pseudorandom (or clustered) sub-
AppendixA.
carrier allocation would be unable to achieve this multiuser
diversitygain.
A. Scheme1
The resulting power gains as a function of iteration number
is illustrated for one typical channel instance in Fig. 5. Both The DSA algorithm is separately applied for each (spatial)
MGSS and DSA-swap tend to be very close to the optimum subchannel to determine the subcarrier allocation. This is a
solution (achieved by OCSA) after three to five iterations. straightforward extension of the DSA algorithm, which takes
PENGetal.:INVESTIGATIONOFDYNAMICSUBCARRIERALLOCATIONINMIMO–OFDMASYSTEMS 2997
no account of correlation and no consideration of one spatial
subchannelrelativetotheotherspatialsubchannels.
B. Scheme2
Thisschemeattemptstoexploitcorrelation(primarilytothe
benefit of STBC systems) by choosing the same subcarrier
allocations for all spatial subchannels. This scheme allocates
each subcarrier on the basis of the maximum channel gain of Fig.7. Exampleforscheme4.
allthespatialsubchannelsforthatsubcarrieranduser.
C. Scheme3
This is an alternative to scheme 2, which allocates each
subcarrier on the basis of the average channel gain of all the
spatialsubchannelsforthatsubcarrieranduser.
Fig.8. Exampleforscheme5.
D. ComparisonofSchemes1,2,and3
subchannel. If this occurs, that subcarrier will be replaced by
Since scheme 1 considers DSA of each spatial subchannel the next best subcarrier (and the previous allocation check
separately (using different sets of subcarriers in spatial sub- repeatedforthatsubcarrier).
channels),performanceineachspatialsubchannelcanachieve There is an example for scheme 4 (Fig. 7). Provided there
the same DSA gain as in a SISO system with the DSA al- are two spatial subchannels A (first row in the figure) and B
gorithm. If spatial channels are uncorrelated, spatial diversity (secondrowinthefigure),thesubcarrierallocationofacertain
gain is as high as it can be (relative to the equivalent MIMO user (subchannel) has been decided by the DSA algorithm
system in a correlated channel). An increased signal-to-noise based on channel gain of spatial subchannel A. Currently,
ratio(SNR)gaincanbeachievedbecauseofreceiverdiversity subcarriersshouldbeallocatedforthesameuserunderspatial
andmorefreedomfortheBStoallocateavailablesubcarriers. subchannel B. The best subcarrier through ranking by metric
Schemes 2 and 3 enforce the same subcarrier allocation for of channel gain is “15” (the number of a certain subcarrier).
all spatial subchannels. The effect of this allocation is similar However, it can be found that “15” has been already used for
tothatofaddingextramultiplecomponentswiththesameallo- thesameuserindifferentspatialsubchannel.The“15”hasbeen
catedsubcarriersby“DSA”algorithmwithmetricofmaximum abandoned and the next best subcarrier “17” is chosen by the
(scheme2)oraverage(scheme3)channelgainoverallspatial rulesofscheme4.
subchannels. The system can enjoy both spatial diversity gain
and DSA gain as well. This provides for a simpler algorithm
B. Scheme5
andimplementationwithoutadditionalhardwareirrespectiveof
the DSA mechanism or channel equalization at the receivers, Inthisscheme,notonlyistheallocationofthesamesubcar-
butitmightreasonablybeexpectedthattheDSAgainofeach riertodifferentspatialsubchannelsprevented,buttheallocation
spatialsubchannelwillbereduced. of near adjacent subcarriers is also prevented. The number of
nearadjacentsubcarriersavoidedinthisprocessisdenotedq.It
isnoteworthythatq maybeassumedtotakeavalueofonein
V. DSASCHEMESTOCOMBATCHANNELCORRELATION
scheme4andzeroinscheme1,inwhichcase,schemes1and
Asiswellknown,thespatial-correlationpropertiesofthera- 4maybeviewedassubsetsofscheme5.
diochannelsareakeytoMIMOsystemcapacity.Twoadaptive- Similar to scheme 4, there is an example for scheme 5
multiuser subcarrier-allocation algorithms extended from the (Fig.8).UndersubchannelB,notonly“15”isabandoned,the
schemesdescribedaboveareappliedtocombatthedebilitating “17”and“10”whichfallwithinrangeof“15”±10(hereq is
effects of correlation on a MIMO–OFDMA system. For each equaltoten)arenotallowedforthisuser.Theruleofscheme5
user,thesubcarrierallocationisperformedinafashion,which isforcingtheuseofsubcarrier132eventhoughitisthreesteps
reduces correlation while still seeking a near-maximal alloca- furtherdowntherankinglist.
tion of channel energy. The details of the processes of these
twoschemesaredescribedinAppendixB.
C. ComparisonBetweenTheseSchemes
Since the channel is frequency-continuous, assigning sym-
A. Scheme4
bols to the adjacent subcarrier locations of an initially chosen
Aswithscheme1,theDSAisappliedindependentlyacross subcarrier location should perform similarly (the exception
spatial subchannels. Additionally, a check is performed to being the case where the coherence bandwidth is not signif-
identify cases in which the same subcarrier has already been icantly greater than the subcarrier spacing). If the channels
allocated to the same user in a previously considered spatial arecorrelated,theadjacentsubcarrierlocationsinotherspatial
2998 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.56,NO.5,SEPTEMBER2007
TABLE I TABLE II
MODULATIONPARAMETERSINOFDMA CHANNELMODEL
TABLE III
CORRELATIONSCENARIOS
subchannels will also be correlated to some extent. Scheme 4
onlyconsidersthespatialcorrelationifthesamesubcarriersare
chosen.Scheme5willreducespatialcorrelationfurtherbutat
theexpenseofsomereductionintheDSAgain.
VI. SIMULATIONENVIRONMENTANDPARAMETERS
The performance of the DSA algorithm is evaluated by Furthermore,itisassumedthattheMSshaveperfectknowledge
simulation.ThesimulationconsidersmainlyQPSKmodulated, ofthechanneltransferfunctionforthosesubcarriersallocated
rate-1/2 convolutionally coded (CSI-soft Viterbi decoded), to them and that this is used for equalization and decoding
COFDMoperatingwithabandwidthof100MHzasacandidate purposes.
4GPHY.IntheSISO–OFDMAcase,thesimulationsatdiffer- ForOFDMAandDSAalgorithms,16usersareconsidered,
entmodulationmodeswithdifferentconvolutionalcodingrates andthereare768usablesubcarriersinall.Simulationparame-
(TableI)areperformedaswellforcomparisonpurposes.Note tersaresummarizedinTablesIandII.
that, in Table I, the values in brackets specify the parameters
for SM with two transmitters, and the values not in brackets
A. InUncorrelatedMIMOChannels
specify the parameters for the cases of SISO and STBC with
twotransmitters. Allthreeschemes for MIMOare firstsimulatedinuncorre-
Amultipathchannelwithexcessdelayof1600ns,witheach latedchannelswithresultspresentedinSectionVII.
path suffering from independent Rayleigh fading, was used in
[17]and[18]fortheperformanceevaluationofsimilar4GPHY
proposals. On this basis, a similar channel model—referred to B. SimulationsinCorrelatedMIMOChannels
as channel “E”—is used here, which is specified by European
The simulation is further extended to consider correlated
Telecommunications Standards Institute (ETSI) Broadband
MIMOchannels.Thederivedmodelsarebasedon[23],which
RadioAccessNetwork(BRAN)[19].Channelmodel“E”cor-
includesthepartialcorrelationbetweenthepathsinthechannel.
respondstoapicocell-typeoutdoorenvironmentwithnonline-
Two antennas at the BS and two antennas at the MS are
of-sightconditionsandlargedelayspread[20].Thermsdelay
considered. The MS is simulated in an urban environment
spread is 250 ns, and the excess delay is 1760 ns with tap
surrounded by numerous or few local scatters, which results
spacingof10ns.
in the lower or higher correlation between two antennas. BS
An addition channel scenario is also considered to investi-
antennas are located on the rooftop level of the surrounding
gatetheperformanceinanenvironmentwithhighermultipath
buildings, which follows a Laplacian function in a typical
delays.Achannelmodelcorrespondingtoavehicularmicrocell
urbanenvironment.Thecorrelationscenariosconsideredcanbe
environmentthatwasemployedinthedevelopmentof2Gand
seen in Table III. The spatial-correlation matrix of the MIMO
3G [21], [22]—referred to here as channel model “V”—is
radio channel R is the Kronecker product of the spatial-
employed. This channel model has an rms delay spread of MIMO
correlationmatrix(R ,R )attheBSandtheMS[24],[25].
370nsandanexcessdelayof2690nswiththesametapspacing BS MS
A selection of results for different correlation scenarios is
asthechannelmodelE.
shownforSTBCandSM.
TheuseofbothSTBCandSMisconsidered.The2000i.i.d.
quasi-static random channel samples are used in each simula-
tion,andthesubcarrierallocationisupdatedviatheappropriate
VII. SIMULATIONRESULTS
DSAschemeforeachsuchsample.
ItisassumedthattheDSAalgorithmisimplementedbythe In order to evaluate the proposed algorithm and schemes
BS, and that, the BS has perfect knowledge of the channel- andcomparetheperformancesindifferentcases,thefollowing
gain matrix and uses this to determine subcarrier allocation. simulationresultsarepresented.