Simulated Annealing and Multiuser Scheduling in Mobile

18 Pages·2014·0.29 MB·English

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CChhaapptteerr 60
Simulated Annealing and Multiuser Scheduling
in Mobile Communication Networks
Raymond Kwan,M.E.Aydin and Cyril Leung
Additionalinformationisavailableattheendofthechapter
http://dx.doi.org/10.5772/45869
1. Introduction
Adaptive modulation and coding (AMC) is an effective way for improving the spectral
efficiency in wireless communication systems. By increasing the size of the modulation
scheme constellation, the spectral efficiency can be improved, generally at the cost of a
degradederrorrate. Asimilartrade-offispossiblebyusingahigherratechannel code. Byan
appropriatecombination of the modulationorderand channel code rate, we can designaset
of modulation and coding schemes (MCSs), from which an MCS is selected in an adaptive
fashion in each transmission-time interval (TTI) in order to maximize system throughput
under different channel conditions. The use of AMC yields a rich variety of scheduling
strategies [25]; [12]. In practice, a commonly encountered constraint is that the probability
oferroneousdecodingofaTransmissionBlockshouldnotexceedsomethresholdvalue[11].
Multiple orthogonal channelization codes (multicodes) can be used to transmit data to a
singleuser,therebyincreasingthe per-userbitrate and the granularityofadaptation [11,16].
In Wideband Code-Division Multiple Access (WCDMA), the channelization codes are often
referred to as Orthogonal Variable Spreading Factor (OVSF) codes. The number of OVSF
codes per base station (BS) is quite limited due to the orthogonality constraint [11] and thus
OVSFcodesandtransmitpowerarescarceresources. Fig.1showsthenumberofOVSFcodes
asafunctionofthespreadingfactorforWCDMA.Notethatalowervalueofspreadingfactor
corresponds to a higher bit rate and vice versa. According to Fig. 1, if a spreading factor of
2 is needed, the system can allocate at most two such OVSF codes. On the other hand, if
a spreading factor of 4 is required, a total of 4 such codes can be allocated. In High Speed
Downlink Packet Access (HSDPA), a fixed spreadingfactor of 16 has been specified, thereby
limitingthe numberofOVSFcodesto161.
The allocationof the number ofOVSF codes(or multicodes)and the MCS level foreach user
depends on the strength of the received signal at the user, which, in turn, depends on 1) the
quality of the wirelesschannel, and 2) the level of the transmit power to the respective user.
1Inprinciple,16OVSFcodescanbeused.However,onecodeisallocatedforotherpurposessuchassignalling.Thus,
amaximumof15codescanbeallocatedfordatatraffic[11].
©2012Kwanetal.,licenseeInTech.Thisisanopenaccesschapterdistributedunderthetermsofthe
CreativeCommonsAttributionLicense(http://creativecommons.org/licenses/by/3.0),whichpermits
unrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
114 Simulated Annealing – Single and Multiple Objective Problems
2 Will-be-set-by-IN-TECH
As shown inFig.2, ifthe spreadingfactor and the number ofOVSF codesarefixed,one way
to increasetheuserbitrateistoincreasetheMCSlevel. AseachMCSlevelisassociatedwith
a specificsignal quality requirement,the highestMCS level that can be allocated dependson
thechannelqualityattheuserreceiver,whichisstochasticbynature. Thus,atagivenchannel
quality at the receiver, the MCS level can be increased by increasing the transmit power to
the user. Another way to increase the user bit rate at a fixed spreading factor is to fix the
MCS level while increasing the number of OVSF codes allocated to the respective user, as
shown in Fig. 3. In order to achieve a given signal quality requirement for each OVSF code,
a higher power level is required to be allocated to this user. Thus, the general problem of
HSDPA resourceallocationboilsdowntothejointallocationofuser-specificMCS,numberof
OVSF codes, and power level over all users connected to a given base station, subject to the
constraints of code and power resources as shown in Fig.4. It is important to note that this
allocation is done very rapidly (on the orderof two or more milliseconds)in orderto exploit
the channel diversity of the users. HSDPA is based on a shared channel concept, in which
multiple users share the channel in a time-multiplexed fashion, and the process of resource
allocationisperformedatregulartimeintervals. Notethat inHSDPA,as showninFig.5, the
shared channel is a dual to the dedicated channel in which the bit rate for each user is kept
constant overarelativelylongtimeperiodbyappropriateclosed-looppowercontrol.
Figure1. OrthogonalVariableSpreadingFactor(OVSF)codetree.
For simplicity,the downlink transmit power isnormally held constant (orslowlychanging)2
inHSDPA [11]. A numberof schedulingalgorithmshave beenproposedforHSDPA [7]. The
most commonly encountered ones are (1) round-robinin which users areallocated resources
in turn, regardlessof channel conditions (2) Max C/I in which resourcesare allocated to the
user with the best channel condition (3) proportional fair in which resourcesare assigned to
theuserwiththerelativelybestchannelcondition. Otherschedulersincludeminimumbitrate
(MBR),MBRwithproportionalfairnessand minimumdelay(MD).
Inexploitingmultiuserdiversity,acommonwaytoachievethebestnetworkthroughputisto
assign resources to a user with the largest signal-to-noise ratio (SNR) among all backlogged
2Insomecases,thespecificationstipulatesaslightpowerreductionforamobilewithanexceptionallygoodchannel
quality[22].
Simulated Annealing and Multiuser Scheduling in Mobile Communication Networks 115
SimulatedAnnealingandMultiuserSchedulinginMobileCommunicationNetworks 3
Figure2. Bitrateandchannelqualityrequirementtrade-offforHSDPA.
Figure3. Bitrateandchannelqualityrequirementtrade-offforHSDPA.
116 Simulated Annealing – Single and Multiple Objective Problems
4 Will-be-set-by-IN-TECH
Figure4. ResourceallocationinHSDPA.
users (i.e. users with data to send) at the beginning of each scheduling period[5]. However,
due to limited mobile capability, a user might not be able to utilize all the radio resources
available at the BS. Thus, transmission to multiple users during a scheduling period may be
more resource efficient. In [2, 15], the problem of downlink multiuser scheduling subject to
limitedcodeandpowerconstraintsisaddressed. Itisassumedin[15]thattheexactpath-loss
and receivedinterferencepowerateveryTTIforeachuserarefedbacktotheBS.Thiswould
requirealargebandwidthoverhead.
In this chapter, the problem of optimal (maximum aggregate throughput) multiuser
scheduling in HSDPA is addressed3. The MCSs, numbers of multicodes and power levels
for all users are jointly optimized at each scheduling period, given that only limited CSI
information, as specified in the HSDPA standard [22], is fed back to the BS. This problem
corresponds to a general resource allocation formulation for HSDPA, as compared to those
in the existing literature, where resources are typically not allocated jointly among users
for simplicity. Due to the inherent complexity, an integer programming formulation is
proposedfor the above problem. Due to the complexityof obtaining an optimal solution, an
3Thematerialspresentedherearemostlybasedonthecontentsin[14].
Simulated Annealing and Multiuser Scheduling in Mobile Communication Networks 117
SimulatedAnnealingandMultiuserSchedulinginMobileCommunicationNetworks 5
Figure5. Resourceallocationforsharedanddedicatedchannels.
evolutionarysimulatedannealing(ESA)approachisexplored. Itisshownthat ESA canprovide
anear-optimumperformancewithsignificantlyreducedcomplexity.
2. System model
In a communication system, the quality of the channel is often quantified by the Signal to
InterferenceandNoiseRatio(SINR),whichisdefinedastheratioofthereceivedsignalpower
relative to the power contribution from interference and noise. A better channel quality is
representedbyahigherreceivedsignalpowerandasmallerinterferenceandnoisepower.
We consider downlink transmissions from a BS to a number of mobile users. Let P denote
i
the downlinktransmitpowerto useri, h denote the linkgainfromthe BS touseri,and I be
i i
the total receivedinterference and noise powerat useri. The receivedSINR for useri isthen
givenby
h P
γ = i i, i = 1,...,N, (1)
i
I
i
where N isthe numberofusersand
N
∑ P ≤ P (2)
i T
i=1
where P is the total HSDPA power constraint. Ideally,the user would measurethe received
T
SINR, and report its value back to the BS. Upon receiving the SINR value for this user, the
BS would decide what MCS and the number of multicodes that the user can be allocated,
takingintoaccountalltheresourceconstraintsthattheBShas. However,ifeachuseriwereto
send back itsexactSINR value γ to the BS, the requiredfeedbackchannel bandwidth would
i
be impractically large. As specified in [22], the channel quality information fed back by a
118 Simulated Annealing – Single and Multiple Objective Problems
6 Will-be-set-by-IN-TECH
mobile, also known as the channel quality indicator (CQI), can only take on a finite number of
non-negativeintegervalues{0,1,...,K}. Accordingto[22],theCQIisprovidedbythemobile
viatheHighSpeedDedicatedPhysicalControlChannel (HS-DPCCH).EachCQIvaluemaps
directly to a maximum bit rate4 that a mobile can support, based on the channel quality and
mobile capability [23], while ensuring that the block error rate (BLER) does not exceed 10%.
Finally, upon receiving the CQIs from all the users, the BS decides on the most appropriate
combinationofMCSandnumberofmulticodesforeachuser.
Although the mapping between the CQI and the SINR is not specified in [22], it has been
discussed in various proposals [18]; [13]. In [8], a mapping is proposed in which the system
throughput is maximized while the BLER constraint is relaxed. Let γ˜ = 10log (γ ) be the
i 10 i
receivedSINRvalue,indB,foruseriandletq betheCQIvaluethatuserireportsbacktothe
i
BSviaHS-DPCCH.Themappingbetweenq andγ˜ cangenerallybeexpressedasapiece-wise
i i
linearfunction[6,8,18]
0 γ˜ ≤ t
i i,0
q = ⌊c γ˜ +c ⌋ t < γ˜ ≤ t (3)
i ⎧ i,1 i i,2 i,0 i i,1
>
q γ˜ t
⎨ i,max i i,1
where the terms {c ,c ,t ,t }⎩aremodeland mobile capability dependentconstants, and
i,1 i,2 i,0 i,1
⌊.⌋ denotes the floor function. Due to the quantization operation implied in (3), γ˜ cannot
i
generally be recovered exactly from the value of q alone. It should be noted that the region
i
t < γ˜ ≤ t is the operating regionfor the purpose of link adaptation. This regionshould
i,0 i i,1
be chosen large enough to accommodate the SINR variations encountered in most practical
scenarios [11], i.e. the probability that γ˜ falls outside this region should be quite small. As
i
partofourproposedprocedure,γ˜ isapproximatedas
i
γ˜† = γ˜(l)+ γ˜(u)−γ˜(l) ξ, (4)
i i i i
(cid:5) (cid:6)
where
q −c
(l) i i,2
γ˜ = , (5)
i c
i,1
q +1−c
(u) i i,2
γ˜ = , (6)
i c
i,1
and ξ is a uniformly distributed random variable, i.e. ξ ∼ U(0,1). In a more conservative
design, the value of ξ could be set to 0. Note that this approximation assumes that γ˜ is
i
(l) (u)
uniformlydistributedbetween γ˜ and γ˜ foragivenvalueofq .
i i i
For q = 0 and q = q , γ˜ could be approximated as t and t respectively, or more
i i i,max i i,0 i,1
generallyast −ξ and t +ξ respectively,with ξ and ξ followingsomepre-defined
i,0 i,0 i,1 i,1 i,0 i,1
probabilitydistributions. Finally,the estimatedvalue of γi isgivenby γˆi = 10γ˜i†/10. Werefer
to the mappingfromSINR to q in(3) as the forwardmapping, and the approximationofSINR
i
basedonthereceivedvalueofq in(4)asthereversemapping.
i
4Inthischapter,thebitratereferstothetransportblocksize,i.e. themaximumnumberofradiolinkcontrol(RLC)
protocoldatabit(PDU)bitsthatatransportblockcancarry,dividedbythedurationofaTTI,i.e.2ms[11].
Simulated Annealing and Multiuser Scheduling in Mobile Communication Networks 119
SimulatedAnnealingandMultiuserSchedulinginMobileCommunicationNetworks 7
3. Joint optimal scheduling
Notethatthevalueofthechannelquality,q ,reportedbyuseriindicatestherateindexthatis
i
associatedwiththemaximumbitratethattheusercanbesupportedbytheBS,andisrelated
jointlytoarequirednumberofOVSFcodes(multicodes)andMCS.Thenumberofmulticodes
and MCS assigned to each user as well as the estimated SINR values of the users determine
the transmit power required by the BS. Since the number of multicodes and transmit power
arelimited,theBSmightnotbeabletosimultaneouslysatisfythebitraterequestsforallusers
as indicatedby {q ,i = 1,...,N}. Therefore,foraset{q ,i = 1,...,N},the BSmustcalculate
i i
asetofmodifiedCQIs,{J ,i = 1,...,N},forallusersbytakingintoaccountthetransmitpower
i
and numberofmulticodesconstraints.
Fromtheforwardandreversemappingsin(3)and (4),themodifiedCQIsarechosenas
J = min max η (γ˜†,φ ),0 ,q ,i = 1,...,N (7)
i i i i i,max
(cid:5) (cid:5) (cid:6) (cid:6)
where φ isthe poweradjustmentfactorforuseri,i.e. γˆ (cid:6)→ φ γˆ ,and
i i i i
η (γ˜†,φ ) = ⌊c γ˜†+10log φ +c ⌋, (8)
i i i i,1 i 10 i i,2
(cid:5) qi,max−(ci,1γ˜i†+ci,(cid:6)2)
0 ≤ φ ≤ 10 10ci,1 . (9)
i (cid:7) (cid:8)
Fig.6summarizesthe conversionprocessfromthe receivedCQI, q ,tothe final assignedrate
i
index, J .
i
Figure6. TheconversionprocessfromthereceivedCQI,q ,fromthemobiletotheassignedrateindex J
i i
atthebasestation. ([14]©IET)
ThemultiuserjointoptimalschedulingproblemP1canbeexpressedas
N Ji
∑ ∑
P1 : max a r (10)
i,j i,j
A,φ
i=1j=0
subjectto(7)-(9)and
J
i
∑ a = 1, ∀i, (11)
i,j
j=0
N Ji
∑ ∑ a n ≤ N , (12)
i,j i,j max
i=1j=0
a ∈ {0,1}, (13)
i,j
N
∑ φ ≤ N. (14)
i
i=1
120 Simulated Annealing – Single and Multiple Objective Problems
8 Will-be-set-by-IN-TECH
In (10), J is the maximum allowable CQI value for user i and r denotes the achievable bit
i i,j
rate for user i and CQI value j [22]; the decision variable a is equal to 1 if rate index j is
i,j
assigned to user i; otherwise, a = 0. In (12), N is the maximum number of multicodes
i,j max
available for HSDPA at the BS and n is the required number of multicodes for user i and
i,j
CQIvalue j [22]. Dependingonmulticodeavailability,the assignedcombinationofMCSand
the number ofmulticodes may correspondto a bitrate that is smallerthan that permittedby
J . The constraint in (14) can be obtained by substituting P = φ P /N into (2). The objective
i i i T
in the optimization problem P1 is to choose A = {a } and φ = {φ } at each TTI so as to
i,j i
maximizethesumbitrateforallusers,subjectto(7)-(9)and(11)-(14).
4. Linearization
It is important to note that the quantity J , which appears in the upper summation index in
i
(10), is itself a function of the decision variable φ . On the other hand, φ is related to J via a
i i i
non-linearrelationship(9). Thus,theproblemP1isnotastandardlinearintegerprogramming
problem. Assuchaproblemishighlynon-linear, aglobaloptimalsolutionisverydifficultto
obtain. To solve problem P1 with linear integer programming methods, the problem needs
to be appropriately transformed into a linear problem by introducing additional auxiliary
variables. Thefirststepistore-formulatethemodelasfollows:
N qi,max
′ ∑ ∑
P1 : max b a r (15)
i,j i,j i,j
A,φ
i=1 j=0
subjectto
q
i,max
∑ b a = 1, ∀i, (16)
i,j i,j
j=0
N qi,max
∑ ∑ b a n ≤ N , (17)
i,j i,j i,j max
i=1 j=0
togetherwith(7)-(9),(13)-(14),wherethenewvariable b
i,j
>
0,j J
i
b = (18)
i,j
(cid:9)1,j ≤ J
i
isintroducedtolimittherateindex jtonohigherthan J .
i
After the above re-formulation, Problem P1′ is still non-linear due to terms involving the
producta b ,andthepresenceofthefloorfunction ⌊.⌋andthelogarithmin(7). Subsequent
i,j i,j
linearlization of Problem P1′, involves introducing a new decisionvariable m = a b and
i,j i,j i,j
re-writingtheproblemasfollows:
N qi,max
′′ ∑ ∑
P1 : max m r (19)
i,j i,j
A,B,φ
i=1 j=0
Simulated Annealing and Multiuser Scheduling in Mobile Communication Networks 121
SimulatedAnnealingandMultiuserSchedulinginMobileCommunicationNetworks 9
subjectto
q
i,max
∑ m = 1, ∀i, (20)
i,j
j=0
N qi,max
∑ ∑ m n = ≤ N , (21)
i,j i,j max
i=1 j=0
m ≤ b , ∀i,j (22)
i,j i,j
m ≤ a M, ∀i,j (23)
i,j i,j
m ≥ b −(1−a )M, ∀ i,j (24)
i,j i,j i,j
e −φ ≤ (1−ω )M, ∀ i,j, (25)
i,j i i,j
φ −e ≤ (1−ω )M, ∀ i,j, (26)
i i,j+1 i,j
q
i,max
J = ∑ jω ,∀ i, (27)
i i,j
j=0
j− J ≤ (1−b )M, ∀i,j (28)
i i,j
J +1−j ≤ b M, ∀ i,j (29)
i i,j
q
i,max
∑ ω = 1 (30)
i,j
j=0
b ,a ,m ,ω ∈ {0,1} (31)
i,j i,j i,j i,j
togetherwith(14),where
−M if j = 0
ei,j = ⎧10 j−(ci1,10γ˜ci†i,1+ci,2) if1 ≤ j ≤ q (32)
⎪ (cid:7) (cid:8) i,max
⎪
⎨M if j = q +1,
i,max
⎪
⎪
and M is a large number. In th⎩is new formulation, constraints (22)-(24) model the product
a b , while (25)-(27) models the floor and the max functions in (7) and the constraint in
i,j i,j
(9). The constraints (28)-(30) are used to linearize the expression defined in (18). Note
that the introduction of auxiliary variables increases the size of the model, and, thereby,
increases the complexity of the problem. The linearized Problem P1′′ was solved using
a commercial optimization software package implementing the branch-and-bound method
[19]. An alternative method to solveProblem P1 isto usemeta-heuristics and is discussedin
Section5.
5. Simulated annealing
Meta-heuristic approaches attract much attention with their success in solving hard
combinatorial and optimization problems. One of these successful approaches is Simulated
annealing (SA) [24], which is proven to be a powerful meta-heuristic approach used for
optimizationinmanycombinatorialproblems. InSA,aprobabilisticdecisionmakingprocess
is typically involved, in which a control parameter, often known as temperature τ, is used
to control the probability of accepting a poorer solution in the neighborhood of the current