joint user pairing and resource allocation for multiuser sc-fdma
TRANSCRIPT
Joint User Pairing and Resource Allocationfor Multiuser SC-FDMA Transmission
Joint User Pairing and Resource Allocationfor Multiuser SC-FDMA Transmission
Wolfgang H. Gerstacker and Michael A. Ruder
University of Erlangen-NürnbergChair of Mobile Communications
Eurecom September 14, 2011
OutlineOutline
1 Introduction
2 System Model
3 Equalizers for SC-FDMA
4 Criteria for User Grouping and Resource Allocation
5 Algorithms for Time / Frequency Domain Resource Allocation
6 Numerical Results
7 Conclusions
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA11
IntroductionIntroduction
Basic IdeaBasic Idea
System withNuser usersOne transmit antenna per userOne base station with Nu antennas
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA22
IntroductionIntroduction
Basic IdeaBasic Idea
System withNuser usersOne transmit antenna per userOne base station with Nu antennas
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA22
IntroductionIntroduction
Considered ScenariosConsidered Scenarios
User Pairing/Grouping:
Nu users transmit on the same time and frequency resourceNu = 2 ⇒ user pairingNu > 2 ⇒ user grouping
Pairing/Grouping Criteria:
CapacityBER
Resource Allocation:
TDMA scheme: transmit in subsequent time slots, using entirebandwidthFDMA scheme: transmit in same time slot, on differentfrequency chunks
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA33
IntroductionIntroduction
Considered ScenariosConsidered Scenarios
User Pairing/Grouping:
Nu users transmit on the same time and frequency resourceNu = 2 ⇒ user pairingNu > 2 ⇒ user grouping
Pairing/Grouping Criteria:
CapacityBER
Resource Allocation:
TDMA scheme: transmit in subsequent time slots, using entirebandwidthFDMA scheme: transmit in same time slot, on differentfrequency chunks
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA33
IntroductionIntroduction
Considered ScenariosConsidered Scenarios
User Pairing/Grouping:
Nu users transmit on the same time and frequency resourceNu = 2 ⇒ user pairingNu > 2 ⇒ user grouping
Pairing/Grouping Criteria:
CapacityBER
Resource Allocation:
TDMA scheme: transmit in subsequent time slots, using entirebandwidthFDMA scheme: transmit in same time slot, on differentfrequency chunks
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA33
System ModelSystem Model
SC-FDMA TransmitterSC-FDMA Transmitter
M -DFTW
SubcarrierMapping
Ko
N -IDFTVH
CPinsertion
Pin
ai[k] Ai[µ] Bi[ν] bi[κ] bci[κ]
Figure: SC-FDMA transmitter structure for user i in pair o.
W: M -point DFT matrixKo: subcarrier mapping matrix for group o ∈ {1, . . . , O}V: N -point DFT matrixPin: cyclic prefix insertion matrix
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA44
System ModelSystem Model
SC-FDMA ReceiverSC-FDMA Receiver
+CP
removalPout
N -DFTV
n1[κ]
...rc1[κ] r1[κ] R1[ν]
KH1
KHO
Y1,1[µ]
Y1,O[µ]
+CP
removalPout
N -DFTV
nNR[κ]
...rcNR
[κ] rNR[κ] RNR
[ν]KH
1
KHO
YNR,1[µ]
YNR,O[µ]
......
Figure: SC-FDMA BS receiver structure.
nl[κ]: spatially and temporally white Gaussian noise at receive antenna lPout: cyclic prefix removal matrixV: N -point DFT matrixKo: subcarrier mapping matrix for group o ∈ {1, . . . , O}
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA55
System ModelSystem Model
V-MIMO ChannelV-MIMO Channel
Signal at the lth receive antenna:
rcl[κ] =
Ntx∑i=1
qh∑λ=0
hl,i[λ] bci[κ− λ] + nl[κ]
hl,i[λ]: discrete-time subchannel impulse response characterizesthe transmission from user i to the lth receive antennaincluding transmit and receiver input filtering
λ ∈ {0, 1, . . . , qh}qh: channel orderNtx: number of users being transmitted within one subframe
(Nu for TDMA scheme, Nusers for FDMA scheme)
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA66
System ModelSystem Model
V-MIMO ChannelV-MIMO Channel
Signal at the lth receive antenna in matrix-vector notation:
rcl =
Ntx∑i=1
Hl,i bci + nl,
Hl,i: channel convolution matrix for transmission from user ito receive antenna l
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA66
Equalizers for SC-FDMAEqualizers for SC-FDMA
Linear MMSE Equalizer for SC-FDMALinear MMSE Equalizer for SC-FDMA. . .
. . .
r1[κ]
rNR[κ]
n1[κ]
nNR[κ]
FrequencydomainMMSE
LE
R1[ν]
RNR[ν]
N–DFT
N–DFT
V
V
a1[k]
a2[k]remove
remove
CP
CPrc1[κ]
rcNR[κ]
Pout
Pout
Filter matrix Fo for each pair o in frequency domainError variance of the pth user within pair o:
σ2eu(o,p)
=1
M
M−1∑µ=0
Σ2pp[νoffset + νo + µ]
Σ2pp[ν]: error variance on νth subcarrier for user p
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA77
Equalizers for SC-FDMAEqualizers for SC-FDMA
SIC Equalizer for SC-FDMASIC Equalizer for SC-FDMA
+ gHo,η
yc
−
aη
HγQfHo,γ
y
zaγaγ
Figure: SC-FDMA SIC equalizer structure for two users.
Filter vectors fo,γ and go,η for each user γ and η of pair oEqualization order depends on SINR after equalization
SINRbiased,p{o} = σ2au(o,p)
/σ2eu(o,p)
with
σ2eu(o,p)
= σ2au(o,p)
− fHo,p ϕyoau(o,p)[0]
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA88
Criteria for User Grouping and Resource AllocationCriteria for User Grouping and Resource Allocation
Random Grouping and Resource AllocationRandom Grouping and Resource Allocation
Random grouping
Random allocation of users to resources
⇒ Huge potential is wasted
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA99
Criteria for User Grouping and Resource AllocationCriteria for User Grouping and Resource Allocation
Capacity GroupingCapacity Grouping
Capacity of group o:
Co =1
M
M−1∑µ=0
ld det(INR
+SNR
NuHo[νoffset + νo + µ]
×HHo [νoffset + νo + µ]
)Aim: find a mapping function u(o, p) that maximizes the sum ofthe capacities of all individual groups:
Csum =
O∑o=1
Co.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1010
Criteria for User Grouping and Resource AllocationCriteria for User Grouping and Resource Allocation
Bit Error Rate Grouping IBit Error Rate Grouping I
Approximation for BER of an uncoded transmission:
BER ≈ Nmin
ld(M)Q
(√d2
min
Eb
N0
),
Nmin: average number of nearest neighbors of a signalpoint of the modulation alphabet
M: size of the modulation alphabetQ(·): complementary Gaussian error integrald2
min: normalized minimum squared Euclidean distance= 3 ld(M)/(M− 1) for QAM constellations
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1111
Criteria for User Grouping and Resource AllocationCriteria for User Grouping and Resource Allocation
Bit Error Rate Grouping IBit Error Rate Grouping I
Approximation for BER of an uncoded transmission:
BER ≈ Nmin
ld(M)Q
(√d2
min
Eb
N0
),
BER for each user p within the group o can be approximatedby
BERu(o,p)≈Nmin
ld(M)Q(√
ζ SINRub,u(o,p) Gc
),
ζ = 3R (M−1)
Gc: gain of the channel code
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1111
Criteria for User Grouping and Resource AllocationCriteria for User Grouping and Resource Allocation
Bit Error Rate Grouping IIBit Error Rate Grouping II
Average BER for group o
BER{o} = 1/Nu
Nu∑p=1
BERu(o,p),
Average BER for all Nuser users is
BERtotal =Nu
Nuser
O∑o=1
BER{o},
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1212
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
Algorithm for Time Domain Resource AllocationAlgorithm for Time Domain Resource Allocation
Two-dimensional optimization problem
Hungarian Algorithm (HA) finds solution fast
HA needs polynomial time vs. double factorial for full search
Symmetric cost matrix with entries for each pair
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1313
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Problem FormulationFD Resource Allocation – Problem Formulation
Combined optimization of resource allocation and user pairing⇒ three-dimensional optimization problem
A three-dimensional assignment problem is in general NP-hard
Task: find that mapping function u(o, p), that eithermaximizes the sum capacity or minimizes the average BER forall users
Each value of o ∈ {1, 2, . . . , O} stands for the number ofthe considered frequency chunk
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1414
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Problem FormulationFD Resource Allocation – Problem Formulation
Combined optimization of resource allocation and user pairing⇒ three-dimensional optimization problem
A three-dimensional assignment problem is in general NP-hard
Task: find that mapping function u(o, p), that eithermaximizes the sum capacity or minimizes the average BER forall users
Each value of o ∈ {1, 2, . . . , O} stands for the number ofthe considered frequency chunk
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1414
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Full SearchFD Resource Allocation – Full Search
Compute sum capacity (Csum) or BER for all possible groups(BERtotal) and group/chunk combinations u(o, p)
Choose combination with the maximum sumcapacity/minimum average BER
If the frequency bandwidth is divided into O = Nuser/Nu
disjoint chunks the total number of combinations is
OFS =
(Nuser
Nu
)·(Nuser −Nu
Nu
)· · ·(
2 ·Nu
Nu
)·(Nu
Nu
)=
Nuser!
(Nu!)Nuser/Nu
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1515
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Full SearchFD Resource Allocation – Full Search
Compute sum capacity (Csum) or BER for all possible groups(BERtotal) and group/chunk combinations u(o, p)
Choose combination with the maximum sumcapacity/minimum average BER
If the frequency bandwidth is divided into O = Nuser/Nu
disjoint chunks the total number of combinations is
OFS =
(Nuser
Nu
)·(Nuser −Nu
Nu
)· · ·(
2 ·Nu
Nu
)·(Nu
Nu
)=
Nuser!
(Nu!)Nuser/Nu
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1515
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Hungarian AlgorithmFD Resource Allocation – Hungarian Algorithm
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
Before HA
user Nuser − 1
user Nuser
user 7
user 8
. . .
. . .
user 1
user 2RBs
After HA
Figure: Example for result of HA for the optimization of the resourceallocation of pairs.
HA finds the best assignment of O given user groups to O chunks.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1616
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Hungarian AlgorithmFD Resource Allocation – Hungarian Algorithm
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
Before HA
user Nuser − 1
user Nuser
user 7
user 8
. . .
. . .
user 1
user 2RBs
After HA
Figure: Example for result of HA for the optimization of the resourceallocation of pairs.
HA finds the best assignment of O given user groups to O chunks.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1616
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Binary Switching Algorithm IFD Resource Allocation – Binary Switching Algorithm I
An exchange of users of different groups can be realized by thebinary switching algorithm (BSA)
Based onSimply try to exchange users between different groupsCompute the resulting cost/weight function BERtotal/Csum
Perform the exchange which yields the maximumdecrease/increase of the cost/weight function of all consideredtrials
To limit complexity of the BSA ⇒ confine the number of usersthat can be switched simultaneously to Nsw
Number of total switches for Nsw = 1
OBSA =Nu · (Nuser −Nu) +Nu · (Nuser − 2Nu) + . . .+Nu ·Nu
=1
2(N2
user −Nu ·Nuser).
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1717
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Binary Switching Algorithm IFD Resource Allocation – Binary Switching Algorithm I
An exchange of users of different groups can be realized by thebinary switching algorithm (BSA)
Based onSimply try to exchange users between different groupsCompute the resulting cost/weight function BERtotal/Csum
Perform the exchange which yields the maximumdecrease/increase of the cost/weight function of all consideredtrials
To limit complexity of the BSA ⇒ confine the number of usersthat can be switched simultaneously to Nsw
Number of total switches for Nsw = 1
OBSA =Nu · (Nuser −Nu) +Nu · (Nuser − 2Nu) + . . .+Nu ·Nu
=1
2(N2
user −Nu ·Nuser).
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1717
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Binary Switching Algorithm IIFD Resource Allocation – Binary Switching Algorithm II
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 1
user 1 user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 2
user 2
user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 3
user 3 user Nuser − 1
user Nuser
......
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1818
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Binary Switching Algorithm IIFD Resource Allocation – Binary Switching Algorithm II
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 1
user 1 user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 2
user 2
user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 3
user 3 user Nuser − 1
user Nuser
......
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1818
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Binary Switching Algorithm IIFD Resource Allocation – Binary Switching Algorithm II
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 1
user 1 user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 2
user 2
user 3
user 4
user Nuser − 1
user Nuser
user 1
user 2
user 3
user 4
. . .
. . .
user Nuser − 1
user Nuser
RBs
BSA with user 3
user 3 user Nuser − 1
user Nuser
......
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1818
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IFD Resource Allocation – Combined HA+BSA I
Initialization: random groups assigned to random chunks
First step: use HA to find optimum allocation of given groupsto chunksBUT HA does not exchange users between chunks
Second step: BSA exchanges Nsw = 1 users between chunks
Iterations: repeat first and second step for Nit iterations
Convergence of the algorithm is guaranteed in principleBUT resulting solution might not be the optimum one
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1919
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IFD Resource Allocation – Combined HA+BSA I
Initialization: random groups assigned to random chunks
First step: use HA to find optimum allocation of given groupsto chunksBUT HA does not exchange users between chunks
Second step: BSA exchanges Nsw = 1 users between chunks
Iterations: repeat first and second step for Nit iterations
Convergence of the algorithm is guaranteed in principleBUT resulting solution might not be the optimum one
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA1919
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Combined HA+BSA IIFD Resource Allocation – Combined HA+BSA II
user 1
user 2
user 3
user 4RBs
Starting point
user 3
user 4
user 1
user 2RBs
HA test
user 1
user 4
user 3
user 2RBs
BSA testsuser 3
user 1
user 4
user 2RBs
user 2
user 4
user 1
user 3RBs
user 3
user 2
user 1
user 4RBs
Example for HA+BSA for the pairing and resource allocation ofNuser = 4 users and Nu = 2 users per group.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2020
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Complexity AnalysisFD Resource Allocation – Complexity Analysis
Number of computations of the capacity/BER for the HA+BSAwith Nit iterations
QHA+BSA =Nit ·(
1Nu
2N2user + (N2
user −Nu ·Nuser))
=Nit ·((
1Nu
2 + 1)N2
user −Nu ·Nuser
).
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2121
Algorithms for Time / Frequency Domain Resource AllocationAlgorithms for Time / Frequency Domain Resource Allocation
FD Resource Allocation – Complexity AnalysisFD Resource Allocation – Complexity Analysis
HA+BSAFull Search
Q−→
Nuser −→
Nit
8 10 12 14 16 18 20 22 24100
102
104
106
108
1010
1012
1014
1016
Complexity Q of the full search and of the HA+BSA for Nu = 4and Nit ∈ {1, 2, 5, 10, 20}, respectively.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2121
Numerical ResultsNumerical Results
Numerical Results INumerical Results I
BERCapRandomMMSE LESIC equalizer
BLER
−→
10 · log10(Eb/N0) [dB] −→
MMSE LE
SIC
0 2 4 6 8 10 1210−3
10−2
10−1
100
BLER versus Eb/N0 for TD resource allocation, Nuser = 20,Nu = 2, different pairing criteria, 10 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2222
Numerical ResultsNumerical Results
Numerical Results IINumerical Results II
BERCapRandom
BLER
−→
Nuser −→2 4 6 8 10 12 14 16 18 20
10−3
10−2
10−1
100
BLER versus Nuser for TD resource allocation, Eb/N0 = 8 dB,Nu = 2, different pairing criteria, MMSE LE, 10 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2323
Numerical ResultsNumerical Results
Numerical Results IIINumerical Results III
HA+BSA BERFull Search BERHA+BSA CapFull Search CapRandom
BLER
−→
10 · log10(Eb/N0) [dB] −→0 2 4 6 8 10 12
10−3
10−2
10−1
100
BLER versus Eb/N0 for FD res. alloc., Nuser = 10, Nu = 2,Nit = 20, different pairing criteria, MMSE LE, 10 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2424
Numerical ResultsNumerical Results
Numerical Results IVNumerical Results IV
HA+BSA BERFull search BERHA+BSA CapFull search CapRandom
BLER
−→
10 · log10(Eb/N0) [dB] −→−4 −2 0 2 4 6 8
10−3
10−2
10−1
100
BLER versus Eb/N0 for FD resource allocation, Nuser = 8,Nu = 4, Nit = 10, MMSE LE, 20 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2525
Numerical ResultsNumerical Results
Numerical Results VNumerical Results V
HA+BSA BER Nit = 20
HA+BSA BER Nit = 10
HA+BSA Cap Nit = 20
HA+BSA Cap Nit = 10
Random
BLER
−→
10 · log10(Eb/N0) [dB] −→−4 −2 0 2 4 6 8
10−3
10−2
10−1
100
BLER versus Eb/N0 for FD resource allocation, Nuser = 16,Nu = 4, MMSE LE, 20 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2626
Numerical ResultsNumerical Results
Numerical Results VINumerical Results VI
Nit = 50
Nit = 40
Nit = 30
Nit = 20
Nit = 10
Nit = 5
Nit = 2
Nit = 1Random
BLER
−→
10 · log10(Eb/N0) [dB] −→
Nit
0 2 4 6 8 10 1210−3
10−2
10−1
100
BLER versus Eb/N0 for FD resource allocation, Nuser = 20,Nu = 2, BER grouping, MMSE LE, 20 MHz bandwidth.
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2727
ConclusionsConclusions
SummarySummary
Random user grouping and resource allocations wastes hugepotential
Hungarian Algorithm finds optimum solution for twodimensional time domain resource allocation and user pairingproblem
Full search finds optimum solution for three dimensionalfrequency domain resource allocation and user groupingproblem with extremely high complexity
Proposed iterative HA+BSA finds close to optimum solutionfor frequency domain resource allocation and user groupingproblem at much lower complexity
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2828
ConclusionsConclusions
SummarySummary
Random user grouping and resource allocations wastes hugepotential
Hungarian Algorithm finds optimum solution for twodimensional time domain resource allocation and user pairingproblem
Full search finds optimum solution for three dimensionalfrequency domain resource allocation and user groupingproblem with extremely high complexity
Proposed iterative HA+BSA finds close to optimum solutionfor frequency domain resource allocation and user groupingproblem at much lower complexity
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2828
ConclusionsConclusions
Future WorkFuture Work
Lower bound for capacity pairing (orthogonality in randomGaussian channels, famous balls-and-bins problem)
Power allocation not yet implemented
Rate adaptation not considered
4× 4 V-MIMO with two transmit antennas per mobile
⇒ Use of network simulator necessary
W.H. Gerstacker et al.W.H. Gerstacker et al. – Joint User Pairing and Resource Allocation for Multiuser SC-FDMA– Joint User Pairing and Resource Allocation for Multiuser SC-FDMA2929