PrecodingDesignsin Multiuser Multicell Wireless Systems ...€¦ · Ph.D. Defense Department of...
Transcript of PrecodingDesignsin Multiuser Multicell Wireless Systems ...€¦ · Ph.D. Defense Department of...
Precoding Designs in Multiuser
Multicell Wireless Systems:Competition and Coordination
Duy H. N. NguyenPh.D. Defense
Department of Electrical and Computer Engineering
McGill University, Montreal, Quebec, CANADA
July 10, 2013
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Outline
1 Introduction and Motivation
2 Research ContributionsDownlink Beamforming for Power MinimizationBlock-Diagonalization PrecodingMulticell MIMO Multiple-Access Channel (MIMO-MAC)Multicell MIMO Broadcast Channel (MIMO-BC)
3 Conclusion
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The Future of Wireless Communications
Figure courtesy of Informa Telecoms & Media.
Rapid increase in subscriptions to mobile broadband services
Higher throughput, higher robustness, and better coverage3 / 31
The Future of Wireless Communications
Figure courtesy of QUALCOMM Inc.
Technical challenges: efficient utilization of the radio spectrum
4 / 31
MIMO Communications
( )log 1 SNRC = + min( , ) log(SNR)C M N≈
M N
SISO MIMO
Multiple-input Multiple-Output (MIMO): using multipletransmit/receive antennas
MIMO precoding (beamforming) → Higher spectral efficiency
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MIMO Configurations
Single-cell SISO Single-cell MIMOSingle-cell MISO
Single-cell MU-MIMO
Competitive
Multicell MU-MIMO
Coordinated
Multicell MU-MIMO
ICI Coordination
ICI = Inter-cell Interference
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Coordinated Multipoint Transmission/Reception
Cellular networks → inter-cell interference (ICI)Coordinated Multipoint Transmission/Reception (CoMP)
Coordinate simultaneous transmissions from multiple BSs to the MSs Actively deal with the ICI by the means of MIMO precoding
CoMP is a key technology for Long-Term Evolution (LTE)-Advanced
CoMP ModesCompetition versus Coordination
Interference Aware (IA) versus Interference Coordination (IC)
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Challenges in CoMP Precoding Designs
A paradigm shift in precoding designsIndependent per-cell approach to coordinated multicell approach
Large-scale and distributed multicell network
CSI: difficult to acquire
Limited backhaul links for control/signaling
Nonconvex precoding design problems
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Research Statement
Competition and Coordination in Multicell Wireless SystemsDistributed strategies in precoding designs and ICI management
Distributed algorithms for precoding designs and ICI management
Local computation with local CSI
Define and quantize the control/signaling messages
Achievable optimality versus computational complexity
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Research Contributions
Develop low-complexity and distributed algorithms
Devise the structure of the CoMP precoders
Devise the message exchange mechanism
Expose new perspectives and understanding the interactions betweenthe coordinated BSs in a CoMP systemDesign criteria:
Power minimization and Sum-rate maximization IA and IC Uplink and Downlink
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Downlink Beamforming for PowerMinimization: A Game-Theoretical Approach
ICI
ICI
1MS-12MS-1
1MS-2
2MS-2
BS-1 BS-2
Beamforming design to minimize the transmit power at each BSGuaranteed SINR requirement at each MS
SINRqi ≥ γmin
qi ,∀q,∀i (1)
[J1] D. H. N. Nguyen and T. Le-Ngoc, “Multiuser downlink beamforming in multicell wireless systems: A game theoretical
approach,” IEEE Trans. Signal Process., vol. 59, no. 7, pp. 3326–3338, Jul. 2011.
[J2] D. H. N. Nguyen and T. Le-Ngoc, “Efficient coordinated multicell beamforming with dynamic base-station assignment
consideration,” to appear in IET Communications, 2013.
[C1] D. H. N. Nguyen and T. Le-Ngoc, “Competitive downlink beamforming design in multiuser multicell wireless systems,”
in Proc. IEEE Global Commun. Conf., Miami, FL, USA, Dec. 2010, pp. 1–6.
[C2] D. H. N. Nguyen and T. Le-Ngoc, “Efficient coordinated multicell beamforming with per-base-station power
constraints,” in Proc. IEEE Global Commun. Conf., Houston, TX, USA, Dec. 2011, pp. 1–5.
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Downlink Beamforming Game (IA mode)
SINR at a particular MS
SINRqi =
∣
∣wHqihqqi
∣
∣
2
K∑
j 6=i
∣
∣wHqjhqqi
∣
∣
2+ r−qi
,
where r−qi : sum ICI + noise.
Each BS is aware of the ICI at itsconnected MSs and selfishly
adjusts its precoders accordingly
( )1
21 0,z CN σ
111Hh
211Hh
( )2
21 0,z CN σ
w
w
( )1
22 0,z CN σ
( )2
22 0,z CN σ
11w
21w
11uBS-1
BS-2
21u
12u
22u
1x
2x 122Hh
222Hh
11y
21y
12y
22y
112Hh
Multicell game GP =(
Ω, Pq(W−q)q∈Ω , tq(Wq)q∈Ω
)
Players Ω: base-stations Utility function: tq(Wq) =
∑K
i=1‖wqi‖
2
Set of admissible strategies: Pq(W−q) =
SINRi(Wq) ≥ γmin
i , ∀i
W⋆ = W⋆q
Qq=1
is a Nash Equilibrium (NE) if
tq(W⋆q) ≤ tq(Wq), ∀Wq ∈ Pq(W
⋆−q), ∀q ∈ Ω. (2)
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Downlink Beamforming Game (cont.)
Study the NE of game GP
Unique NE if it exists
→ Best response strategies provedto converge (standard functions)
Sufficient and necessaryconditions: low ICI guaranteesthe NE’s existence
IC to obtain Pareto-optimality0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.2
0.4
0.6
0.8
1
P1
P2
NE of game G
Pareto−optimal tradeoff curve
NE of game G’
minimum required power at cell−2
minimum required power at cell−1
To improve the NE’s efficiency, modify the utility function
sq(Wq) =
K∑
i=1
‖wqi‖2+
Q∑
r 6=q
K∑
j=1
πqrj
∥
∥WHq hqrj
∥
∥
2
,
where πqrj : interference price charged on the ICI
The new game G′P is able to obtain a Pareto-optimal solution
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Convergence
0 1 2 3 4 5 6 7 8 95
6
7
8
9
10
Number of iterations (Competitive design)
Pq/σ
2 in d
B
Cell−1Cell−2Cell−3
0 1 2 3 4 5 6 7 8 95
6
7
8
9
10
Number of iterations (Competitive design with pricing)
Pq/σ
2 in d
B
Cell−1Cell−2Cell−3
0 5 10 15 20 25 300
10
20
30
40
50
Number of iterations (Competitive design)
Pq/σ
2 in d
B
Cell−1Cell−2Cell−3
0 5 10 15 20 25 300
5
10
15
Number of iterations (Competitive design with pricing)
Pq/σ
2 in d
B
Cell−1Cell−2Cell−3
IA mode
IA mode with pricing with partial inter-cell CSI
IC mode: IA mode with the right pricing schemeand full inter-cell CSI BS BS
BS
MS
MS
MS
MSMS
MS
d
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Competition versus Coordination
Prob. of Convergence Transmit Power
0.3 0.5 0.7 0.9 1.10
0.2
0.4
0.6
0.8
1
d
Prob
abili
ty o
f th
e E
xist
ence
of
an E
quili
briu
m
IA Mode (C)IA Mode (C1)IC ModeIA Mode − Pricing
0.3 0.5 0.7 0.9 1.1−10
0
10
20
30
d
Ave
rage
Pow
er C
onsu
mpt
ion
P
tota
l/σ2 (
in d
B)
IA ModeIC ModeIA Mode − Pricing
Target SINRs: γqi = 10 dB (dashed lines) and γqi = 0 dB (solid lines)
Coordination −→ power savings, better coverage
Interference pricing −→ limit ICI −→ improve the efficiency of thegame’s NE
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Block-Diagonalization Precoding:Competition and Coordination
ICI
ICI
1MS-12MS-1
1MS-2
2MS-2
BS-1 BS-2
Precoding design to maximize the sum-rate at each cellPower constraint at each BSBlock-Diagonalization (BD) precoding: suppress intra-cell interferenceBD-Dirty Paper Coding (BD-DPC): to further enhance the sum-rateperformance
[J3] D. H. N. Nguyen, H. Nguyen-Le, and T. Le-Ngoc, “Block-diagonalization precoding in a multiuser multicell MIMO
system: Competition and coordination,” submitted to IEEE Trans. Wireless Commun., Apr. 2013.
[C3] H. Nguyen-Le, D. H. N. Nguyen, and T. Le-Ngoc, “Game-based zero-forcing precoding for multicell multiuser
transmissions,” in Proc. IEEE Veh. Technol. Conf., San Francisco, CA, USA, Sep. 2011.
[C4] D. H. N. Nguyen and T. Le-Ngoc, “Block diagonalization precoding game in a multiuser multicell system,” in Proc.
IEEE Wireless Commun. and Networking. Conf., Shanghai, China, Apr. 2013.16 / 31
BD Precoding - Competition
Multicell game GR =(
Ω, Sqq∈Ω , Rq(Qq)q∈Ω
)
Players Ω: base-stations Utility function: Rq(Qq) =
∑K
i=1log∣
∣I+HHqqi
R−1
−qi(Q−q)HqqiQqi
∣
∣
Set of admissible strategies
Sq =
Qqi :
K∑
i=1
Tr Qqi ≤ Pq, Qqi 0, HqqjQqi = 0, ∀j 6= i
(Q⋆q,Q
⋆−q) is a NE of game GR if
Rq
(
Q⋆q,Q
⋆−q
)
≥ Rq
(
Qq,Q⋆−q
)
, ∀Qq ∈ Sq, ∀q ∈ Ω. (3)
Obtain closed-form best-response (water-filling) strategies by solving
maximizeQq1
,...,QqK
Rq(Qq,Q−q) (4)
subject to Qqi ∈ Sq,∀i.
Convergence proved by the contraction mapping
A NE is always existent and unique at low ICI
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BD Precoding - Coordination
Joint weighted sum-rate maximization
maximizeQ1,...,QQ
Q∑
q=1
ωqRq(Qq,Q−q) (5)
subject to Qqi ∈ Sq,∀i,∀q.
Nonconvex → iterative linear approximation (ILA)to Q per-cell convex problems
maximizeQq1
,...,QqK
ωqRq(Qq,Q−q)−
K∑
i=1
TrAqiQqi
subject to Qqi ∈ Sq,∀i, (6)
where Aqi : interference price charged on the ICI
Nonconvex
Problem
Linear
Approximation
Multiple Convex
Problems
Local Optimal
Solution
Jaco
bi or
Ga
uss-S
eid
el
Monotonic convergence to a local maximum (Gauss-Seidel updateproved, Jacobi update observed)Distributed implementation with message exchange between BSs tocompute the price Aqi ’s 18 / 31
Convergence
Competition Coordination
0 2 4 6 8 10 120
20
40
60
80
100
Number of Iterations
Ach
ieva
ble
Sum
−ra
te (
bits
/s/H
z)
Network Sum−rateCell−1 Sum−rateCell−2 Sum−rateCell−3 Sum−rate
0 10 20 30 40 500
20
40
60
80
100
Number of Iterations
Ach
ieva
ble
Sum
−ra
te (
bits
/s/H
z)
Network Sum−rateCell−1 Sum−rateCell−2 Sum−rateCell−3 Sum−rate
Solid lines: BD & Dashed lines: BD-DPC
BD-DPC → higher sum-rate than BD
Coordination → higher sum-rate than competition
Coordination → slower to converge thancompetition
BS
BSBS
MS
MSMS
MS
d
MS
MS
MS
MSMS
( )0, 3
( )1,0( )1,0−
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Network Sum-rate
versus BS-MS Distance versus Transmit Power
0.3 0.4 0.5 0.6 0.7 0.8 0.940
60
80
100
120
140
Intra−cell BS−MS distance d
Ach
ieva
ble
Net
wor
k S
um−
rate
(bi
ts/s
/Hz)
BD Precoding − IA modeBD Precoding − IC modeBD−DPC Precoding − IA modeBD−DPC Precoding − IC modeDPC Precoding − IA modeDPC Precoding − IC mode
10 14 18 22 2640
50
60
70
80
90
100
Transmit Power to AWGN Ratio P/σ2 in dB
Ach
ieva
ble
Net
wor
k S
um−
rate
(bi
ts/s
/Hz)
BD Precoding − IA modeBD Precoding − IC modeBD−DPC Precoding − IA modeBD−DPC Precoding − IC modeDPC Precoding − IA modeDPC Precoding − IC mode
DPC > BD-DPC > BD
Coordination >> Competition, especially at high ICI region
Performance saturated at high ICI region with competition
→ Coordination
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Multicell MIMO-MAC - Coordination
ICI
ICI
1MS-12MS-1
1MS-2
2MS-2
BS-1 BS-2
Successive interference cancelation (SIC) on a per-cell basisPrecoding design to maximize the weighted sum-rate in the uplink
maximizeX1,...,XQ
Q∑
q=1
ωq log
∣
∣
∣
∣
∣
I+R−1
q
(
K∑
i=1
HqqiXqiHHqqi
)∣
∣
∣
∣
∣
(7)
subject to TrXqi ≤ Pqi , ∀i, ∀q
Xqi 0, ∀i, ∀q.
[J4] D. H. N. Nguyen and T. Le-Ngoc, “Sum-rate maximization in the multicell MIMO multiple-access channel with
interference coordination,” to appear in IEEE Trans. on Wireless Commun., 2013.
[C5] D. H. N. Nguyen and T. Le-Ngoc, “Sum-rate maximization in the multicell MIMO multiple-access channel with
interference coordination,” in Proc. IEEE Wireless Commun. and Networking. Conf., Paris, France, Apr. 2012.
21 / 31
ILA Solution Approach
Approximation and decomposition into Q per-cell outer problems
maximizeXq1
,...,XqK
ωq log
∣
∣
∣
∣
∣
Rq +
K∑
i=1
HqqiXqiHHqqi
∣
∣
∣
∣
∣
−
K∑
i=1
TrAqiXqi (8)
subject to TrXqi ≤ Pqi , ∀i
Xqi 0,
where Aqi : interference pricing charged on the ICI.Further decomposition into K per-user inner problems
maximizeXqi
ωq log∣
∣
∣I+R−1
qiHqqiXqiH
Hqqi
∣
∣
∣− TrAqiXqi (9)
subject to TrXqi ≤ Pqi ,Xqi 0,
where Rqi = Rq +∑K
j 6=iHqqjXqjHHqqj .
Monotonic convergence to a local maximum (Gauss-Seidel updateproved, Jacobi update observed)
Distributed implementation with message exchange between BSs tocompute the price Aqi ’s
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WMMSE Solution Approach
Transform the original nonconvex problem into a matrix weightedsum-MSE minimization problem (WMMSE)
minimizeWqi
,Vqi,Uqi
Q∑
q=1
ωq
K∑
i=1
[
Tr WqiEqi − log |Wqi |]
(10)
subject to Tr
VqiVHqi
≤ Pqi ,∀q,∀i,
where Vqi : transmit beamformer, Uqi : receive beamformer, Wqi :weight matrix, and Eqi : MSE matrix.
Not jointly convex, but convex in each set of variables Vqi , Uqi , Wqi
Iterative update across each set of variables in closed-form solutions
Distributed implementation with monotonic convergence to a localoptimum proved (also a local optimum of the original problem)
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Convergence
Outer Loop Inner Loop
0 10 20 30 400
20
40
60
80
Number of Outer−loop Iterations
Ach
ieva
ble
Net
wor
k S
um−
rate
(bi
ts/s
/Hz)
ILA − JacobiILA − Gauss−SeidelWMMSECompetition
0 5 1050
60
70
0 2 4 6 8 100
5
10
15
20
Number of Inner−loop Iterations
Ach
ieva
ble
sum
−ra
te a
t cel
l−1
(bits
/s/H
z)
MAC Sum−rate with PenaltyMAC Sum−rate
Monotonic convergence for both ILA and WMMSE algorithms
ILA: Jacobi (simultaneous) update converges faster than Gauss-Seidel(sequential) update
ILA converges faster than WMMSE
Coordination → higher network sum-rate than competition
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Network Sum-rate
Full Convergence 10 Iterations
0.2 0.3 0.4 0.5 0.6 0.7 0.820
60
100
140
180
Intra−cell BS−MS distance d
Ach
ieva
ble
netw
ork
sum
−ra
te (
bits
/s/H
z)
Network MIMOILA AlgorithmWMMSE AlgorithmCompetition
0.2 0.3 0.4 0.5 0.6 0.7 0.840
60
80
100
120
Intra−cell BS−MS distance d
Ach
ieva
ble
netw
ork
sum
−ra
te (
bits
/s/H
z)
ILA − 10_randomWMMSE − 10_randomILA − 10_iterationWMMSE − 10_iterationCompetition − 10_iteration
Full convergence: ILA ≈ WMMSE > Competition
Limited iteration: ILA > WMMSE > Competition
Coordination: require BS ↔ BS signaling
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Multicell MIMO-BC - Coordination
ICI
ICI
1MS-12MS-1
1MS-2
2MS-2
BS-1 BS-2
Dirty Paper Coding (DPC) on a per-cell basisPrecoding design to maximize the weighted sum-rate in the downlink
maximizeQ1,...,QQ
Q∑
q=1
ωq
K∑
i=1
log
∣
∣
∣Rqi +Hqqi
(
∑i
j=1Qqj
)
HHqqi
∣
∣
∣
∣
∣
∣Rqi +Hqqi
(
∑i−1
j=1Qqj
)
HHqqi
∣
∣
∣
(11)
subject toK∑
i=1
TrQqi ≤ Pq, ∀q; Qqi 0, ∀i, ∀q.
[J5] D. H. N. Nguyen and T. Le-Ngoc, “Sum-rate maximization in the multicell MIMO broadcast channel with interference
coordination,” submitted to IEEE Trans. Signal Process., Apr. 2013.
[C6] D. H. N. Nguyen and T. Le-Ngoc, “Sum-rate maximization in the multicell MIMO broadcast channel with interference
coordination,” in Proc. IEEE Int. Conf. Commun., Budapest, Hungary, Jun. 2013.26 / 31
ILA Solution Approaches
Approximation and decomposition into Q per-cell outer problems
maximizeQq1
,...,QqK
ωq
K∑
i=1
log
∣
∣
∣Rqi+Hqqi
(
∑i
j=1Qqj
)
HHqqi
∣
∣
∣
∣
∣
∣Rqi+Hqqi
(
∑i−1
j=1Qqj
)
HHqqi
∣
∣
∣
−
K∑
i=1
TrAqQqi (12)
subject to
K∑
i=1
TrQqi ≤ Pq, Qqi 0, ∀i,
where Aq: interference pricing charged on the ICI.
Still a nonconvex problem
Connection to the MAC problem via the uplink-downlink duality
maximizeXq1
,...,XqK
ωq log
∣
∣
∣
∣
∣
I+K∑
i=1
HHqqi
XqiHqqi
∣
∣
∣
∣
∣
−K∑
i=1
TrXqi (13)
subject to Xqi 0, ∀i,
where Hqqi = R−1/2qi Hqqi(Aq + λI)−1/2, λ: Lagrangian multiplier.
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ILA Solution Approaches
Nonconvex
Problem
Linear
Approximation
Multiple Outer
Problems
Local Optimal
Solution
Jacobi or Gauss-Seidel
BC MAC
Update λ
MAC-BC Transformation
Convergence and global optimality of the outer problem provedDistributed implementation with monotonic convergence to a localoptimum proved (also a local optimum of the original problem)
WMMSE algorithm Similar to the multicell MIMO-MAC Transform to an equivalent WMMSE problem Iterative updates to each set of variables
28 / 31
Convergence
Outer Loop Inner Loop
0 10 20 30 40 500
10
20
30
40
50
60
Number of Iterations
Ach
ieva
ble
Net
wor
k S
um−
rate
(bi
ts/s
/Hz)
ILA − Gauss−SeidelILA − JacobiDPC−WMMSEDPC Competition
0 5 1040
50
600 5 10 15
10
15
20
Sum
−ra
te
BC−DPC Sum−rate with PenaltyBC−DPC Sum−rate
0 5 10 150.5
1
1.5
2
Tra
nsm
it po
wer
0 5 10 150
0.5
1
1.5
λ
Number of Iterations
Convergence to the globally optimal solution of the outer problem
Monotonic convergence for both ILA and WMMSE algorithms
ILA: Jacobi (simultaneous) update converges faster than Gauss-Seidel(sequential) update
Coordination → higher network sum-rate than competition
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Network Sum-rate
Full Convergence 10 Iterations
0.3 0.4 0.5 0.6 0.7 0.8 0.930
40
50
60
70
80
90
Intra−cell BS−MS distance d
Ach
ieva
ble
netw
ork
sum
−ra
te (
bits
/s/H
z)
ILA − Gauss−SeidelDPC−WMMSEDPC CompetitionWMMSE
0.3 0.4 0.5 0.6 0.7 0.8 0.930
40
50
60
70
80
90
Intra−cell BS−MS distance d
Ach
ieva
ble
netw
ork
sum
−ra
te (
bits
/s/H
z)
ILA − Gauss−SeidelILA − JacobiDPC−WMMSEDPC CompetitionWMMSE
Full convergence: ILA ≈ WMMSE > Competition
Limited iteration: ILA > WMMSE > Competition
Nonlinear precoding (DPC) > Linear precoding
30 / 31
Conclusion and Q&A
Multicell multiuser MIMO to improve spectral efficiency
Multicell coordination → power savings, sum-rate enhancement overmulticell competition
Precoding with multicell coordination: more complex, more signaling
Various precoding techniques: linear MMSE, BD and BD-DPC, MACwith SIC, BC with DPC
Q&A31 / 31