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

huu.n.nguyen@mail.mcgill.ca

July 10, 2013

1 / 31

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

2 / 31

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

5 / 31

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

6 / 31

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)

7 / 31

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

8 / 31

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

9 / 31

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

10 / 31

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.

11 / 31

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)

12 / 31

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

13 / 31

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

14 / 31

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

15 / 31

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

17 / 31

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−

19 / 31

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

20 / 31

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

22 / 31

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)

23 / 31

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

24 / 31

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

25 / 31

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.

27 / 31

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

29 / 31

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