[width=1.7cm]figures/kthengrgb.jpg [1em]optimizing

Optimizing Resource Allocation in60 GHz Wireless Access Networks

George Athanasiou, Pradeep Chathuranga Weeraddana,Carlo Fischione

Electrical Engineering School and Access Linnaeus Center,KTH Royal Institute of Technology, Stockholm, Sweden

{georgioa, chatw, carlofi}@kth.se

Ericsson Research 06.03.13

Athanasiou, Weeraddana, Fischione (KTH) Optimizing RA in 60 GHz WNs Ericsson Research 06.03.13 1 / 51

Group


Group Activities

• Research interests• Wireless networking analysis and optimization with applications to 3/4/5G• Wireless sensor networks• Smart grids• Wireless industrial control

• Research projects• European Institute of Technology, Car2X Communications, 2013• European Institute of Technology, LTE in Smart Grids, 2013• Hycon2 EU project, Highly-complex and networked control systems,

2010-2014• Hydrobionets EU project, Autonomous control of large-scale water

treatment plants based on self-organized wireless BI0MEM sensor andactuator networks, 2011-2014

• Swedish Research Council, In-Network Optimization, 2012-1014

• Educational activities• Teaching at PhD, Master and Bachelor level


Outline

• Past, Present and Future in wireless communications

• 60 GHz millimeterWave wireless technology

• Optimizing resource allocation

• Distributed client association (DAA)

• Numerical analysis of DAA

• Conclusions and open research topics


Outline








Growth of Mobile Traffic




2012: 70% mobile traffic growth compared to 2011



2012: 51% of the mobile traffic was video



2012: 12 times the entire global internet traffic in 2000



2017: 13 times higher compared to 2012

LTE Deployment


LTE Deployment


2012: 0.9% of mobile connections

LTE Deployment


End of 2013: # of mobile connected devices > earth population

LTE Deployment


2017: 4G will represent 10% of connections and 45% of mobile traffic

LTE Deployment


2017: 2/3 will be video

LTE Deployment


2017: 2,7 GB mobile traffic per smartphone per month

Mobile Traffic Offloading


The amount of traffic offloaded from smartphones will be 46%, and the amount oftraffic offloaded from tablets will be 71% in 2017 (Cisco, 2013)

90% of all cellular base stations will be small cells by 2016 (IEEE Spectrum Magazine,Informa Telecoms & Media, 2013)

Priorities

• High bandwidth

• High coverage

• Green

• Cheap


Evolution or Revolution?

• Infrastructure moves closer to the users

• Devices communicate directly (D2D)

• Base station is “dying”

• Heterogeneous networks converge


Mobile Data Offloading


Cost

reduction

Capacity improvement

Mobile Data Offloading


Cost

reduction

Capacity improvement

Are there better solutions for mobile data offloading?

Outline








60 GHz Wireless Access Networks

• Unlicensed short range transmissions inthe 60 GHz millimeter wave (mmW) band

• Achieve Gbps communication

• Reduced interference

• Low-cost mmW transceivers


MillimeterWave Band

• History (J.C. Bose, 1897)

• High path loss

• High oxygen absorption


60 GHz Wireless Standards

• IEEE 802.11ad

• WiGig

• IEEE 802.15.3c

• WirelessHD

• ECMA-387


Applications


60 GHz to the Mobile

• 60 GHz small base stations (eg. on lamp posts)

• Downlink offload traffic in 60 GHz band with uplink LTE feedback

• 60 GHz radio on mobile device in receive-only mode


Outline






• Conclusions open research topics


Optimizing Client Association in60 GHz Wireless Access Networks



• Goal: Minimize the maximum access point (AP) utilization in thenetwork and ensure fair load distribution

• Solution: Distributed algorithm for client association based onLagrangian duality theory and subgradient methods

• Results: Theoretical and numerical analysis


G. Athanasiou, P. C. Weeraddana, C. Fischione and L. Tassiulas, “Optimizing Client Associationin 60 GHz Wireless Access Networks”, arXiv:1301.2723, Cornell University Library, 2013 [Online].Available: http://arxiv.org/abs/1301.2723

http://arxiv.org/abs/1301.2723

System Model

• N = {1, . . . , N} APs and M = {1, . . . ,M} clients

• Achievable rate from AP i to client j ∈Mi is

Rij = W log2

(1 +

PijGij(N0 + Ij)W

)• Qj is the demanded data rate of client j


W System bandwidth

Pij Transmission power of AP i to client j

Gij Power gain from AP i to client j

N0 Power spectral density of the noise

Ij Interference spectral density at client j

Mi Set of clients that can be associated to AP i

Nj Set of APs that client j could be associated with

i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

System Model

• Channel utilization between AP i and client j is

βij =QjRij

• Utilization of AP i is ∑j∈Mi

βijxij

• (xij)j∈Mi are binary decision variables, which indicate the clientassociation

xij =

{1 if client j is associated to AP i0 otherwise


Client Association Problem Formulation

minimize maxi∈N

∑j∈Mi

βij xij

subject to Qjxij ≤ Rij , i ∈ N , j ∈Mi∑i∈Nj xij = 1, j ∈M

xij ∈ {0, 1}, j ∈M, i ∈ Nj

• Variable: (xij)i∈N , j∈Mi

• Main problem parameters: (βij)i∈N ,j∈Mi , (Qj)j∈M, (Rij)i∈N ,j∈Mi

• Constraints: a) The demand of client j is less or equal to theachievable rate from AP i to client j, b) Client j can only be assignedto one AP, c) The decision variables are binary


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Equivalent Epigraph Form

minimize t

subject to∑

j∈Miβij xij ≤ t, i ∈ N∑

i∈Nj xij = 1, j ∈Mxij ∈ {0, 1}, j ∈M, i ∈ Nj

• Variable: (xij)i∈N , j∈Mi and t

• Main problem parameters: (βij)i∈N ,j∈Mi

• Mixed integer linear program (MILP)


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Solution Method Challenges

• Existing MILP solvers are centralized

• Typically based on global branch and bound algorithms ⇒ theworst-case complexity grows exponentially with the problem size

• Even small problems, with a few tens of variables, can take a verylong time

• Our approach: Lagrangian duality + Subgradient methods ⇒decentralized


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Lagrangian Duality

Partial Lagrangian

L(t,x,λ

)= t+

∑i∈N

λi

( ∑j∈Mi

βijxij − t)

= t

(1−

∑i∈N

λi

)+∑j∈M

∑i∈Nj

βijλixij

λ = (λi)i∈N : multipliers for the first set of inequality constraints

Dual functiong(λ)

= inft∈IRx∈X

L(t,x,λ

)X =

{x=(xij)j∈M,i∈Nj

∣∣∣∣∣ ∑i∈Nj

xij=1, xij∈{0, 1}, j ∈M i∈Nj

}.


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Lagrangian Duality

Dual problem

maximize g(λ) =∑

j∈M gj(λ)

subject to∑

i∈N λi = 1

λi ≥ 0, i ∈ N

• Variables: λ = (λi)i∈N

• gj(λ) is the optimal value of the subproblem

minimize∑

i∈Nj βijλixijsubject to xj ∈ Xj ,

with the variable xj .


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Lagrangian Duality

Dual problem

maximize g(λ) =∑

j∈M gj(λ)

subject to∑

i∈N λi = 1

λi ≥ 0, i ∈ N

• Variables: λ = (λi)i∈N

• gj(λ) is the optimal value of the subproblem

minimize∑

i∈Nj βijλixijsubject to xj ∈ Xj ,

with the variable xj .


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

solved @ client j

Subgradient Method

Subgradient method to solve dual problem

λ(k+1) = P(λ(k) − αku(k)

)• P : Euclidean projection onto the unit simplex Π = {λ

∣∣ ∑i∈N λi = 1, λi ≥ 0}

• αk > 0 is the kth step size

• u(k) =

(u(k)i

)i∈N

: a subgradient of −g at λ(k), where

u(k)i = −

∑j∈Mi

βijx?ij ,

and (x?ij)j∈Miis the solution of the ith subproblems with λ = λ(k)


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

Subgradient Method

Subgradient method to solve dual problem

λ(k+1) = P(λ(k) − αku(k)

)• P : Euclidean projection onto the unit simplex Π = {λ

∣∣ ∑i∈N λi = 1, λi ≥ 0}

• αk > 0 is the kth step size

• u(k) =

(u(k)i

)i∈N

: a subgradient of −g at λ(k), where

u(k)i = −

∑j∈Mi

βijx?ij ,

and (x?ij)j∈Miis the solution of the ith subproblems with λ = λ(k)


i = 1 i = 3

i = 2

j = 1

23 (Q3)

45

6

7 8

9

10

R33R13

price update

Outline








DAA Illustrationa

. init

price broadcast

determine local association

clients signals its best AP

AP i computes ui

construct u / compute prices

stopping criterion ?

.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. init

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcastprice broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast

determine local associationdetermine local association

clients signals its best APclients signals its best AP

AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes uiAP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui

construct u / compute pricesconstruct u / compute prices


.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui


stopping criterion ?stopping criterion ?

.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit




AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast






.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. initinit

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. init

price broadcast



AP i computes ui



.

.

YES

NOAP 1 AP 2

AP 3


DAA Illustrationa

. init







.

..

YES

NOAP 1 AP 2

AP 3


DAA Properties


Proposition

Let g(k)best denote the best dual objective value found after k subgradient

iterations, i.e., g(k)best = max{g(λ(1)), . . . , g(λ(k))}. Then, ∀ε > 0

∃n ≥ 1 such that ∀k k ≥ n⇒(d? − g(k)

best

)< ε.

Theorem

The optimal duality gap of the mixed integer linear program is boundedas follows:

p? − d? ≤ (N + 1)(%+ maxj∈M

%j) ,

where % = maxi∈N ,j∈Mi βij and %j = mini∈Nj βij . Moreover, therelative duality gap (p? − d?)/p? diminishes to 0 as M →∞.

Implementation Over Existing Standards

• Initially the clients follow the RSSI-based association policy that IEEE802.11ad and IEEE 802.15.3c define

• DAA is periodically executed to correct possible suboptimalclient associations by reallocating the available resources


Implementation Over Existing Standards

• APs trigger the initialization of DAA by setting a special bit into thebeacon frame

• Information exchange is performed through the control frames orpiggy-backing the data frames


Outline








Numerical Analysis

• Consider a multi-user multi-cell environment

• Compare DAA to• Random association• RSSI-based association (IEEE 802.11)• Optimal association (IBM CPLEX)

• Measure• Convergence• Scalability• Time efficiency• Fairness


Topologies

• SNR operating point at a distance d from any AP

SNR(d) =

{P0λ

2/(16π2N0W ) d ≤ d0

P0λ2/(16π2N0W ) · (d/d0)−η otherwise

• Radius of each cell r is chosen such that SNR(r) = 10 dB

• Clients are uniformly distributed at random, among the circular cells


λ Wavelength

d0 Far field reference distance

η Path loss exponenti = 1 i = 3

i = 2

i = 1 i = 3

i = 2 i = 4

i = 5

Convergence of DAA

• Average primal objective value from DAA after k subgradient

iterations: P(k) = (1/T̄ )∑T̄

T=1 p(k)best(T )

• Average dual optimal value by DAA: D? = (1/T̄ )∑T̄

T=1 d?(T )


50 100 150 200 250 300

1.2

1.4

1.6

1.8

2

2.2

subgradient iterations, k

avera

ge o

bje

ctive v

alu

e

random policy, Prand

RSSI, PRSSI

DAA, P(k)

optimal primal value, P*

optimal dual value, D*

5 APs, 100 clients

50 100 150 200 250 300

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4


avera

ge o

bje

ctive v

alu

e


RSSI, PRSSI

DAA, P(k)



5 APs, 200 clients

Convergence of DAA

• Convergence time is affected by the number of APs and clients: Thesmaller the network, the faster DAA converges


50 100 150 200 250 300

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1


ave

rag

e o

bje

ctive

va

lue


RSSI, PRSSI

DAA, P(k)



3 APs, 30 clients

50 100 150 200 250 300

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5


avera

ge o

bje

ctive v

alu

e


RSSI, PRSSI

DAA, P(k)



10 APs, 100 clients

Scalability of DAA

• Performance improvement increases while the network becomes biggerand more loaded

• DAA performs close to optimal


20 30 40 50 60 70 80 90 100

1

1.5

2

2.5

3

3.5

4

total number of clients, M

avera

ge o

bje

ctive


RSSI, PRSSI

DAA, P(1000)

optimal primal, P*

optimal dual, D*

2 APs

50 100 150 200 250 300 350 400 450 500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


avera

ge o

bje

ctive


RSSI, PRSSI

DAA, P(1000)

optimal primal, P*

optimal dual, D*

10 APs

Scalability of DAA

• Considering constant load, the average objective value decreases whilethe number of APs increases

• DAA performs close to optimal


2 4 6 8 10 12 14

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

total number of APs, N

ave

rag

e o

bje

ctive

va

lue


RSSI, PRSSI

DAA, P(1000)

optimal primal, P*

optimal dual, D*

40 clients

2 4 6 8 10 12 140.5

1

1.5

2

2.5

3

3.5

4

total number of APs, N

ave

rag

e o

bje

ctive

va

lue


RSSI, PRSSI

DAA, P(1000)

optimal primal, P*

optimal dual, D*

100 clients

Optimality of DAA

• Average relative duality gap:

Ave-RDG = (1/T̄ )∑T̄

T=1(p?(T )− d?(T ))/p?(T )

• Average relative duality gap taking into account the best primalfeasible objective value from DAA after K iterations at time slot T :

Ave-RDG-best-achieved = (1/T̄ )∑T̄

T=1(p(K)best(T )−d?(T ))/p

(K)best(T )


100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

number of clients, M

rela

tive d

ualit

y g

ap %

2−APs

3−APs

4−APs

5−APs

10−APs

100 200 300 400 500 6000

1

2

3

4

5

6

7

8

number of clients, M

rela

tive d

ualit

y g

ap w

.r.t the b

est prim

al valu

e %

2−APs

3−APs

4−APs

5−APs

10−APs

Fairness Achieved by DAA

• Jain’s fairness index:

J (k)(T ) =(∑i∈N

Y(k)i (T )

)2/(N

∑i∈N

Y(k)i (T )2),

Y(k)i (T ) =

∑j∈Mi

βijx(k)ij (T ) and x

(k)ij (T ) is the solution (best

feasible) resulted from DAA at time slot T after k iterations


50 100 150 200 250 300 350 400 450 500

0.88

0.9

0.92

0.94

0.96

0.98

1


fairn

ess in

de

x

Optimal (CPLEX)

DAA

RSSI

random policy

Speed and Resources Used by DAA

• Empirical CDF plots of the number of iterations for M = 100, 200,300 clients, with N = 10 APs

• Trade-off between optimality and complexity


0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time, t (sec)

CD

F(t

)

Empirical CDF

DAA, M=100

optimal (CPLEX), M=100

DAA, M=200


DAA, M=300


100 150 200 250 300 350 400 450 500

500

1000

1500

2000

2500

3000


ave

rag

e t

ime

to

fin

d t

he

o

ptim

al/su

bo

ptim

al so

lutio

n (

se

c)

optimal (CPLEX)

DAA

Outline








Conclusions

• 60 GHz wireless technology: characteristics, benefits, challenges,applications

• Distributed association algorithm (DAA) for optimizing resourceallocation in 60 GHz wireless access networks

• Performance evaluation of DAA: Asymptotically optimal,convergence, time efficiency and fairness

• Integration of DAA into current standards


Open Research Topics

• 60 GHz channel modeling

• Medium Access Control (MAC)

• Connectivity maintenance, blockage and directivity

• Coexistence and cooperation with existing wireless technologies

• Multi-hop communications

• ...



Thank you

Optimizing Resource Allocation in60 GHz Wireless Access Networks

George Athanasiou, Pradeep Chathuranga Weeraddana,Carlo Fischione

Electrical Engineering School and Access Linnaeus Center,KTH Royal Institute of Technology, Stockholm, Sweden

{georgioa, chatw, carlofi}@kth.se

Ericsson Research 06.03.13


[width=1.7cm]figures/kthengrgb.jpg [1em]optimizing

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