cooperative base station coloring - university of...

© Robert W. Heath Jr. (2015)

Cooperative Base Station Coloring Achieving dynamic clustering gain from static partitions Robert W. Heath Jr. Wireless Networking and Communications Group Department of Electrical and Computer Engineering The University of Texas at Austin http://www.profheath.org

Joint work with Jeonghun Park and Namyoon Lee

Funded by Huawei and NSF-CCF-1218338


2

Out-of-cluster interference is a fundamental limit

A. Lozano, R. W. Heath, and J. Andrews, “Fundamental Limits of Cooperation,” IEEE Transactions on Information Theory, 2013

SNR

Spec

tral

Effi

cien

cy

Spectral efficiency ceiling at high SNR

It is impossible to reap benefits from full coordination of all the base stations

There are some benefits to coordination at moderate SNRs


Static clustering inspired by backhaul network

u  Predefined cooperation clusters, heavily investigated in prior work* u  Value of clustering depends heavily on the locations of the users

3 K. Huang and J. G. Andrews, “An Analytical Framework for Multicell Cooperation via Stochastic Geometry and Large Deviations,” IEEE Transactions on Information Theory, 2013

J. Zhang, R. Chen, J. G. Andrews, A. Ghosh, and R. W. Heath, “Networked MIMO with Clustered Linear Precoding,” IEEE Transactions on Wireless Communications, 2009

O. Simeone, O. Somekh, H. V. Poor, and S. Shamai, “Local Base Station Cooperation Via Finite-Capacity Links for the Uplink of Linear Cellular Networks,” IEEE Transactions on Information Theory, 2009.

L user at the cluster edge J user at the cluster center


Dynamic clustering centered around the user

u  Dynamic cooperation clusters, also investigated in prior work* u  Creates a challenging scheduling problem

4

J user at the cluster center

A. Papadogiannis, D. Gesbert, and E. Hardouin, “A Dynamic Clustering Approach in Wireless Networks with Multi-Cell Cooperative Processing,” in Proc. of IEEE ICC, 2008 N. Lee, R. W. Heath Jr., D. Morales, and A. Lozano, “Base station cooperation with dynamic clustering in super-dense cloud-RAN,” in Proc. of IEEE Globecom Workshop, 2013. N. Lee, D. Morales, A. Lozano, and R. W. Heath, “Spectral Efficiency of Dynamic Coordinated Beamforming,” IEEE Transactions on Wireless Communications, 2015

J user also at the cluster center

Base station is conflicted


Alternative is semi-static clustering

Static clustering

5

Dynamic clustering

Semi-static clustering – multiple predefined cluster patterns

Semi-static clustering gives the benefits of dynamic clustering with low complexity


6

Semi-static clustering uses cluster patterns

…… …

… … …

…

…

…

…

…

…

… … …

… … …

… … …

…

… … …

… …

… … …

… … …… ……

… … …… ……

… … …… …… f1 f2 f3 f4

Different carriers assigned to each cluster

base stations

subscribers

coordination clusters


How are cluster patterns formed in irregular topologies?

u  In practice, BS topology is irregular, patterns not obvious

u  Needs framework to design and analyze cluster pattern in irregular network topologies

7

−10 −8 −6 −4 −2 0 2 4 6 8 10−10

−8

−6

−4

−2

0

2

4

6

8

10

X coordinate

Y co

ordi

nate

Base station


8

Graph theoretic approach for interference models

−15 −10 −5 0 5 10 15 20−20

−15

−10

−5

0

5

10

15

Delaunay triangulation (Dual graph)

Characterization of cooperation set by the graph

2nd order Voronoi (Delaunay triangulation graph)

Voronoi diagrams of line segmentsFarthest-point Voronoi diagrams

RoundnessHigher-order Voronoi diagramsComputing the farthest-point Voronoi diagramRoundness

Second order Voronoi diagram

Computational Geometry Lecture 13: More on Voronoi diagrams

V2 (d0,d1)

V2 (d0,d2)

V2 (d0,d8)

V2 (d0,d9)

V2 (d0,d10)

d0

d1

d2

d3

d4

d5d6

d7

d8

d9

d10

1st order Voronoi (frequency reuse)

−15 −10 −5 0 5 10 15 20−20

−15

−10

−5

0

5

10

15

d0

d1

d2

d3

d4

d5d6

d7

d8

d9 d10


u  Our approach is edge coloring ª  : set of edges, : set of vertices, and ª Design a coloring function : such that if and then

u  Other work that uses graph coloring ª Training resource allocation for cooperative networks[Chen et al.]

ª Resource allocation for dynamic clustering[Chang et al.]

9

Avoid base station conflicts

Z. Chen, X. Hou, and C. Yang, “Training Resource Allocation for User-centric Base-station Cooperation Networks,” IEEE Transactions on Vehicular Technology, 2015. Y. Chang, Z. Tao, J. Zhang, and C. Kuo, “A Graph-Based Approach to Multi-Cell OFDMA Downlink Resource Allocation,” in Proc. IEEE Globecom, 2008. Y. Chang, Z. Tao, J. Zhang, and C. Kuo, “A Graph Approach to Dynamic Fractional Frequency Reuse (FFR) in Multi-Cell OFDMA Networks,” in Proc. IEEE ICC, 2009.

Weisstein, Eric W. "Edge Coloring." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EdgeColoring.html

fC(E) E ! {1, ..., }v 6= w (u, v) , (u,w) 2 E c (u, v) 6= c (u,w)

E V v, w, u 2 V


10

Use coloring to build pair-wise cooperation sets 1/3

1. Tessellate a network plane with 2nd order Voronoi cells

d0

d1 d2

d3

V2 (d0,d1) V2 (d0,d2)

V2 (d1,d3) V2 (d2,d3)

V2 (d1,d2)

V2 (d0,d3)

d0

d1 d2

d3

J. Park, N. Lee, and R. W. Heath, “Cooperative Base Station Coloring for Pair-wise Multicell Coordination,” submitted to IEEE Transactions on Communications, available on ArXiv


11


d0

d1 d2

d3

V2 (d0,d1) V2 (d0,d2)

V2 (d1,d3) V2 (d2,d3)

V2 (d1,d2)

V2 (d0,d3)

d0

d1 d2

d3

P1

P1

P2

P2P3

P3

G = (V, E)

BSs locations

Delaunay triangulation

2. Draw a graph

3. Solve edge-coloring for the drawn graph (color = pattern)


12


d0

d1 d2

d3

V2 (d0,d1) V2 (d0,d2)

V2 (d1,d3) V2 (d2,d3)

V2 (d1,d2)

V2 (d0,d3)

P1 :

P2 :

P3 :

4. Serve a user according to designed pattern

} Different time-frequency resources for different patterns

No conflict with edge-coloring!

d1

d0

d2

d3


General network application

13

−20 −15 −10 −5 0 5 10 15 20−20

−15

−10

−5

0

5

10

15

20

X coordinate

Y co

ordi

nate

Base station

−2 −1 0 1 2 3

−1

0

1

2

3

4

5

X coordinateY

coor

dina

te

Base station!!!!:!Base!sta(on!!!!!:!User!

d0

d1

d2

d3

d4

d5 1. Tessellate a network plane with 2nd order Voronoi cell Follow same

procedure

2. Draw a graph

−10 −8 −6 −4 −2 0 2 4 6 8 10−10

−8

−6

−4

−2

0

2

4

6

8

10

X coordinate

Y co

ordi

nate

Base station

−5 −4 −3 −2 −1 0 1 2 3 4 5−5

−4

−3

−2

−1

0

1

2

3

4

5

X coordinate

Y co

ordi

nate

d0

d2

d3

d4

d5

d6

d7d8

P1

P2

P3

P4

P6

P5

P1

P2

P2

P4

P7

P1 P1

P5

P2

P5

3. Solve edge-coloring for the drawn graph (color = pattern)


How many resources are required in the network?

u  Related to number of colors for edge-coloring (chromatic index)

u  Vizing’s theorem ª A simple planar graph of maximum degree Δ has chromatic index Δ or Δ+1 in general

ª Δ means the maximum number of connected edges to a vertex ª  The required resources are dominated by Δ

14

Need Δ+1 time-frequency resources to cover all the clusters


Example for Vizing’s theorem

15

Edge Coloring

Vizing’s theorem holds! Maximum degree determines the number of colors

Maximum degree =5

Number of colors =5

Problem Only one vertex with large degrees can cause color (resource) explosion!


Edge-cutting algorithm

u  If one vertex (BS) that has large Δ can cause resource explosion u  Can improve the network performance by sacrificing a few users

16 −5 −4 −3 −2 −1 0 1 2 3 4 5−5

−4

−3

−2

−1

0

1

2

3

4

5

X coordinate

Y co

ordi

nate

d0

d2

d3

d4

d5

d6

d7d8

P1

P2

P3

P4

P6

P5

P1

P2

P2

P4

P7

P1 P1

P5

P2

P5

−5 −4 −3 −2 −1 0 1 2 3 4 5−5

−4

−3

−2

−1

0

1

2

3

4

5

X coordinate

Y co

ordi

nate

d0

d2

d3

d4

d5

d6

d7d8

P1

P2

P3

P4

P6

P5

P1

P2

P2

P4

P7

P1 P1

P5

P2

P5

Save the resource of P6

Users here cannot be protected

Edge Cutting


Models for analysis

u  Signal model

u  Intra-cluster interference management method

ª Coordinated beamforming (CBF)

17

y` = kd0

k��/2 �h`0

�TV`

0

s`0| {z }

desired signal

+ kdjk��/2 �h`j

�TV`

js`j| {z }

intra�cluster interference

+X

dv2N`\C`

kdvk��/2 �h`v

�TV`

vs`v

| {z }out�of�cluster interference

+n`

Channel vector Distance from a BS to our user h`

i 2 CN , CN (0, 1)Precoding matrix

Vì =

⇥vì,1, ...,v

ì,K

⇤,v`

i,k 2 CN ,��v`

i,k

�� = 1

maximize :

��h`0

�Tv`0,k

��2

subject to :

��h`0

�Tv`0,k0

��2= 0 for k0 6= k

��h`j

�Tv`j,k00

��2= 0 for dj 2 C` and 1 k00 K

: cluster pattern index `


u  Lower bound on ergodic spectral efficiency (fixed geometry)

u  Lower bound on ergodic spectral efficiency (random geometry, PPP)

Analyzing bounds on average achievable rates

18

E1

Llog2

�1 + SINR|`

�� 1

Llog2

1 +

exp ( (N � 2K + 1))

KP

dv2D`(kdvk / kd0k)��

+ kd0k� /SNR

!

where D` = {dv|dv 2 N`\C`}

cluster pattern cluster # of used colors (resources)

E1

Llog2

�1 + SIR|`

�� E

1

L

�log2

1 +

��2 � 4

�

8Kexp ( (N � 2K + 1))

!

# of users

J. Park, N. Lee, and R. W. Heath, “Cooperative Base Station Coloring for Pair-wise Multicell Coordination,” submitted to IEEE Transactions on Communications, available on ArXiv


Proof sketch

u  Lower bound ª For non-negative random variable and ,

u  Calculating ,

19

Elog2

✓1 +

S

I + 1

◆�� log2

✓1 +

eE[lnS]

E [I + 1]

◆.

S I

E [I]

E

2

4kd1k�X

di2�\B(0,kd2k)

kdik��h`i

�TV`

i

��2

3

5=KE

2

4kd1k�X

di2�\B(0,kd2k)

kdik��

3

5

=KEr1,r2

2

4E�\B(0,r2)

2

4r�1X

di2�\B(0,r2)

kdik��

��kd1k = r1, kd2k = r2

3

5

3

5

=KEr1,r2

r�1 2⇡�

Z 1

r2

r1��dr

�=

2K⇡�

� � 2

Z 1

r2=0

Z r2

r1=04 (�⇡)2 e��⇡r22r�+1

1 r3��2 dr1dr2

=8K

�2 � 4

User communicates with two nearest BSs = protection ball B (0, kd2k)


20

Other approaches for performance comparison

BS 1 BS 2

BS 3 BS 4

BS 1 BS 2

BS 3 BS 4

BS 1 BS 2

BS 3 BS 4

BS 1 BS 2

BS 3 BS 4

BS 1 BS 2

BS 3 BS 4

Single cell operation •  No interference management is applied

Fractional frequency reuse •  Adjacent BS uses different sub-band

Random clustering •  BS cluster is made

with arbitrary rule (No coloring)

Conventional strategies - square grid model application example


u  Ergodic spectral efficiency of edge users

Comparison results

21

−10 −5 0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

SNR (dB)Er

godi

c sp

ectra

l effi

cienc

y (b

ps/H

z)

Proposed Clustering (simulationProposed Clustering (analytical lower bound)Proposed Clustering with ∆ EC=7

Proposed Clustering with ∆ EC=10

Proposed Clustering with ∆ EC=3

Random ClusteringFractional Frequency ReuseSingle Cell Operation

Performance improvement by edge-cutting

−10 −5 0 5 10 15 20 250

0.5

1

1.5

SNR (dB)

Sum

erg

odic

spec

tral e

fficie

ncy

(bps

/Hz)

Proposed Clustering (simulation)Proposed Clustering (analytical lower bound)Random ClusteringFractional Frequency ReuseSingle Cell Operation

Symmetric network case •  No need edge-cutting

Asymmetric network case •  More irregular •  Edge-cutting might be needed

2x 1.5x


Concluding remarks u  Main benefits

ª Any active user can communicate with two nearest BSs ª No BS is conflicted ª Can be combined with scheduling for greater gains

u  Possible drawbacks and solutions ª Only useful for pairwise cooperation? – Two is enough* ª  Edge-coloring demands too much complexity? – No done frequently ª Too many resources can be required? – Edge cutting

u  Application ª Carrier aggregation

u  Future direction ª Application to millimeter wave to reduce blockage effects

22 N. Lee, D. Morales, A. Lozano, and R. W. Heath, “Spectral Efficiency of Dynamic Coordinated Beamforming,” IEEE Transactions on Wireless Communications, 2015


Questions

23

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