Blind Interference Alignmentfor

Small CellsFurkan Can Kavasoglu

Yichao Huang

2/28/13

Outline• Background

• Related Papers in Literature• Blind Interference Alignment• Small Cells

• Initial Steps• BIA Design Based on Clustered Small Cells (Intra vs Inter-cell Interference)• Problem Definition and System Model• Rate Equations• Simulation Results

• Further Steps• Power Control• Scheduling / Code Assignment• Performance with non constant channel assumption• Super-symbol design at Transmitter Side• Partial Connectivity / Threshold Design• Soft Clustering / Graph Model

BACKGROUND• Related Papers in Literature• Blind Interference Alignment• Small Cells

Related Papers In Literature2010 :

“Exploiting Channel Correlations –Simple Interference Alignment Schemes with no CSIT”Syed Ali Jafar. Globecom 2010

2011:

“Aiming Perfectly in the Dark –Blind Interference Alignment Through Staggered Antenna Switching” Tiangao Gou, Chenwei Wang , Syed Ali Jafar. IEEE Trans on Signal Processing June 2011

“Design and Operation of Blind Interference Alignment in Cellular and Cluster Based Systems” Chenwei Wang, Haralabos C. Papadopulos, Sean A. Ramprashad, Giuseppe CaireITA 11

“Improved Blind Interference Alignment in a Cellular Environment using Power Allocation and Cell Based Clusters” Chenwei Wang, Haralabos C. Papadopulos, Sean A. Ramprashad, Giuseppe Caire. ICC 11

2012:

“Blind Interference Alignment” Syed Ali Jafar. IEEE JSAC June 2012

“Elements of Cellular Blind Interference Alignment Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity” Syed Ali Jafar arXiv March 2012

“Data Sharing Coordination and Blind Interference Alignment for Cellular Networks” Salam Akoum, Chung Shue Chen, Merouane Debbah, Robert W. Heath Jr. Globecom 2012

2013:

“Topological Interference Management through Index Coding” Syed Ali Jafar. arXiv January 2013

Blind Interference Alignment

• Blind Interference Alignment Scheme for vector broadcast channel:• Transmitter with M antennas• K receivers each equipped with a reconfigurable antenna can switch among

M preset modes• Key Insight: BIA is achieved because of the ability of the receivers to switch

between reconfigurable antenna modes to create short term channel fluctuations patterns that are exploited by the transmitter

Blind Interference Alignment

• System Model:

• 2x1 MISO BC

Blind Interference Alignment

• K User 2x1 MISO BC

Blind Interference Alignment

• 2 User 3x1 MISO BC

Blind Interference Alignment

• 3 User 3x1 MISO BC

Small Cells

INITIAL STEPS• BIA Design Based on Clustered Small Cells (Intra vs Inter-

cell Interference)• Problem Definition and System Model• Rate Equations• Simulation Results

BIA Design on Clustered Small Cells

• BIA is firstly designed for K user MISO Broadcast Channels

• It completely removes the intra cell interference

• Then for cellular network consideration of BIA:• Synchronized same BIA code usage across all cells (assume reaming

interference as noise)• Network coordination (clustering and data sharing) and deal with all cellular

network as one MISO Channel

• Some problems may arise for small cell scenario. Note that each small cell serves very limited number of users

Synchronized BIA Across All Cells

• The main problem is that since the number of users in each cell is small, then the

ratio of 𝑅𝑒𝑎𝑚𝑖𝑛𝑔 𝐼𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑛𝑐𝑒

𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑛𝑐𝑒still be high

• Then how to deal with the inter-cell interference for small cells ?

Network Coordination and Clustering

• Consider network as a clustered /coordinated big cell• No inter-cell interference• Cost:

• Data Exchange• Super symbol structure become long

Proposed Transmission Scheme

• Aim is as follows:• Use BIA code so that nobody in the neighboring small cells do not

use the same code.

• By doing this we will cope with the inter-cell interfering users (unlike Synchronized BIA)

• Still we need to design a transmission scheme across all small cells (that may have some inter-cell interference effect to each other) so that :

• We can use Mx1 MISO BIA code for NK user over N small cells

Comparison

Rate Equations – Sync BIA

• Normalized rate for user k (C = cluster size, N=number of cells)

𝑆𝑦𝑛𝑐 𝐵𝐼𝐴 =𝑀 − 1 𝐾−1

𝑀 − 1 𝐾 + 𝐾 𝑀 − 1 𝐾−1 E 𝑙𝑜𝑔𝑑𝑒𝑡 𝐼 +𝐾 +𝑀 − 1 𝑃

𝑀2𝐾𝐻1

𝑘𝐻1

𝑘 +

𝑅𝑧−1

𝑅𝑧 = 𝑁𝑜𝐼 + 𝑖=2𝐶 𝑃 𝐾+𝑀−1

𝑀2𝐾𝐻𝑖

𝑘𝐻𝑖

𝑘 ++ 𝑗=1,𝑗∉𝐶

𝑁 𝑃( 𝐻𝑗𝑘 𝐻𝑗

𝑘 +)

𝐻𝑖𝑘= 𝑔(𝑑𝑖,𝑘)

1

𝐾ℎ𝑖

𝑘(1)

1

𝐾ℎ𝑖

𝑘(2)

⋮1

𝐾ℎ𝑖

𝑘(𝑀 − 1)

ℎ𝑖𝑘(𝑀)

𝐻𝑖𝑘= 𝑔(𝑑𝑖,𝑘)

ℎ𝑖𝑘(1)

ℎ𝑖𝑘(2)

⋮

ℎ𝑖𝑘(𝑀 − 1)

ℎ𝑖𝑘(𝑀)

Rate Equations – Prop BIA

𝑃𝑟𝑜𝑝. 𝐵𝐼𝐴 =𝑀 − 1 𝐶𝐾−1

𝑀 − 1 𝐶𝐾 + 𝐶𝐾 𝑀 − 1 𝐶𝐾−1 E 𝑙𝑜𝑔𝑑𝑒𝑡 𝐼 +𝐶𝐾 +𝑀 − 1 𝑃

𝑀2𝐶𝐾𝐻1

𝑘𝐻1

𝑘 +

𝑅𝑧−1

𝐻𝑖𝑘= 𝑔(𝑑𝑖,𝑘)

1

𝐶𝐾ℎ𝑖

𝑘(1)

1

𝐶𝐾ℎ𝑖

𝑘(2)

⋮1

𝐶𝐾ℎ𝑖

𝑘(𝑀 − 1)

ℎ𝑖𝑘(𝑀)

𝑅𝑧 = 𝑁𝑜𝐼 + 𝑗=1,𝑗∉𝐶𝑁 𝑃( 𝐻𝑗

𝑘 𝐻𝑗𝑘 +

)

𝐻𝑖𝑘= 𝑔(𝑑𝑖,𝑘)

ℎ𝑖𝑘(1)

ℎ𝑖𝑘(2)

⋮

ℎ𝑖𝑘(𝑀 − 1)

ℎ𝑖𝑘(𝑀)

Rate Equations –Network BIA

𝑁𝑒𝑡𝑤 𝐵𝐼𝐴 =𝐶𝑀 − 1 𝐶𝐾−1

𝐶𝑀 − 1 𝐶𝐾 + 𝐶𝐾 𝐶𝑀 − 1 𝐶𝐾−1E 𝑙𝑜𝑔𝑑𝑒𝑡 𝐼 +

𝐶𝐾 + 𝐶𝑀 − 1 𝑃

(𝐶𝑀)2𝐶𝐾𝐻 𝑘 𝐻 𝑘 +

𝑅𝑧−1

𝐻 𝑘 =

𝑔(𝑑1,𝑘)

𝐶𝐾ℎ1

𝑘1

𝑔(𝑑2,𝑘)

𝐶𝐾ℎ2

𝑘1 ⋯

𝑔(𝑑𝐶,𝑘)

𝐶𝐾ℎ𝐶

𝑘1

𝑔(𝑑1,𝑘)

𝐶𝐾ℎ1

𝑘2

𝑔(𝑑2,𝑘)

𝐶𝐾ℎ2

𝑘2 ⋯

𝑔(𝑑𝐶,𝑘)

𝐶𝐾ℎ𝐶

𝑘2

⋮⋮

𝑔(𝑑1,𝑘)

𝐶𝐾ℎ1

𝑘(𝐶𝑀 − 1)

𝑔(𝑑2,𝑘)

𝐶𝐾ℎ2

𝑘𝐶𝑀 − 1 ⋯

𝑔(𝑑𝐶,𝑘)

𝐶𝐾ℎ𝐶

𝑘𝐶𝑀 − 1

𝑔(𝑑1,𝑘)

𝐶𝐾ℎ1

𝑘𝐶𝑀

𝑔(𝑑2,𝑘)

𝐶𝐾ℎ2

𝑘𝐶𝑀 ⋯

𝑔(𝑑𝐶,𝑘)

𝐶𝐾ℎ𝐶

𝑘𝐶𝑀

𝑅𝑧 = 𝑁𝑜𝐼 + 𝑗=1,𝑗∉𝐶𝑁 𝑃( 𝐻𝑗

𝑘 𝐻𝑗𝑘 +

)

𝐻𝑖𝑘= 𝑔(𝑑𝑖,𝑘)

ℎ𝑖𝑘(1)

ℎ𝑖𝑘(2)

⋮

ℎ𝑖𝑘(𝐶𝑀 − 1)

ℎ𝑖𝑘(𝐶𝑀)

Simulation

• (M=2 , K=2, C = 1-9, N=100)• Over 2D model of small cells 10x10 grid• 2 transmit antenna at each base station, each user has one receive

antenna• Cluster size from 1 cell to 9 cells.• Small cell power P=20dBm• Cell range 30m• Path loss 15.3+37.6*log(d)• Noise No= -104dBm• Users located (2 user at each base station) at distance d symmetrically

(horizontally), change d from 1 to 30m.• Calculate rate for one user and multiply with CN (Each user is

symmetric). Total Cluster Network Rate (Normalized for each time slot)

Simulation

200 250 300 350

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0 5 10 15 20 25 3020

25

30

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Distance (meters)

Tota

l N

etw

ork

Rate

N=1 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

0 5 10 15 20 25 3015

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Distance (meters)

Tota

l N

etw

ork

Rate

N=2 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

200 250 300 350

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Simulation

0 5 10 15 20 25 3010

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Distance (meters)

Tota

l N

etw

ork

Rate

N=3 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

200 250 300 350

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0 5 10 15 20 25 300

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Distance (meters)

Tota

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ork

Rate

N=5 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

Simulation

0 100 200 300 400 500 6000

100

200

300

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600

0 5 10 15 20 25 300

5

10

15

20

25

Distance (meters)

Tota

l N

etw

ork

Rate

N=1 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

0 5 10 15 20 25 300

10

20

30

40

50

60

70

Distance (meters)

Tota

l N

etw

ork

Rate

N=3 / Rate is normalized for each time slot

Sync BIA

Proposed Solution

Network Coordination

0 100 200 300 400 500 6000

100

200

300

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500

600

FURTHER STEPS• Power Control• Scheduling / Code Assignment• Performance with non constant channel assumption• Super-symbol design at Transmitter Side• Partial Connectivity / Threshold Design• Soft Clustering / Graph Model

Super Symbol Design At Transmitter Side

• Using Random unitary matrix at transmitter side

𝑋 =𝑈1𝑈10

𝑥11

𝑥21 +

𝑈20𝑈2

𝑥12

𝑥22

𝑦1(1)

𝑦1(2)

𝑦1(3)

=ℎ𝑈1ℎ𝑈10

𝑥11

𝑥21 +

ℎ𝑈20ℎ𝑈2

𝑥12

𝑥22

𝑦2(1)

𝑦2(2)

𝑦2(3)

=

𝑔𝑈20

𝑔𝑈2

𝑥12

𝑥22 +

𝑔𝑈1𝑔𝑈10

𝑥11

𝑥21

Rank 1 Interference to be canceled

𝑋 =𝑈1𝑈20

𝑥11

𝑥21 +

𝑈20𝑈2

𝑥12

𝑥22 -Again one user still have rank 1 instead of full rank

-Super-symbol design should be longer if we want to create the diversity at transmitter side

THANK YOU