Flexible Backhaul Design for Cellular Interference Management · 2015-03-25 · Flexible Backhaul...

transcript

Flexible Backhaul Design for Cellular Interference Management

Venu Veeravalli

Director, Illinois Center for Wireless Systems

Coordinated Science Lab

ECE Department University of Illinois at Urbana-Champaign

Interference in Cellular Networks

Interference Management is critical in dense wireless networks

Veeravalli – ICNC 2/18/15

K-User Interference Channel

Tx1 Rx1

Information Theory & Interference Management

•  Exact characterization of capacity o  Very hard problem; still mostly

•  Approximate characterization of capacity o  Within constant number of bits/sec o  Provides some architectural

insights

•  Degrees of freedom (DoF) o  Pre-log factor of sum-capacity in

high SNR regime o  Number of interference free

sessions per channel use o  Simplest of the three, but can

provide useful insights

Tx1 Rx1

DoF and PUDoF for K-User IC

•  User orthogonalization o  Every user gets an

interference free channel once every K channel uses

o  DoF = 1 or Per User DoF (PUDoF) = 1/K.

•  Outer Bound on DoF [Host-Madsen, Nosratinia ‘05] o  DoF ≤ K/2 or PUDoF ≤ 1/2

•  Amazingly, this outer bound is

achievable via linear interference suppression!

Interference Alignment [Cadambe & Jafar ‘08]

Tx1 Rx1

Linear Transmit/Receive Strategies

Interference Channel

End-to-End matrix is Diagonal è No Interference!

# streams = Size of the Diagonal matrix

Channel

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

[1,1] [1,2] [1,3]

[2,1] [2,2] [2,3]

[3,1] [3,2] [3,3]

Transmit Beams

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Receive Beams

U[1] 0 00 U[2] 00 0 U[3]

⎢⎢⎢⎢

⎥⎥⎥⎥

Interference Alignment with Symbol Extensions (Cadambe & Jafar)

3 Symbol Extensions

4 interference free streams è PUDoF = 4/9

Asymptotic Interference Alignment

# symbol extensions

PUDoF of 0.5 is achieved asymptotically

0 20 40 60 80 1000.44

Asymptotic Interference Alignment

# symbol extensions

0 200 400 600 800 1000 1200 14000.32

0.53 User

4 User

Choi, S.W. and Jafar, S.A. and Chung, S.Y. , “On the beamforming design for efficient interference alignment”, IEEE Communication Letters , 2009

Interference Alignment: Summary

+  Achieves optimal PUDoF for fully connected channel

-  Requires global channel state information (CSI)

-  Requires large number of symbol extensions

Tx Cooperation Through the Backhaul: DoF Analysis

Transmitter Cooperation – 2 Users

No Cooperation Per user DoF = 1/2

Time Sharing

Full Cooperation Per user DoF = 1

Zero-Forcing Tx beams

Tx1 W1

Tx2 W2 Rx2

Rx1 Tx1 W1

Tx2 W2 Rx2

Backhaul

Transmitter Cooperation – K Users

Per user DoF = 1/2 Interference Alignment

Per user DoF = 1 Zero-Forcing Tx beams

(Broadcast Channel)

•  To achieve PUDoF of 1: o  every message needs to be known at every Tx o  Load on backhaul network increases by a factor of K

•  What happens with partial cooperation?

K-User Interference Channel No Cooperation

K-User Interference Channel Full Cooperation

Cooperative Transmission with Transmit Set Size Constraint

•  Each message is jointly transmitted using at most M transmitters (max backhaul

load factor = M )

•  Message i transmitted

jointly using transmitters in set

•  Consider all message

assignments satisfying cooperation constraint

Ti, |T

i| ≤ M

Backhaul

Tx1 W1

Tx2 W2 Rx2

Tx3 W3 Rx3

Cooperative Transmission: Clustering

Per user DoF = 1/2

Achievable w/o any cooperation!

No Degrees of Freedom Gain!

Tx1 W1

Tx2 W2 Rx2

Tx3 W3

Tx4 W4 Rx4

Cooperative Transmission: Spiral Message Assignments

Wi is available at transmitters {i,i+1,…,i+M-1}

Tx1 W1

Tx2 W2 Rx2

TxM WM

TxM+1 WM+1 RxM+1

Backhaul

Partial Cooperation: Matrix Interpretation

Channel

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

[1,1] [1,2] [1,3]

[2,1] [2,2] [2,3]

[3,1] [3,2] [3,3]

Transmit Beams

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Receive Beams

U[1] 0 00 U[2] 00 0 U[3]

⎢⎢⎢⎢

⎥⎥⎥⎥

H[1] [3]1 2[1] [2]2 1

[2] [3]2 1

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

M: # non-zero blocks in the columns of V

Example: K=3, M=2

Each receiver chooses an interference direction Transmitters oblige the receivers

PUDoF of 2/3 with only 3 symbol extensions

Tx1 W1

Tx2 W2 Rx2

Tx3 W3 Rx3

Spiral Message Assignment: Results [Annapureddy, El Gamal, VVV – IT’12]

•  DoF with spiral message assignment satisfies:

•  Proof of Achievability:

o  First M-1 users enjoy interference-free communication

o  Interference occupies half signal space at each other

receiver

Generalization of interference alignment scheme

K +M −1

2≤ DoF(K,M ) ≤dK +M −1

Fully Connected IC with Cooperative Transmission: Summary

•  Transmit cooperation constraint M < K

•  Spiral assignment: backhaul load factor = M

•  Interference alignment can be used to achieve DoF gains

•  Symbol extension requirements less stringent

•  As K is increased with M fixed, PUDoF è 1/2

No asymptotic PUDoF gain!

Backhaul

Tx1 W1

Tx2 W2 Rx2

Tx3 W3 Rx3

Tx Cooperation in Locally (Partially) Connected Interference Networks

Locally (partially) connected interference channel!

Locally Connected IC Model

Wyner Model: L =1

Tx i is connected to receivers {i, i+1,…, i+L}

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5

Results for Wyner Model [Lapidoth, Shamai, Wigger ‘07]

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 Tx5

Rx6 Tx6

Backhaul load factor =1

PUDoF (L=1,M=2) = 2/3 > 1/2

Results for Wyner Model [Lapidoth, Shamai, Wigger ‘07]

•  Spiral transmit sets

•  PUDoF (L=1,M) = M/(M+1) Backhaul load factor = M/2

•  Local cooperation can achieve PUDoF gains for locally connected channels

•  Achievable scheme relies on only: o  Zero-forcing transmit beamforming

o  Local CSI

o  Fractional reuse

•  No interference alignment/symbol extensions

Is spiral message assignment optimal?

Example with M=1

Interference-aware message assignment + Fractional reuse

PUDoF(L =1,M =1) = 1

2 PUDoF(L =1,M =1) = 23

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Example: Wyner Interference Model

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 X5

Backhaul load factor =6/5 PUDoF (L=1,M=2) = 4/5 > 2/3

Locally Connected IC with Cooperative Transmission [El Gamal, Annapureddy, VVV, IT ‘14]

•  Result: Under cooperation constraint of M

•  Corollary:

• With interference avoidance constraint:

2M + L≤ PUDoF(L,M ) ≤ 2M + L −1

2M + L

PUDoF(L =1,M ) = 2M

PUDoF(L,M ) = 2M

2M + L

DoF Upper Bound: Useful Message Assignments

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Assigning W3 to Tx1 not useful

Cooperative Transmission for IC: Summary

•  Local Cooperation o  no PUDoF gain for fully connected channel

o  is optimal for locally connected channel

•  Interference aware message assignments allow for higher throughput

•  Fractional reuse and zero-forcing transmit beam-forming are sufficient to achieve PUDoF gains, without need for symbol extensions and interference alignment

Tx Cooperation with Backhaul Load Constraint

Backhaul Load Constraint

• More natural cooperation constraint that takes into account overall backhaul load:

|i∈[K ]∑ T

K≤ B

•  Solution under transmit set size constraint can be used to provide solutions under backhaul load constraint

Wyner’s Model with Backhaul Load Constraint

Result:

PUDoF(B) = 4B −1

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Recall: PUDoF(M ) = 2M

Coding Scheme for B=1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 X5

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

3 PUDoF = 2

5 PUDoF = 4

8users

PUDoF (B =1) = 3

Application to L-connected network

Result: Using only zero-forcing transmit beamforming and fractional reuse:

Tx i is connected to receivers {i, i+1,…, i+L}

PUDoF(L,B =1) ≥ 1

2,∀L ≤ 6

without need for interference alignment and symbol extensions

Rx1 Tx1

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx5 Rx5

Locally (partially) connected interference channel!

Interference Graph for Single Tier

Tx,Rx pair

Interference Graph without Intrasector Interference

Partition into Noninterfering Tx-Rx pairs

Rx2 Tx2

Rx3 Tx3

Rx4 Tx4

Tx1 Rx1

Rx5 Tx5

Rx6 Tx6

B = 6 × 6

9= 4; PUDoF = 6

Rx2 Tx2

Rx3 Tx3

Tx6 Rx6

Rx1 W1

3; PUDoF = 4

PUDoF without Intrasector Interference

PUDoF = 7/15 with backhaul load factor B = 1

Cooperation through Backhaul

•  Similar gains in DoF for other cellular interference models, with only zero-forcing and fractional reuse •  Gains improve with asymmetric cooperation and

interference aware message assignment •  Gains in DoF can also be obtained for uplink with

decoded messages being exchanged through backhaul [V. Ntranos, M. Maddah-Ali, G. Caire ‘14]

o  Requires multiple antennas at both mobiles and basestations

o  For same backhaul load factor, gain is smaller than on downlink with Tx cooperation

Summary

•  Infrastructure enhancements in backhaul can be exploited through cooperative transmission to lead to significant rate gains o Minimal or no increase in backhaul load o  Fractional reuse and zero-forcing transmit beam-

forming are sufficient to achieve rate gains o No need for symbol extensions and interference

alignment •  Open Questions:

o  Partial/unknown CSI o Network dynamics and robustness to link erasures o  Joint design with message passing schemes for

uplink

References

•  V. Cadambe and S. A. Jafar, “Interference Alignment and Degrees of Freedom of the K-User Interference Channel,” IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3425 –3441, Aug. 2008.

•  V. S. Annapureddy, A. El Gamal, and V. V. Veervalli, “Degrees of Freedom of Interference Channels with CoMP Transmission and Reception,” IEEE Trans. Inf. Theory, vol. 58, no. 9, pp. 5740-5760, Sep. 2012.

•  A. Wyner, “Shannon-Theoretic Approach to a Gaussian Cellular Multiple-Access Channel,” IEEE Trans. Info Theory, vol. 40, no. 5, pp.1713 –1727, Nov. 1994.

•  A. Lapidoth, S. Shamai (Shitz) and M. A. Wigger, “A linear interference network with local Side-Information,” in Proc. IEEE International Symposium on Information Theory (ISIT), Nice, Jun. 2007. Also in IEEE Trans. on Information Theory 2014.

•  A. ElGamal, V.S. Annapureddy, and V.V. Veeravalli. “Interference Channels with CoMP: Degrees of Freedom, Message Assignment, and Fractional Reuse.” IEEE Transactions on Information Theory, 60(6): 3483-3498, June 2014.

•  A. El Gamal, V. V. Veeravalli, ”Flexible backhaul design and degrees of freedom for linear interference networks,” in Proc. IEEE International Symposium on Information Theory (ISIT), pp.2694-2698, Hawaii, June-July 2014.

•  V. Ntranos, M. A. Maddah-Ali, and G. Caire, “Cellular interference alignment,” CoRR, vol. abs/1402.3119, 2014. [Online]. Available: http://arxiv.org/abs/1402.3119

Flexible Backhaul Design for Cellular Interference Management · 2015-03-25 · Flexible Backhaul...

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