degrees of freedom for interference networks aided by relays bounds and achievable schemes

Institut fürNachrichtentechnik

17.04.2023 University of Tehran, Faculty of Engineering, Department of Communication Engineering

Tehran University

ن خودپسندی مانع تحصیل علم است امام هادی ع:

و انسان را بسوی نادانی و خواری می کشاند.


2

Degrees of Freedom for Interference Networks aided by Relays: Bounds and achievable schemes

Amin Azari, Master Thesis Defense

Under supervision of:Prof. Lahouti (Supervisor)

Prof. Weber(Advisor)

Center for Wireless Multimedia Communication(CWMC)Communication Engineering Department

School of Electrical and Computer EngineeringFaculty of Engineering

University of Tehran


17.04.2023 3 University of Tehran, Faculty of Engineering, Department of Communication Engineering

Outline: Motivation System model and problem formulation First scenario: Full CSI at sources and relays

AIN extension lower bound on DoF MSE transceiver design lower bound on DoF Rank-based necessary conditions upper bound on DoF RIA scheme lower bound on DoF

Second scenario: Full CSI with secrecy constraint Rank-based necessary conditions upper bound on DoF

Third scenario: Limited CSI Rank-based necessary conditions upper bound on DoF

Conclusions

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Motivation:

Finding the maximum achievable DoF for KIC-JR Full CSI Limited CSI Secrecy constraints

Insights to the DoF performance of systems with Non-generic channels Keyhole channels

Devising Achievable schemes Full CSI Limited CSI Secrecy constraints

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Conclusions

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System model and Problem formulation:

K-User Interference Channel aided by J relays (KIC-JR)

- K sources- K paired destinations- J Relays

Problem formulation: Feasibility of a DoF touple

- General condition that should be satisfied by any DoF tuple achievable through linear IA

Achievable scheme for KIC-JR

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System model: relays

Conventional relay (relay with delay) Conventional relays cannot increase DoF in following scenarios

- Fully connected systems- Full CSI available in transmitters

Conventional relays can increase DoF in following scenarios- Partially connected systems- Limited CSI available in transmitters- No power constraint in relay

DoF performance of KU-IC is known no open problem

Instantaneous Relay: relay without delay For 2IC-1R, using AIN scheme, DoF improvement has been reported. The equivalent channels between sources and destinations, including

the relays, have structure. non generic The capacity region, and DoF performance is not known in theory.

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Instantaneous Relay: Full duplex relay with isolation Smart relays vs. dumb relays


System model: Instantaneous relays

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Conclusions

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AIN extension and evaluation:

Proposed for 2IC-1R (M antennas at each node) Work is done in two steps:

- Align streams at relay- Neutralize interferences at destinations

We extended this scheme to general IC. Considering the necessary conditions for AIN in

Source dimension:

Relay dimension, alignment:

Destination dimension, neutralization:

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AIN extension and evaluation:

We have found the upper bound on DoF of interference network any number of users, relays, and antennas at each node.

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Numerical Results for 3IC-JR via AIN

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Conclusion:• Lower bound of DoF of KIC-JR.

1 2 3 4 5 6 7 8 9 100

5

10

15

Number of antennas at each node

: S

um

De

gre

es

of F

ree

do

m

J=0 TDMAJ=0 IAMax DoFJ=1 AINJ=2 AINJ=3 AINJ=4 AINJ=5 AIN

d







Conclusions

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MSE-transceiver design and evaluation:

We investigated MSE transceiver design for KIC-JR

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MSE function Convex over each of the transmit/receive/processing filter matrices Not convex on all the matrices jointly

Propose Iterative algorithm Given two sets of filters, design the third set optimally Convergent, but convergence to global minimum is not guarantied.

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Given two sets of filters, the optimal expression for the other one:

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Simulation results:3IC-JR, J=1:2

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Conclusion:• Lower bound on DoF of KIC-JR• Numerical insights to the DoF performance of KIC-JR

d 1 2 3 4 5 60

2

4

6

8

10

12

14

Number of antennas at each node

: S

um

De

gre

es

of F

ree

do

m

TDMAIAAIN-1IRSMSEM-1IRAIN-2IRsSMSEM-2IRs



Simulation results: signal space analysis after SMSEM convergence

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System model: 2IC-1RNumber of antennas at each node=2Sum DoF = 3

Destination 1

Destination 2

Source 1

Source 2

rank()=1 ?!rank()=1 ?!

Conclusion:• Insight to optimal structure of achievable scheme

d







Conclusions

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Checking feasibility of equations imposed by DoF touple:

Linear Interference Alignment equations imposed by DoF touple:

Theorem 5.1 in Report : Rank based necessary conditions for satisfying above equations:

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Upper Bound From feasibility checking

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Lemma 5.1 in report: Minimum number of elements in a random designed matrix, which should be changed for rank deficiency.

d

Counting the number of equations, and free variables for aligning signals in dimensions:




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Theorem 5.2 in report: The equivalent channel between ith souce and kth destination () should have rank deficiency.

Counting the number of equation, and free variables:




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Available dimensions

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Lemma 5.2 in report: For any two users and in KIC-1R, the sum of and should be less equal than .



Main theoretical results from analysis of upper bound:

Exact DoF Performance of 2IC-JR, each node is equipped with antennas: J=0

- DoF= Theorem 5.6 in report J=1

- DoF= Theorem 5.4 in report J2

- DoF=2 Theorem 5.5 in report

Exact DoF Performance of KIC-()R, each node is equipped with antennas: DoF= Theorem 5.5 in report

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Numerical Results for 3IC-JR, J=1:2

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Conclusion:• Upper bound on DoF of KIC-JR• Insight to optimal structure of achievable scheme

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Conclusions

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Restricted Interference Alignment (RIA) scheme

First Step: Restricting interferences of each transmitter

- Rank deficiency of cross channels- Using the rank deficient cross channels:

– Alignment by transmit filters– Neutralization by transmit filters– Alignment-Neutralization by transmit filters, and relays

Second Step: Aligning interferences from all sources in each destination.

Third Step: Zero forcing at each destination.

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U1

U2

U1

U2

U3 U3

RIA for 3IC-2R

First Step Second Step Third Step

R1

R2

d




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Conclusion:• Design a Near optimal achievable scheme for KIC-JR• Lower bound on DoF of KIC-JR d







Conclusions

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KIC-JR with secrecy constraints

Existent methods in literature: Artificial Noise Alignment

- Proposed for 2U-IC- Not efficient, especially when K is more than 2.

Interference Alignment for Secrecy- Efficient, but not secure when 2 (or more) eavesdroppers

cooperate.

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KIC-JR with secrecy constraints

Using Instantaneous relays: Rank deficient cross channels Null-space based transmit filters Resistant to any kind of cooperation between eavesdroppers.

We have investigated the upper bounds on achievable SDoF.

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Conclusions

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KIC-JR with limited CSI

Availability of total CSI at transmitters may be impossible. The instantaneous relays are responsible for two phases of RIA:

Restricting interferences of each transmitter. Aligning interferences from all sources in each destination.

We have investigated the upper bounds on achievable DoF for KIC-JR, without CSI at transmitters.

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Normalized DoF with limited CSINormalized secure DoF d

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

Number of Antennas at each node

No

rma

lize

d s

um

SD

oF

an

d s

um

Do

F w

itho

ut C

SI







Conclusions

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Contributions and conclusion:

Different scenarios: Full CSI Limited CSI Secrecy constraints

Schemes: Designing, and evaluating RIA scheme Designing, and evaluating SMSEM scheme Extending, and evaluating AIN scheme

DoF performance Exact DoF performance of 2IC-JR Exact DoF performance of KIC-()R Lower bound for DoF of KIC-JR Upper bound for DoF of KIC-JR Upper bound for Secure DoF of KIC-JR Upper bound for DoF of KIC-JR with limited CSI

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Future Works:

DoF performance of non-generic channels Exact DoF performance of KIC-JR Generalized DoF performance of KIC-JR

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References

1) V. R. Cadambe and S. A. Jafar, “Interference alignment and the degrees of freedom for the K user interference channel,” IEEE Transactions on Information Theory, vol. 54, no. 8, pp. 3425–3441, Aug 2008.

2) El Gamal, A.; Hassanpour, N., "Relay-without-delay," Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on , vol., no., pp.1078,1080, 4-9 Sept. 2005

3) Lee, Namyoon, and Syed A. Jafar. "Aligned interference neutralization and the degrees of freedom of the 2 user interference channel with instantaneous relay."arXiv preprint arXiv:1102.3833 (2011).

4) Xie, Jianwei, and Sennur Ulukus. "Secure degrees of freedom of one-hop wireless networks." arXiv preprint arXiv:1209.5370 (2012).

5) Yetis, C.M.; Tiangao Gou; Jafar, S.A.; Kayran, A.H., "Feasibility Conditions for Interference Alignment," Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE , vol., no., pp.1,6, Nov. 30 2009-Dec. 4 2009

6) Hui Shen; Bin Li; Meixia Tao; Xiaodong Wang, "MSE-Based Transceiver Designs for the MIMO Interference Channel," Wireless Communications, IEEE Transactions on , vol.9, no.11, pp.3480,3489, November 2010

7) Razaviyayn, M.; Lyubeznik, G.; Zhi-Quan Luo, "On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel," Signal Processing, IEEE Transactions on , vol.60, no.2, pp.812,821, Feb. 2012

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Thanks for your kind attention.

Questions?

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Supporting Slides



Interference alignment

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AIN scheme: 2IC-1R

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Simulation Results

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-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Stream 1,1 via DL

Stream 2,1 via DLStream 1,2 via DL

Stream 1,1 via RL

Stream 2,1 via RL

Stream 1,2 via RL

Resultant Stream 1,1Resultant Stream 2,1

Resultant Stream 1,2

2 desired streams

Interfering stream is cancelled

-2 -1.5 -1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Stream 1,1 via DLStream 2,1 via DL

Stream 1,2 via DL

Stream 1,1 via RL

Stream 2,1 via RLStream 1,2 via RL

Resultant Stream 1,1

Resultant Stream 2,1Resultant Stream 1,2

2 interfering streamsare aligned and

occupied1 dimensionDesired stream

Received streams at user 1 of 2IC-1R, and M=2.

Received streams at user 2 of 2IC-1R, and M=2.

degrees of freedom for interference networks aided by relays bounds and achievable schemes

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