1. Institut fr Nachrichtentechnik 04.06.2015 UNIVERSITT ROSTOCK
| FAKULTT INFORMATIK UND ELEKTROTECHNIK Degrees of Freedom for
Interference Networks with Instantaneous Relays Amin Azari Tehran
University
2. Institut fr Nachrichtentechnik Motivation Find the maximum
achievable DoF for interference network with instantaneous
relay(s). How? Devise an achievable scheme, - Find lower bound via
this scheme Linear transceiver design - Find lower bound via
simulation Checking feasibility for polynomial system of equations
- Checking properness - Find upper bound (If the bound is the same
as lower bound, then?) Find upper bound by rate regions -
Investigating GDoF 04.06.2015 2UNIVERSITT ROSTOCK | FAKULTT
INFORMATIK UND ELEKTROTECHNIK
3. Institut fr Nachrichtentechnik Basics Interference Network
Interference Channel X channel Interference Alignment Conventional
Relays Instantaneous Relays 04.06.2015 3UNIVERSITT ROSTOCK |
FAKULTT INFORMATIK UND ELEKTROTECHNIK Different number of antennas
in each node , = , , + = , , , , [] = = , [] + [] = []
4. Institut fr Nachrichtentechnik Aligned Interference
Neutralization (AIN) Scheme Work is done in two steps: Align
Interference in relay Neutralized interference in destinations.
04.06.2015 4UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK We want to find bounds on its oprtaion. For 2-user
IC, DoF=1 For 2-user IC with IR, DoF=3/2
5. Institut fr Nachrichtentechnik Bound on DoA Using AIN
04.06.2015 5UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK Considering the necessary conditions for AIN in
Sources Relays Destinations We have found the maximum achievable
DoF in general interference network, and similified results have
been investigated for Interference Channel X Channel
6. Institut fr Nachrichtentechnik Lower Bound from
MSE-transceiver design Iterative algorithms for minimizing Sum-MSE,
Max-MSE, and Interference leakage have been investigated as linear
interference alignment schemes. 04.06.2015 6UNIVERSITT ROSTOCK |
FAKULTT INFORMATIK UND ELEKTROTECHNIK However, the total MSE
function is convex over each of the transmit/receive/processing
filter matrices; it is not convex on all the matrices jointly.
Power constraint at sources Power constraint at relays
7. Institut fr Nachrichtentechnik Lower Bound from
MSE-transceiver design 04.06.2015 7UNIVERSITT ROSTOCK | FAKULTT
INFORMATIK UND ELEKTROTECHNIK
8. Institut fr Nachrichtentechnik Upper Bound From Properness
of System 04.06.2015 8UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK Align all the interferences at kth destination in a
subspace of dimensions, and guarantee that there are free
dimensions for desired signals in kth destination. , = 0, rank( ,
)= , Number of equations number of variables polynomial system in
is proper. For generic channels (without structure) Improperness
infeasibility Satisfying the second condition by itself???
9. Institut fr Nachrichtentechnik Upper Bound From Properness
of System Channels are not generic Improperness infeasibility???
Using this inequality check the properness of polynomial system for
a given DoF tuple. For any DoF tuple, one could check this
inequality, and choose the best one. We did this in simulation
results. DoF tuple for 3U_IC:{1, 1, 1}, 0 04.06.2015 9UNIVERSITT
ROSTOCK | FAKULTT INFORMATIK UND ELEKTROTECHNIK , and are the
number of antennas at ith user, and relay, respectively for K-user
IC.
10. Institut fr Nachrichtentechnik SIMULATION RESULTS
04.06.2015 10UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK Normalized Sum DoF versus number of Relays for 3U-IC
0 1 2 3 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Nr DoF/M AIN.,=1 P,==1
AIN.,==1.5 P.,==1.5 AIN.,==2 P,==2 IA
11. Institut fr Nachrichtentechnik SIMULATION RESULTS
04.06.2015 11UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK Sum DoF versus number of antennas at each node for
s3r2. 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 Number of Antennas at each
node SumDoF TDMA IA AIN AIN-SE Proper Proper-SE MSE
12. Institut fr Nachrichtentechnik SIMULATION RESULTS
04.06.2015 12UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK 0 20 40 60 80 100 0 50 100 150 200 250 300 Number of
anttenas at each node SumDoF s3r1 s3r2 s3r3 s3r4 s3r5 s3r6 s3r7
Max. 3User 0 10 20 30 40 50 60 70 80 90 1 1.2 1.4 1.6 1.8 2 2.2 2.4
2.6 2.8 3 Number of Antennas at each node NormalizeSumDoF s3r1 s3r2
s3r3 s3r4 s3r5 s3r6 s3r7 Max. 3User 0 10 20 30 40 50 60 70 80 90 1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Number of Antennas at each
node NormalizeSumDoF s2r1 s2r2 s2r3 Max. 2User Number of antennas
at each node 72% Answer to our question, 6 months ago.
13. Institut fr Nachrichtentechnik Future works Rate regions
for instantaneous relay aided interference channel Generalized
Degrees of freedom Documentations Amin Azari, Farshad Lahouti, H.
Al-Shatri, and T. WeberAligned Interference Neutralization for
Instantaneous Relay Aided Interference Networks Amin Azari, Farshad
Lahouti, H. Al-Shatri, and T. WeberBounds on Achievable DoF in
Instantaneous Relay Aided Interference Channel 04.06.2015
13UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND ELEKTROTECHNIK
14. Institut fr Nachrichtentechnik 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. 34253441, Aug 2008. 2) Syed
A. Jafar, ``Interference Alignment: A New Look at Signal Dimensions
in a Communication Network'', Foundations and Trends in
Communications and Information Theory, Vol. 7, No. 1, pages: 1-136,
2011. 3) El Gamal and N. Hassanpour, Relay without Delay," in Proc.
IEEE ISIT 2005, Adelaide, Australia, Sep. 2005. 4) N. Lee and S. A.
Jafar, Aligned Interference Neutralization and the Degrees of
Freedom of the 2 User Interference Channel with Instantaneous
Relay, available at http://arxiv.org/abs/1102.3833, pp. 117, 2011.
04.06.2015 14UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND
ELEKTROTECHNIK
15. Institut fr Nachrichtentechnik 04.06.2015 15UNIVERSITT
ROSTOCK | FAKULTT INFORMATIK UND ELEKTROTECHNIK Questions? Thanks
for your kind attention.