1. 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. 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. 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. 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. 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. 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. 7. Institut fr Nachrichtentechnik Lower Bound from MSE-transceiver design 04.06.2015 7UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND ELEKTROTECHNIK
8. 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. 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. 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. 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. 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. 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. 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. 15. Institut fr Nachrichtentechnik 04.06.2015 15UNIVERSITT ROSTOCK | FAKULTT INFORMATIK UND ELEKTROTECHNIK Questions? Thanks for your kind attention.