Retrospective Interference Alignment for the 3-user MIMO Interference Channel with Delayed CSIT

1. Retrospective Interference Alignmentfor the 3-user MIMO Interference Channel with Delayed CSIT M. Torrellas, A. Agustin and J. Vidal Universitat Politècnica Catalunya (UPC) marc.torrellas.socastro@upc.edu

2. Motivation • Manyworkshaveshownthat use of linear beamforming at transmitters and receivers can be used to manageinterference in wirelessnetworks. • In thecontext of theinterferencechannel (IC), InterferenceAlignment (IA) conceptsprovideeachuserhalfthe cake but... • at thecost of assumingperfect and instantaneouschannelstateinformation at thetransmitterside (CSIT) • Whataboutfeedbackerrors? And feedbackdelay? • Maddah-Ali et al. (MAT) proposedthedelayedCSITframeworkin [MAT12], wherecompletelyoutdatedCSIT can be exploitedforIA in theBC. Thistype of IAwassubsequentlydenoted as RetrospectiveIA (RIA) and extended to the SISO IC. • Weextendthose ideas to theMIMO IC case, and getinsightintohowadditionalantennas at eachsideimpactthe total degrees of freedom (DoF) of a networkwithdelayed CSIT.

3. Summary System model Review of RIA for SISO RIA for MIMO Results Conclusions

4. System Model • Eachtransmitterdeliversbsymbols toitspair • Weconsidertwophases (W = W1 + W2) • InterferingSensing (IS) phase • RIA phase • Allterminals are active duringallphases • Output at thej-th receiver,phasep, slot s: RIA IS

5. System Model • Letconsiderthesignalsreceived at user1alongthefirstphase: • We can groupthesesignals as follows • with interference desired

6. IA constraints and DoF • This is written in general as

7. System Model – CSIT definition • Assuming full CSIR, each receiver doesthefollowingoperation at theend of theISphase: • : ZFfilterpreservinginterferencefromtxi at rxj • : interferencecausedbytxi at rxj,with CSIT to be reportedtotxiafterthefirstphase:

8. Review of RIA for SISO [Maleki12] • ISphase: alluserstransmitsimultaneouslywithrandomi.i.dentries • CSIreport: acquisition of • RIAphase: eachuseraims to alignthetransmittedsignals at bothrxs • Thiswaythetransmittedsignalsprovide linear combinations of desiredsignals, whilemaintainingtherank of receivedinterference

9. RIA for MIMO - Constraints • Constraints that make the scheme reliable for any given antenna setting: • First phase ZF filters • Intersection subspace: • Receiver Space-Time dimensions: • Rank of desired signals after zero-forcing:

10. RIA for MIMO – Problem statement • Overall, the problem is written as

11. RIA for MIMO – Solution • Fortherangetheoptimalvaluesare foundto be • with

12. Results • The achievable DoF as a function of • A: Manyrxantennas, no need of CSIT • C: [Abdoli13] Scaled SISO ICscheme • D: [Vaze12] 2-userICschemes

13. Results • The achievable DoF as a function of • A: Manyrxantennas, no need of CSIT • B: RIAforMIMO. UsefulforN > M • C: [Abdoli13] Scaled SISO ICscheme • D: [Vaze12] 2-userICschemes • [TAV14] presented at ICASSP14

14. Conclusions • We extend the RIA scheme of Maleki et al. for the MIMO case • Ourapproachisbasedonformulating a maximizationproblem, validforanyantennasetting (M,N) • New DoF inner bounds are provided as a function of the ratio among tx/rx antennas and compared with other approaches • Future work: MIMO or K-user extension for other schemes using similar tools, improve outer bounds for the MIMO IC with delayed CSIT

15. Thanks for your attention M. Torrellas, A. Agustin and J. Vidal Universitat Politècnica Catalunya (UPC) marc.torrellas.socastro@upc.edu

16. Backup slides