Interference Alignment Approaches: Delayed CSIT and Alignment Matrix - - PowerPoint PPT Presentation

Interference Alignment Approaches: Delayed CSIT and Alignment Matrix

Jhanak Parajuli

Jacobs University Bremen Under Supervision of

• Prof. Dr. Giuseppe Abreu

January 20, 2015

Motivation

◮ INTERFERENCE: A major problem in multi-user network. ◮ C = dlog(SNR)+olog(SNR). ◮ At high SNR,

problem of capacity characterization= optimization of d.

◮ Interference Alignment is the approach to obtain the optimum d. ◮ In a K-User SISO interference channel optimum d = K 2 ,Each

user gets half the cake, regardless of the number of users.

◮ Interference is not a major problem anymore. ◮ IA aligns all the interference in a common lower dimensional

space.

An Example Scheme

3- User MIMO IA

TX1 . . . M1 Antennas RX1 . . . N1 Antennas TX1 . . . M2 Antennas RX2 . . . N2 Antennas TX1 . . . M3 Antennas RX3 . . . N3 Antennas H21 H11 V1 H31 H22 V2 H33 V3 H32 H12 H23 H13 H11V1 H12V2 H13V3 H22V2 H21V1 H23V3 H33V3 H31V1 H32V2

◮ Requirement of global

channel knowledge.

◮ Complexity increases

with increasing number of users. span(H12V2) = span(H13V3) at Rx1 ⇒ V2 = H−1

12 H13V3

span(H21V1) = span(H23V3) at Rx2 ⇒ V3 = H−1

23 H21V1

span(H31V1) = span(H32V2) at Rx3 ⇒ V1 = H−1

31 H32V2

⇒ V1 = H−1

31 H32H−1 12 H13V3

⇒ V1 = H−1

31 H32H−1 12 H13H−1 23 H21V1

⇒ V1 = eigv

• H−1

31 H32H−1 12 H13H−1 23 H21

Research Area

Approaches to mitigate the requirement of global channel knowledge

◮ Approach I: Design iterative algorithms minimizing the Leakage

interference and maximizing the received power ( Hybrid Optimization). Requires only the distributed channel knowledge.

◮ Approach II: Instantaneous CSIT is difficult to achieve. Delayed

CSIT is shown to improve the DoF using the concept of IA in MISO-BC by Maddah Ali and Tse in their latest works. Our research works on MISO-IFBC with delayed CSIT.

◮ We suggest that the achievable per cell DoF converges to K K+1 in

the case when M = K with delayed CSIT known perfectly. The DoF per cell approaches 1 as the number of users in each cell approach to infinity.

◮ Approach III: USe of Alignment Matrix, the concept used in

Non-linear manifold learning. Transmitters only require to know the local projection matrices.

Alignment Matrix

TX2 . . . M2 Antennas RX2 . . . N2 Antennas TX1 . . . M1 Antennas RX3 . . . N3 Antennas TX3 . . . M3 Antennas H21 H31 H23 H33 H22 H32 Desired Channel Interference Channel

The AM obtained from the sub-matrices Z1 ∈ C c1×l,··· ,Zs ∈ C cs×l of any matrix Z ∈ C N×l is defined as Φ =

s

∑

i=1

Pi, where Pi is obtained by embedding P⊥

Zi

into C N×N according to the position of the rows of Zi. Pi = [(IN)(Ji,:)]TP⊥

Zi(IN)(Ji,:) ∈ C N×N,

P⊥

Zi = I−PZi is the projection onto the

• rthogonal complement of range of Zi

and PZi = ZiZ†

i is the orthogonal

projection onto the range of Zi, while Z†

i

represents the Moore-Penrose pseudo inverse of Zi.