retrospective interference alignment for the 3-user mimo interference channel with delayed csit

May 7, 2014, Florence, Italyhttp://ict-tropic.eu http://spcom.upc.edu

Retrospective Interference Alignmentfor the 3-user MIMO Interference

Channel with Delayed CSIT

M. Torrellas, A. Agustin and J. VidalUniversitat Politècnica Catalunya (UPC)

[email protected]

2

Motivation

Many works have shown that use of linear beamforming at transmitters and receivers can be used to manage interference in wireless networks.

In the context of the interference channel (IC), Interference Alignment (IA) concepts provide each user half the cake but...

at the cost of assuming perfect and instantaneous channel state information at the transmitter side (CSIT)

What about feedback errors? And feedback delay?

Maddah-Ali et al. (MAT) proposed the delayed CSIT framework in [MAT12], where completely outdated CSIT can be exploited for IA in the BC. This type of IA was subsequently denoted as Retrospective IA (RIA) and extended to the SISO IC.

We extend those ideas to the MIMO IC case, and get insight into how additional antennas at each side impact the total degrees of freedom (DoF) of a network with delayed CSIT.

[MAT12] M.A. Maddah-Ali and D. Tse, "Completely Stale Transmitter Channel State Information is Still Very Useful"

IEEE Trans. Inf. Theory, June 2012

Summary

3

1. System model

2. Review of RIA for SISO

3. RIA for MIMO

4. Results

5. Conclusions

4

System Model

Each transmitter delivers b symbols to its

pair

We consider two phases (W = W1 + W2)

Interfering Sensing (IS) phase

RIA phase

All terminals are active during all phases

Output at the j-th receiver, phase p, slot

s : 1 1N M M b b N 1N

IS RIA

1W 2W

5

System Model

Let consider the signals received at user 1 along the first

phase:

We can group these signals as follows

with

desired interference

6

IA constraints and DoF

This is written in general as

NW MW

1 b b NW

p pNW MW

pMW b

MW b

1 21

2

, , and predetermined, only to be designedi j

i

b W W

V ZV

7

System Model – CSIT definition

Assuming full CSIR, each receiver does the following

operation at the end of the IS phase:

: ZF filter preserving interference from tx i at rx j

: interference caused by tx i at rx j, with

1 1NW b NW

1NW b b

CSIT to be reported to tx i after the first phase:

11jV

11jV

, 1

, 1

j j

j j

U

U

8

Review of RIA for SISO [Maleki12]

IS phase: all users transmit simultaneously with random

i.i.d entries

CSI report: acquisition of

RIA phase: each user aims to align the transmitted signals at both rxs

This way the transmitted signals provide linear combinations of

desired signals, while maintaining the rank of received interference

one easy solution

[Maleki12] H. Maleki, S. Jafar, S. Shamai , "Retrospective interference alignment over interference networks", IEEE J. Sel.

Topics Signal Process., Jun.2012

9

RIA for MIMO - Constraints

Constraints that make the scheme reliable for any given antenna

setting:

1. First phase ZF filters

2. Intersection subspace:

3. Receiver Space-Time dimensions:

4. Rank of desired signals after zero-forcing:

10

RIA for MIMO – Problem statement

Overall, the problem is written as

11

RIA for MIMO – Solution

For the range the optimal values are found to

be

with

12

Results

A: Many rx antennas, no need of

CSIT

C: [Abdoli13] Scaled SISO IC

scheme

D: [Vaze12] 2-user IC schemes

The achievable DoF as a function of

[Abdoli13] M.J. Abdoli et al, "On the Degrees of Freedom of -User SISO Interference and X Channels With Delayed CSIT" IEEE Trans. Inf. Theory, Oct. 2013K

The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed C[Vaze12] C.S. Vaze et al, " " , IEEE Trans. Inf. Theory, Jul.SIT 2012

13

Results

A: Many rx antennas, no need of

CSIT

B: RIA for MIMO. Useful for N > M

C: [Abdoli13] Scaled SISO IC

scheme

D: [Vaze12] 2-user IC schemes

[TAV14] presented at ICASSP14

The achievable DoF as a function of

On the Degrees of freedom of the -user MISO Interference Channel with imperfect delaye[TAV14] M. Torrellas et al, " IEEE ICASSP, d CSIT May 4" 201K

[Abdoli13] M.J. Abdoli et al, "On the Degrees of Freedom of -User SISO Interference and X Channels With Delayed CSIT" IEEE Trans. Inf. Theory, Oct. 2013K

The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed C[Vaze12] C.S. Vaze et al, " " , IEEE Trans. Inf. Theory, Jul.SIT 2012

Conclusions

14

We extend the RIA scheme of Maleki et al. for the MIMO case

Our approach is based on formulating a maximization

problem, valid for any antenna setting (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


Thanks for your attention

M. Torrellas, A. Agustin and J. VidalUniversitat Politècnica Catalunya (UPC)

[email protected]


Backup slides

retrospective interference alignment for the 3-user mimo interference channel with delayed csit

Documents