May 7, 2014, Florence, Italy Retrospective Interference Alignment for the 3-user MIMO Interference...
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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)
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 (MAT) proposed the delayed CSIT framework in [MAT12], where completely outdated CSIT can be exploited for IA in the BC.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
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:
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
May 7, 2014, Florence, Italyhttp://ict-tropic.eu http://spcom.upc.edu
Thanks for your attention
M. Torrellas, A. Agustin and J. VidalUniversitat Politècnica Catalunya (UPC)