Retrospective Interference Alignment
for 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
http://ict-tropic.eu
May 7, 2014, Florence, Italy
http://spcom.upc.edu
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completely outdated CSIT can be exploited for IA in the BC.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
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Summary
1.
System model
2.
Review of RIA for SISO
3.
RIA for MIMO
4.
Results
5.
Conclusions
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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 :
N 1
N M
M b
b 1
IS
RIA
W1
W2
N 1
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System Model
 Let consider the signals received at user 1 along the first phase:
desired
interference
 We can group these signals as follows
with
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IA constraints and DoF
 This is written in general as
NWp  MWp
MWp  b
NW  MW
b 1
b  NW
MW  b
b, W1 ,W2
Vi1 and Z j predetermined, only to be designed 
 2
 Vi
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System Model – CSIT definition
 Assuming full CSIR, each receiver does the following operation at
the end of the IS phase:
1
Vj
1
1
Vj
1
 U j , j 1 
U 
 j , j 1 
: ZF filter preserving interference from tx i at rx j
 NW1  b   NW1
: interference caused by tx
i at rx j, with
 NW1  b   b
CSIT to be reported to tx i after the first phase:
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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
one easy solution
 This way the transmitted signals provide linear combinations of desired signals,
while maintaining the rank of received interference
[Maleki12] H. Maleki, S. Jafar, S. Shamai , "Retrospective interference alignment over interference networks", IEEE J. Sel.
Topics Signal Process., Jun.2012
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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:
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RIA for MIMO – Problem statement
 Overall, the problem is written as
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RIA for MIMO – Solution
 For the range
the optimal values are found to be
with
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Results
 The achievable DoF
as a function of
 A: Many rx antennas, no need of CSIT

 C: [Abdoli13] Scaled SISO IC scheme
 D: [Vaze12] 2-user IC schemes
[Abdoli13] M.J. Abdoli et al, "On the Degrees of Freedom of K -User SISO Interference and X Channels With Delayed CSIT" IEEE Trans. Inf. Theory, Oct. 2013
[Vaze12] C.S. Vaze et al, "The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed CSIT" , IEEE Trans. Inf. Theory, Jul. 2012
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Results
 The achievable DoF
as a function of
 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
[Abdoli13] M.J. Abdoli et al, "On the Degrees of Freedom of K -User SISO Interference and X Channels With Delayed CSIT" IEEE Trans. Inf. Theory, Oct. 2013
[Vaze12] C.S. Vaze et al, "The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed CSIT" , IEEE Trans. Inf. Theory, Jul. 2012
[TAV14] M. Torrellas et al, "On the Degrees of freedom of the K -user MISO Interference Channel with imperfect delayed CSIT" IEEE ICASSP, May 2014
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Conclusions
 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
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Thanks for your attention
M. Torrellas, A. Agustin and J. Vidal
Universitat Politècnica Catalunya (UPC)
marc.torrellas.socastro@upc.edu
http://ict-tropic.eu
May 7, 2014, Florence, Italy
http://spcom.upc.edu
Backup slides
http://ict-tropic.eu
May 7, 2014, Florence, Italy
http://spcom.upc.edu
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