Interference Management with Limited Channel State Information in Wireless Networks

Motivation Channel Feedback in Communications Degrees of Freedom (DoF) notion ICR Scheme for Alternating CSIT
Interference Management with Limited
Channel State Information in Wireless
Networks
Mohamed Seif, Amr El-keyi, and Mohammed Naﬁe, "Achievable Degrees of Freedom of the K-user
MISO Broadcast Channel with Alternating CSIT via Interference Creation-Resurrection", IEEE 84th
Vehicular Technology Conference: VTC 2016-Fall, Montreal, Canada, Sept. 2016
Mohamed Seif
Wireless Intelligent Networks Center (WINC), Nile University, Egypt
July 27, 2016
Mohamed Seif Nile University
Interference Management with Limited Channel State Information in Wireless Networks 1

1 Motivation
2 Channel Feedback in Communications
3 Degrees of Freedom (DoF) notion
4 ICR Scheme for Alternating CSIT
5

The Big Problem in Wireless Communications
Figure: An illustrative example for a heterogeneous network.

Interference is a fundamental bottleneck in many wireless
systems

systems
Interference management is getting convoluted
Homogeneous → Heterogeneous

systems
Interference management is getting convoluted
Homogeneous → Heterogeneous
How to manage interference in an efﬁcient manner?

Coding Against Interference
1
Channel state information at transmitter.

Coding Against Interference
Interference shaping using CSIT 1
is a key enabler for
mitigating interference
1
Channel state information at transmitter.

1 Motivation
5

Closed Loop Systems
Figure: Illustration of the CSIT feedback and sharing process.

Challenges in Obtaining Global and Accurate CSIT
Tx
Channel Feedback
User1
User2
User3

Tx
Channel Feedback
User1
User2
User3
Possible error sources in the CSI feedback process
Channel estimation error
Quantization error (e.g., Compressed channel feedback)
Feedback delay (Maddah Ali et al.’12)

Tx
Channel Feedback
User1
User2
User3
Possible error sources in the CSI feedback process
Channel estimation error
Quantization error (e.g., Compressed channel feedback)
Feedback delay (Maddah Ali et al.’12)
CSIT sharing via backhaul links (e.g., CoMP in LTE)

1 Motivation
5

Degrees of Freedom (DoF)
DoF notion:

DoF notion:
1 Lizhong and Tse in IEEE IT Trans. 2003

DoF notion:
1 Lizhong and Tse in IEEE IT Trans. 2003
2 Rigorous approximation to the network capacity in the high
SNR regime.
Mathematically,
C∑(P) = DoFlog(P) + o(log(P)) (1)
where limP→∞
o(log(P))
log(P) = 0.
Alternatively,
It represents the number of interference-free signalling
dimensions in the network.

1 Motivation
5

System Model
The received signal at the ith receiver
is given by
Yi (t) = Hi (t)X(t) + Ni (t), i = 1,...,K
(2)
The total DoF of the network is deﬁned
as
DΣ(K) = max
(d1,d2,...,dK )∈D
d1 + d2 + ⋅⋅⋅ + dK
(3)
UE3
UE1 UE2
UE4
UEi
)(tHi
K-antenna Tx
UEK
Figure: Network Model

CSI Model
Perfect and global CSIR.
Three states of the availability of CSIT
about each receiver:
Perfect CSIT (P): instantaneous
and without error.
Delayed CSIT (D): delay greater
than or equal one time slot
duration (coherence time) and
without error.
No CSIT (N): not available to
transmitter at all.
UE3
UE1 UE2
UE4
UEi
)(tHi
K-antenna Tx
UEK
Introduced by Tandon and Shamai in IEEE IT Trans. 2012 for the 2-user BC

Alternating CSIT Model
The fraction of time associated with
CSIT state S,
λS =
∑
n
t=1 ∑
K
i=1 I(Si (t) = S)
nK
(4)
where n is the number of channel
uses,
∑
S∈{P,D,N}
λS = 1. (5)
UE3
UE1 UE2
UE4
UEi
)(tHi
K-antenna Tx
UEK

ICR Scheme
Phase I: Interference Creation
UE2
UE1
Tx
UE3
1u
2u
3u
),,( 321
1
1 uuuL
),,( 321
1
2 uuuI
),,( 321
1
3 uuuI
N
D
D
Figure: ICR scheme t = 1.

ICR Scheme
UE2
UE1
Tx
UE3
1v
2v
3v
),,( 321
1
1 vvvI
),,( 321
1
2 vvvL
),,( 321
1
3 vvvI
N
D
D

ICR Scheme
UE2
UE1
Tx
UE3
1p
2p
3p
),,( 321
1
1 pppI
),,( 321
1
2 pppI
),,( 321
1
3 pppL
D
D
N

ICR Scheme
Phase II: Interference Resurrection (Based on orthogonal projection pre-coding and PNC)
UE2
UE1
Tx
UE3
),,( 321
2
1 uuuL
),,( 321
2
2 vvvL
),,( 321
2
3 pppL
Old interference
terms from UE3
P
N
P
Based on orthogonal projection pre-coding and PNC

ICR Scheme
Phase II: Interference Resurrection (Based on orthogonal projection pre-coding and PNC)
UE2
UE1
Tx
UE3
),,( 321
3
1 uuuL
),,( 321
3
2 vvvL
),,( 321
3
3 pppL
Old interference
terms from UE2
N
P
P
Based on orthogonal projection pre-coding and PNC

ICR Scheme
UE2
UE1
Tx
UE3
1u 2u 3u
1v 2v 3v
1p 2p 3p
Figure: D∑ = 9
5
, S5
123 = {NDD,DND,DDN,PPN,PNP}.

Synergistic Alternating CSIT
Phase I: Creation Phase II: Resurrection
(NDD,DND,DDN) (PPN,PNP)
(NDD,DDN,DND) (PNP,PPN)
(DND,DDN,DDN) (PPN,NPP)
(DND,DDN,NDD) (NPP,PPN)
(DDN,DND,NDD) (NPP,PNP)
(DDN,NDD,DND) (PNP,NPP)
Table: All synergistic CSIT patterns for the 3-user BC.
Synergy Deﬁnition
Synergy is the interaction of multiple elements in a system to
produce an effect greater than the sum of their individual
effects.

Upper Bound on the DoF for the K-user BC
Bounds were introduced by Tandon et al.’13
DΣ(K) = d1 + d2 + ⋅⋅⋅ + dK ≤
K2
+ (K − 1)∑K
i=1 γi
2K − 1
(6)
where,
γi =
∑n
t=1 I(Si(t) = P)
n
≤ γ,∀i = 1,...,K (7)

DoF Region Characterization for the 3-user BC
Given perfect CSIT distribution (γ1,γ2,γ3),
P1: max
d1,d2,d3
d1 + d2 + d3
s.t. 3d1 + d2 + d3 ≤ 3 + 2γ1 (8)
d1 + 3d2 + d3 ≤ 3 + 2γ2 (9)
d1 + d2 + 3d3 ≤ 3 + 2γ3 (10)
0 ≤ di ≤ 1, ∀i = 1,2,3 (11)

P1: max
d1,d2,d3
d1 + d2 + d3
s.t. 3d1 + d2 + d3 ≤ 3 + 2γ1 (8)
d1 + 3d2 + d3 ≤ 3 + 2γ2 (9)
d1 + d2 + 3d3 ≤ 3 + 2γ3 (10)
0 ≤ di ≤ 1, ∀i = 1,2,3 (11)
Closed form solution,
d∗
i =
3 + 4γi − ∑3
j=1,j≠i γj
5
, ∀i = 1,2,3 (12)

P1: max
d1,d2,d3
d1 + d2 + d3
s.t. 3d1 + d2 + d3 ≤ 3 + 2γ1 (13)
d1 + 3d2 + d3 ≤ 3 + 2γ2 (14)
d1 + d2 + 3d3 ≤ 3 + 2γ3 (15)
0 ≤ di ≤ 1, ∀i = 1,2,3 (16)
Solution,
Given: (γ1,γ2,γ3) = (2
5 , 1
5 , 1
5 )
Optimal DoF tuple: d∗
= (0.84,0.64,0.64)

P1: max
d1,d2,d3
d1 + d2 + d3
s.t. 3d1 + d2 + d3 ≤ 3 + 2γ1 (13)
d1 + 3d2 + d3 ≤ 3 + 2γ2 (14)
d1 + d2 + 3d3 ≤ 3 + 2γ3 (15)
0 ≤ di ≤ 1, ∀i = 1,2,3 (16)
Solution,
Given: (γ1,γ2,γ3) = (2
5 , 1
5 , 1
5 )
= (0.84,0.64,0.64)
Achievable DoF tuple: d = (0.6,0.6,0.6).

P1: max
d1,d2,d3
d1 + d2 + d3
s.t. 3d1 + d2 + d3 ≤ 3 + 2γ1 (13)
d1 + 3d2 + d3 ≤ 3 + 2γ2 (14)
d1 + d2 + 3d3 ≤ 3 + 2γ3 (15)
0 ≤ di ≤ 1, ∀i = 1,2,3 (16)
Solution,
Given: (γ1,γ2,γ3) = (2
5 , 1
5 , 1
5 )
= (0.84,0.64,0.64)
Achievable DoF tuple: d = (0.6,0.6,0.6).
Conjecture: The outer bound can be achieved by adding
multi-cast messaging in the network.

ICR Scheme vs MAT Scheme
Achievable DoF for this network is given by
DΣ(K) =
K2
2K − 1
>
K
1 + 1
2 + ⋅⋅⋅ + 1
K
Delayed CSIT - MAT scheme
(17)
and the distribution of fraction of time of the different states
{P,D,N} required for our proposed scheme is
λP =
(K − 1)2
2K2 − K
,λD =
K − 1
2K − 1
,λN =
1
K
. (18)

Results
1 2 3 4 5 6 7 8 9 10
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
K (users)
DoF
sum
(K)
CSIT with alternation
CSIT with all delayed
Figure: DoF comparison for broadcast channel between all delayed
and alternating CSIT models.

Results
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
K (users)
D
Σ
(K)
Upper bound on the K−user BC, γ=1
Upper bound on alternating CSIT for the K−user BC
Achievable DoF based on ICR scheme
Figure: DoF comparison for the K-user BC.

Questions ?

Thank You !

Interference Management with Limited Channel State Information in Wireless Networks

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