yue tian's 2015 pimrc powerpoint slides
TRANSCRIPT
© CSN Group 2015
On the Performance and Trade-off in Relay-Aided IA with Outdated CSIT
Yue Tian, Mark Beach, Andrew Nix
Communications Systems & NetworksUniversity of Bristol, UK
© CSN Group 2015
Introduction• Interference alignment (IA) is a transmission strategy that use channel
state information (CSI) to improve the capacity of multiuser communication systems. The performance of IA is limited by the accuracy of the CSI.
• In this study, a novel cooperative relay-based interference alignment (RIA) scheme, which aims to improve the Degrees of Freedom (DoF) when the required source-to-destination CSIT is completely outdated.
• The achievable DoF regions by RIA in different channel scenarios are derived. In addition, the trade-off between relay-based and non-relay based IA schemes are analysed.
2
© CSN Group 2015
Background and Motivation (1)
3
• To improve the Degree of Freedom in MIMO system, paper [a] introduced the idea of Interference Alignment(IA).
• The Idea of IA is to use appropriate precoding to compact interfering signals into small dimensional subspaces at each receiver, and at the same time the subspace occupied by the data remains linearly independent of the interference.
• Problem Addressed: It's difficult to achieve perfect globle Channel State Information (CSI) at both the transmitter and receiver sides in practice!
[a] V. Cadambe and S. Jafar, “Interference alignment and degrees of freedom for the K user interference channel,” IEEE Trans. Inf. Theory , vol. 54, no. 8, pp. 3425–3441, Aug. 2008
Concept of Interference Alignment[a]
Figure 2[b]: Concept of MAT IA Scheme with Totally Delayed CSIT
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.© CSN Group 2015
Background and Motivation (2)
4
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.
Figure 2 and Figure 3 indicate the Interference Alignment scheme with totally delayed CSIT and mixed CSIT scenarios. The achieved Degrees of Freedom:
[b] M. A. Maddah-Ali and D. Tse, “Completely stale transmitter channel state information is still very useful,” IEEE Trans. Inf. Theory , vol. 58, no. 7, pp. 4418–4431, Jul. 2012.
[c]Lee, N. and R. W. Heath (2014). "Space-Time Interference Alignment and Degree-of-Freedom Regions for the MISO Broadcast Channel With Periodic CSI Feedback." Information Theory, IEEE Transactions on 60(1): 515-528.
1(1/ K) (1 1/ 2 ... 1/ ) [ ]DoF K b
][)1(
)1()1)(1()1(/12
cKKKn
KKKKnKKDoFTDMAZFSTIA
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.© CSN Group 2015
Background and Motivation (3)
5
Figure 4 [d] : Smooth Bridege between Totally Delayed and Perfect CSIT
• A parameter α was introduced in [d], it set up a bridge which connect to the degree of freedom in totally outdate CSIT(α=1) and perfect CSIT(α=0).
• The proposed RIA scheme are following this idea. Parameters and are introduced to relay based IA scheme to indicate the ratio of feedback delayed time slots to whole coherent time slots and the ratio of feedback delayed user channels to the total propagation user channels, respectively.
[d] S. Yang, M. Kobayashi, D. Gesbert, and X. Yi, “Degrees of freedom of time correlated MISO broadcast channel with delayed CSIT,” Mar. 2012, submitted toIEEE Trans. Inform. Theory, available on arXiv:1203.2550v1 [cs.IT]
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.© CSN Group 2015
Outdated Indicator in Propagation Scenarios
6
• Delayed CSIT Indicator of Coherent Time Slots defines the ratio of feedback delayed channels to coherent time channels:
• Delayed CSIT Indicator of Propagation Channels defines the ratio of feedback delayed user channels to the total propagation user channels:
c
d
TT
dKK
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.© CSN Group 2015
Massive MIMO Relay Based IA Model
7
K
dK
N
M
cTdT
L
Figure 3[c]: Space-Time Interference Alignment with Mixed CSIT.© CSN Group 2015
Massive MIMO Relay Based IA Model
8
Source to Relay Channels
Source to Destination Channels
Relay 1
…….1 2 L3
Relay 2
…….
Relay J
…….
.
.
.
User1
User2
User K
Base Station
…….1
2K
Relay to Destination Channels
kLkk
L
L
hhh
hhhhhh
H
31
22221
11211
3
kkkk
k
k
hhh
hhhhhh
H
31
22221
11211
2
LkLL
k
k
Jj
LkLL
k
k
j
LkLL
k
k
j
hhh
hhhhhh
H
hhh
hhhhhh
H
hhh
hhhhhh
H
21
22221
11211
21
22221
11211
2
21
22221
11211
1
……. …….
…….
…….
Relay Control Station
© CSN Group 2015
Ideal Case for MIMO Relay-Aided IA
9
• The RIA includes two stages propagation.• The SINR at ith user is expressed as:
• The Degree of Freedom is given by:
• The R_i is the transmission rate at ith user.• RIA Precoding Matrix
12 2( ) ( ) ( ) ( ) ( )[ ] [ ] [ ]i i i i iP h n w n I n
( )
1( )lim
logi
KiiiP
RDoF
P
• Base Station design the beamforming to Relay Stations, and the Relay Station design the beamforming to Destination.
• Main idea for designing beamforming in relay is to make all the receivers see the same linear combination for interference signals during time slot by exploiting current CSI and outdated CSI.
Relay N=K
Relay N=K
Relay N=K
Relay N=K
User K
User 3
User 1
User 2
Relay Controlled Station
Base Station
Backhaul Channel
Channel with Perfect CSIT
Channel with Delayed CSIT
© CSN Group 2015
Ideal Case for MIMO Relay-Aided IA
10
• Let , and denote Delayed Parameters
which indicate the Source to Destination Channels (S-D), Source to
Relay Channels (S-R) and Relay to Destination Channels (R-D)
• For the Ideal CSIT Case:
• DoF of Ideal CSIT Case:
,sd sd ,sr sr ,rd rd
2
(K)1
KDoFK
1, 1 , 0, 0 , 0, 0sd sd sr sr rd rdD
© CSN Group 2015
Outdated S-R CSIT Scenarios
11
Case 1.
• Degrees of Freedom:
Case 2.
• Degrees of Freedom:
1 1, 1 , 0 1, 1 , 0, 0sd sd sr sr rd rdD
2 1, 1 , =1,0 <1 , 0, 0sd sd sr sr rd rdD
2
11- )
(K)1
sr
sr
KDoF
K K
(
2
2 (K)1+ ) 1sr
KDoFK
(
© CSN Group 2015
Outdated R-D CSIT Scenarios
12
Case 3.
• Degrees of Freedom:
Case 4.
• Degrees of Freedom:
3 1, 1 , 0, 0 , 1,0 1sd sd sr sr rd rdD
4 1, 1 , 0, 0 , 0 <1, =1sd sd sr sr rd rdD
2
31- )(K)1
rd
rd
KDoF
K
(
2
4 -1 11
(K)1+ rdK
rd k
KDoFK k
© CSN Group 2015
Trade-off Between RIA and NRIA
13
• Trade-off Point in Case 1 and 2:
• Trade-off Point in Case 3 and 4:
11 11
11
2
1 1Ksr k
K
srk
K k
k
1
111
1
1 1(1 K )
1K
rdk
rd
k
K Ke
© CSN Group 2015
Problems on Up-link Estimation
14
• In the cooperative relay control system, the relays’ pilots are mutually orthogonal in up link feedback. Therefore the pilot interference from other relays is negligible in base station channel estimation phase.
• However, non-orthogonal pilots are used in multiusers, resulting in pilot contamination from K-1 interfering users.
• We need a estimator with aim of reducing pilot interference effect and take advantage of the multiple antenna dimensions.
Simple Structure of Up-link Feedback Channels
© CSN Group 2015
Problems on Up-link Estimation
15
Simple Structure of Up-link Feedback Channels
• The idea of Bayesian based estimator is to use the knowledge of channel co-variance to do the channel estimate. The role of co-variance matrices is to capture structure information related to the distribution of the multipath angles of arrival at the base station.
• The co-variance varies slower than the fast fading, the knowledge of channel co-variance can be used to do following channel prediction.
• Two phases of estimation process are formed: in phase one, all the user channels are estimated at the target relay station; in phase two, only desired user’s channel is estimated.
© CSN Group 2015
Up-link Feedback Bayesian Estimator
16
KKKK
K
kdrk
Hdr
drRR
khRkhhp
detdet2
)()(21exp
)(1
1
1
KKKK
KKf
rHr
K
kdrk
Hdr
fdr RRrp
zzkhRkhrhp
detdet2)(
/)()(exp|
1
2
1
1
2
1
1 /)()(exp rHr
K
kdrk
Hdrdr zzkhRkhh
• Gaussian Probability Density Functions:
• According to the Bayes’ Equation, there is:
• The denominator is determined and the numerator is defined as:
© CSN Group 2015
Up-link Feedback Bayesian Estimator
17
• By compute the partial derivative in real dimension and imaginary dimension, we achieve that:
0/arg drdr hh
• By the rule of the Maximum Posteriori Decision, the estimated channel can be achieved as:
ssR
srsrhe
H
HH
dr ~~22
~~)ˆ(
12
ssR
jjsrjsrh
H
HH
dr ~~22
~~ˆIm
12
sRsI
rRsh
Hn
H
dr
2
ˆ
drdr hrhph minarg|maxargˆ
• The final Bayesian Estimate Channel can be derived as:
© CSN Group 2015
Achievable Sum-Rate by MIMO Relay-Aided IA
18
© CSN Group 2015
Conclusions
19
• In this study, a MIMO relay-aided IA is proposed in K MUs' MISO BC to optimize the DoF when the CSI is completely outdated in the S-D channels.
• The achievable sum-DoF by RIA is obtained under the ideal and four non-ideal CSIT cases.
• In addition, the trade-off in RIA is analysed through the numerical results.