Yue Tian's 2015 PIMRC powerpoint slides

© 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On the Performance and Trade-off in Relay-Aided IA with Outdated CSIT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scheme, which aims to improve the Degrees of Freedom (DoF) when the required source-to-destination CSIT is completely outdated.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.

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Background and Motivation (1)

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• 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


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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



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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]


Outdated Indicator in Propagation Scenarios

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• 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


Massive MIMO Relay Based IA Model

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K

dK

N

M

cTdT

L


Massive MIMO Relay Based IA Model

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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

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Ideal Case for MIMO Relay-Aided IA

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• 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

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Ideal Case for MIMO Relay-Aided IA

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• 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

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Outdated S-R CSIT Scenarios

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Case 1.

• Degrees of Freedom:

Case 2.


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

（

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Outdated R-D CSIT Scenarios

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Case 3.


Case 4.


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

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Trade-off Between RIA and NRIA

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• 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

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Problems on Up-link Estimation

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• 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

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Problems on Up-link Estimation

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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.

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Up-link Feedback Bayesian Estimator

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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:

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Up-link Feedback Bayesian Estimator

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• 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:

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Achievable Sum-Rate by MIMO Relay-Aided IA

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Conclusions

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• 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.

© CSN Group 201520

@BristolCSNMany Thanks!

• Email: [email protected]

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Yue Tian's 2015 PIMRC powerpoint slides