mimo broadcast scheduling with limited feedback student: (96325501) director: 2008/10/2 1...

MIMO Broadcast Scheduling with Limited Feedback

Student: 林鼎雄 (96325501)

Director: 李彥文

2008/10/2

1Communication Signal Processing Lab

Outline• Introduction• System model• MIMO broadcast scheduling algorithms

– MIMO Broadcast Scheduling with SINR Feedback

– MIMO Broadcast Scheduling with Selected Feedback

– MIMO Broadcast Scheduling with Quantized Feedback

• Conclusion

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Introduction• Multiuser diversity

– Channel-aware scheduling

– System capacity

– The PDF of

*2log (1 )k

C

*

1,...,( ) arg max ( )k

k Kk t t

1( ) ( ) ( ) , 0K

sf Kf F

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Introduction

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

D e

n s

i t

y

Squared Channel Amplitude

user=2user=8user=16user=24user=32user=40user=48

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Introduction

0 5 10 15 20 25 30 350.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Number of Users

A v

e r

a g

e T

h r

o u

g h

p u

t (

bps/

Hz)

Rayleigh fading channel

AWGN channel

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System model• BS (M antennas) allocates independent

information streams from all M Tx antennas to the M most favorable user (N antennas) with the highest SINR.

• Downlink of a single-cell wireless system– Tx: M antennas, Rx: N antennas ( )– A total of K users ( )

• Only J out of K users are allowed to communicate with BS simultaneously. ( )

•

M NK M

1 J K , ( )

( ) with 1

t t t tk k k k k t

t J J K

Y H X W A

A 2008/10/2


System model• The SINR-based scheduling algorithm

requires the feedback of KN SINR values and the feedback load increases with the increase of the number of receiver antennas

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MIMO Broadcast Scheduling with SINR Feedback

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• This algorithm only requires a feedback of total K SINR values.

• Scheduling Algorithm

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• Throughput analysis

UP

120

( ) log (1 ) ( )( ( )) (16)NKZ ZE R KMN t f t F t dt

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MIMO Broadcast Scheduling with Selected Feedback

• Scheduling Algorithm

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– It can be observed that when λ → 0, (22) is equivalent to (16)

12( ) log (1 ) ( )( ( )) (22)NK

Z ZE R KMN t f t F t dt

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• Feedback load analysis– Assume that l users are selected for

feedback in one time slot (l users satisfying )

– FB(t) is the CDF of Bk

– The probability of l

– Average feedback load of the selected scheduling

1

K

ll

l

L P

(1 ( )) ( ( ))l K ll B B

KF F

l

P

kB

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• Average feedback ratio (FLR) ζ

– FLR is not dependent on the number of user K– When the threshold (λ) is increased, FLR (ζ)

decreases.

1 ( ) (30)MN

Z

K

F

L

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• Throughput-FLR tradeoff– The throughput and FLR both depend on

the threshold λ and decrease when λ increase.

– Throughput-oriented: the scheme is to minimize FLR while guaranteeing a target throughput.

– FLR-oriented: the scheme is to maximize the throughput while attaining a target FLR.

– FLR can be greatly reduced without sacrificing the throughput.

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(1) Target throughput=6.3 bps

(2) λ=10 dB(2) λ=5 dB

(3) Throughput=7.7 bps

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(3) FLR=0.05

(2) λ=10 dB(2) λ=5 dB

(1) Target FLR=0.4

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MIMO Broadcast Scheduling with Quantized Feedback

• Scheduling algorithm

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• Quantization

– The full feedback scheduling where each user feeds a real value Bk to BS.

– The quantized feedback scheduling requires each user to send back a quantized value Q(Bk)

– The number of levels L is determined by the number of bits required to represent a value Bk and L=2b

1

1

1

0, 0

( ) , , 1 ,..., 2

1,

k

k k i k i

k L

B

q Q B i B i L

L B

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.r v V

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– CDF of V• When

• When

– PDF of V

', /K K M 10 V

1i iV

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30Cmmunication Signal Processing Lab


• 1-bit feedback– Each user feeds 1 or 0 back to the BS

according to the threshold λ1.

• If the quantization threshold λ1 is fixed, the total rate will be a constant.

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• Optimal threshold λ1

– The throughput is a function of λ1 and K, simply denote by E(R) = f(K, λ1 ).

– It is not optimal to fix λ1 for various K to enhance the throughout.

– To search for the optimal quantization threshold, we need to solve which is not tractable.

– The optimal threshold should be dependent on K for given M, N and SNR

1

1

( , )0

f K

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Conclusion

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Conclusion• Combined with spatial multiplexing and

receive antenna selection, the proposed scheduling algorithm can achieve high multiuser diversity

• The feedback load can be greatly reduced with a negligible throughput loss with user selection based on SINR

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Reference• Z. Wei and K. B. Letaief, “MIMO Broadcast

Scheduling with Limited Feedback,” IEEE J. Select. Areas Commun., vol. 25, pp. 1457-1467, Sep. 2007.

• D. Gesbert and M. Alouini, “How much feedback is multi-user diversity really worth?,” in Proc. IEEE ICC2004, Int. Conf. Commun., June 20-24, 2004, vol 1, pp.234-238.

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mimo broadcast scheduling with limited feedback student: (96325501) director: 2008/10/2 1...

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