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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
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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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MIMO Broadcast Scheduling with SINR Feedback
• This algorithm only requires a feedback of total K SINR values.
• Scheduling Algorithm
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MIMO Broadcast Scheduling with SINR Feedback
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MIMO Broadcast Scheduling with SINR Feedback
• 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 SINR Feedback
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MIMO Broadcast Scheduling with SINR Feedback
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MIMO Broadcast Scheduling with SINR Feedback
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MIMO Broadcast Scheduling with Selected Feedback
• Scheduling Algorithm
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MIMO Broadcast Scheduling with Selected Feedback
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MIMO Broadcast Scheduling with Selected Feedback
• Throughput analysis
– 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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MIMO Broadcast Scheduling with Selected Feedback
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MIMO Broadcast Scheduling with Selected Feedback
• 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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MIMO Broadcast Scheduling with SINR Feedback
• 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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MIMO Broadcast Scheduling with SINR Feedback
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MIMO Broadcast Scheduling with SINR Feedback
• 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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MIMO Broadcast Scheduling with SINR Feedback
(1) Target throughput=6.3 bps
(2) λ=10 dB(2) λ=5 dB
(3) Throughput=7.7 bps
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MIMO Broadcast Scheduling with SINR Feedback
(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 SINR Feedback
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MIMO Broadcast Scheduling with Quantized Feedback
• Scheduling algorithm
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MIMO Broadcast Scheduling with Quantized Feedback
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MIMO Broadcast Scheduling with Quantized Feedback
• 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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MIMO Broadcast Scheduling with Quantized Feedback
• Throughput analysis
.r v V
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MIMO Broadcast Scheduling with Quantized Feedback
– CDF of V• When
• When
– PDF of V
', /K K M 10 V
1i iV
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MIMO Broadcast Scheduling with Quantized Feedback
• 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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MIMO Broadcast Scheduling with Quantized Feedback
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MIMO Broadcast Scheduling with Quantized Feedback
• 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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MIMO Broadcast Scheduling with Quantized Feedback
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MIMO Broadcast Scheduling with Quantized Feedback
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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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