Transcript MIMO Broadcast Scheduling with Limited Feedback

MIMO Broadcast Scheduling with
Limited Feedback
Student: 林鼎雄 (96325501)
Director: 李彥文
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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
k * (t )  arg max  k (t )
k 1,..., K
– System capacity
C  log 2 (1   k* )
– The PDF of 
f s ( )  Kf ( ) F ( ) K 1,   0
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Introduction
0.5
user=2
user=8
user=16
user=24
user=32
user=40
user=48
0.45
0.4
Density
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
Squared Channel Amplitude
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Introduction
A v e r a g e T h r o u g h p u t (bps/Hz)
2.6
Rayleigh fading channel
AWGN channel
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0
5
10
15
20
25
30
35
Number of Users
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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 ( M  N )
– A total of K users ( K M )
• Only J out of K users are allowed to
communicate with BS simultaneously. ( 1  J  K )
• Ykt   k H tk Xt  Wkt , k  A (t )
A (t )  J with 1  J  K
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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
U
P

E ( R)  KMN  log 2 (1  t ) f Z (t )( FZ (t )) NK 1 dt
0
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(16)
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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

E ( R)  KMN  log 2 (1  t ) f Z (t )( FZ (t )) NK 1 dt (22)

– It can be observed that when λ → 0, (22) is
equivalent to (16)
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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 Bk   )
– FB(t) is the CDF of Bk
– The probability of l
K
Pl    (1  FB ( ))l ( FB ( )) K l
l 
– Average feedback load of the selected scheduling
K
L   l  Pl
l 1
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MIMO Broadcast Scheduling with SINR
Feedback
• Average feedback ratio (FLR) ζ
L
 
K
 1   FZ ( ) 
MN
(30)
– FLR is not dependent on the number of user K
– When the threshold (λ) is increased, FLR (ζ)
decreases.
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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
(3) Throughput
=7.7 bps
(1) Target throughput
=6.3 bps
(2) λ=5 dB
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(2) λ=10 dB
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MIMO Broadcast Scheduling with SINR
Feedback
(1) Target FLR=0.4
(3) FLR=0.05
(2) λ=5 dB
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(2) λ=10 dB
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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
0  Bk  1
 0,

qk  Q( Bk )   i, i  Bk  i 1 , i  1 ,..., L  2
 L  1, B  
k
L 1

– 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
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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 0  V  1
, K'  K / M
• When i  V  i1
– PDF of V
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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 f ( K , 1 )  0 which is not
1
tractable.
– The optimal threshold should be dependent on K
for given M, N and SNR 
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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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