Limited Feedback in Wireless Communication Systems · Adaptive Signal Processing Information Theory...
Transcript of Limited Feedback in Wireless Communication Systems · Adaptive Signal Processing Information Theory...
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Adaptive Signal Processing Information Theory Group
Gwanmo Ku
May 14, 17, and 21, 2013
Limited Feedback in
Wireless Communication Systems
- Summary of “An Overview of Limited Feedback
in Wireless Communication Systems”
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter Receiver
… …
Ant. 1
Ant. 2
Ant. 𝑴𝒕
Ant. 1
Ant. 2
Ant. 𝑴𝒓
Feedback Design
𝐇
Limited Feedback 𝐇
𝐅
Codebook Design
Channel
2
Narrowband (NB) Broadband (BB)
Single User (SU) / Multiple User (MU)
Single Antenna (SA) Multiple Antenna (MA)
Narrowband (NB) Broadband (BB)
𝐒 𝐗
𝐍
𝐘
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter Receiver
Ant. 1 Ant. 1
Feedback Design
𝒉[𝒌]
Limited Feedback 𝐇
𝒇[𝒌]
Codebook Design
3
Narrowband (NB) Broadband
Single User (SU) / Multiple User
Single Antenna (SA) Multiple Antenna
Narrowband Broadband
𝑠[𝑘] 𝑥[𝑘]
𝑛[𝑘]
𝑦[𝑘]
𝒚 𝒌 = 𝒉 𝒌 𝒙 𝒌 + 𝒏[𝒌]
Slow fading
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Adaptive Signal Processing Information Theory Group
SU - SA - NB with Perfect CSI12/22
Received Signal
Adaptive Power Allocation by Waterfilling
𝜌(ℎ) = arg max𝐄ℎ 𝑘 ,𝑥[𝑘] 𝑥 𝑘 2 ≤𝜌
log2(1 + 𝜌 ℎ[𝑘] ℎ[𝑘] 2)
How to measure Channel State ℎ[𝑘] at the receiver?
By Training Sequence from Tx.
𝑦 𝑘 = ℎ 𝑘 𝑥 𝑘 + 𝑛[𝑘]
𝑥 𝑘 = 𝜌(ℎ[𝑘]) 𝑠[𝑘]
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Adaptive Signal Processing Information Theory Group
Water-filling12/22
𝑌𝑗 = 𝑋𝑗 + 𝑍𝑗
𝐼 𝑋1, … , 𝑋𝑘; 𝑌1, … , 𝑌𝑘 ≤ 1
2log(1 +
𝑃𝑖
𝑁𝑖)
𝑘
𝑖=1
𝑗 = 0, … , 𝑘, 𝑍𝑗 ∼ 𝑁(0, 𝑁𝑗), 𝐄 𝑋𝑗2𝑘
𝑗=1 ≤ 𝑃
𝐿 𝑃1, … , 𝑃𝑘 = 1
2log(1 +
𝑃𝑖
𝑁𝑖)
𝑘
𝑖=1
+ 𝜆( 𝑃𝑖
𝑘
𝑖=1
− 𝑃)
𝑃𝑖 = 𝜈 − 𝑁𝑖+ 𝜈 − 𝑁𝑖
+
𝑘
𝑖=1
= 𝑃
1
2
1
𝑃𝑖 + 𝑁𝑖+ 𝜆 = 0
𝜈
Power
Channel
𝑃1
𝑁1 𝑁2
𝑃2
𝑃3 𝑃5
𝑃4 = 0
𝑁3
𝑁4
𝑁5
Channel 1 Channel 2 Channel 3 Channel 4 Channel 5
5
Ref : Elements of Information Theory by Thomas Cover
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Adaptive Signal Processing Information Theory Group
Limited Feedback : SU-SA-NB12/22
1. Quantization of ℎ[𝑘], 𝛾 = ℎ 𝑘 2
2. Rate Quantization by Lloyd algorithm
Find Quantization Level minimizing Distortion Measure
Optimal Rate Partitions associated with Limited feedback
3. On/Off Rate Adaptation
1 bit : On/Off Transmission subject to the channel condition
4. ARQ ACK/NACK Signalling
1 bit : Successful Transmission or Re-transmission Required
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𝐼 𝛾 = 𝑖, 𝛾 ∈ [𝛾𝑖𝑏 , 𝛾𝑖+1
𝑏 ), 𝑖 = 0, … , 𝑄 − 1
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter Receiver
Ant. 1
Ant. 1
Feedback Design
𝒉[𝒌, 𝒍]
Limited Feedback 𝐇
𝒇[𝒌]
Codebook Design
Channel
7
Narrowband Broadband (BB)
Single User (SU) / Multiple User
Single Antenna (SA) Multiple Antenna
Narrowband Broadband
𝑠[𝑘] 𝑥[𝑘] 𝑛[𝑘]
𝑦[𝑘]
𝒚 𝒌 = 𝒉 𝒌, 𝒍 𝒙[𝒌 − 𝒍]
𝑳
𝒍=𝟎
+ 𝒏[𝒌]
𝑳 + 𝟏
Paths
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Adaptive Signal Processing Information Theory Group
SU-SA-BB with Perfect CSI14/22
Received Signal, OFDM Signalling
Post-processing Signal in Frequency Domain
Subcarrier Power Allocation
𝑦 𝑘 = ℎ 𝑘, 𝑙 𝑥[𝑘 − 𝑙]
𝐿
𝑙=0
+ 𝑛[𝑘]
𝐲 𝑘 = diag 𝐡 [𝑘 ] 𝐱 𝑘 + 𝐧 𝑘
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𝑥𝑣[𝑘 ] = 𝑃𝑣 𝑠𝑣[𝑘 ] 𝐱 𝑘 =
𝑥1[𝒌 ]…
𝑥𝑣[𝒌 ]…
𝑥𝑁[𝒌 ]
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Adaptive Signal Processing Information Theory Group
Limited Feedback : SU-SA-BB12/22
1. Subcarrier On/Off Signaling
# subcarrier bits : Active or inactive subcarrier
2. Subcarrier Grouping : Subchannelization
# subchannel bits
3. Order of Pilot Channel Gain
Order index within 𝑵𝒑𝒊𝒍𝒐𝒕! sets, 𝒉𝒎𝒊𝒏,𝒑𝒊𝒍𝒐𝒕𝒔 & 𝒉𝒎𝒂𝒙,𝒑𝒊𝒍𝒐𝒕𝒔
4. Adaptive Modulation and Coding
Level Index : Modulation and Coding Scheme ~ SNR
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter Receiver
… …
Ant. 1
Ant. 2
Ant. 𝑴𝒕
Ant. 1
Ant. 2
Ant. 𝑴𝒓
Feedback Design
𝐇[𝐤]
Limited Feedback 𝐇
𝐅
Codebook Design
Channel
10
Narrowband Broadband
Single User (SU) / Multiple User
Single Antenna Multiple Antenna (MA)
Narrowband (NB) Broadband
𝐬[𝐤] 𝐱[𝐤]
𝐧[𝐤]
𝐲[𝐤]
𝐲 𝑘 = 𝐇 𝑘 𝐱 𝑘 + 𝐧[𝑘]
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Adaptive Signal Processing Information Theory Group
SU-MA-NB with Perfect CSI16/22
Received Signal
𝑀𝑡 × 𝑀𝑟 MIMO System
𝐲 𝑘 : 𝑀𝑟 × 1 Complex Received Vector
𝐇 𝑘 : 𝑀𝑟 × 𝑀𝑡 , each entry has flat fading property
𝐱 𝑘 : Transmitted Symbol with Power Constraint 𝐄𝐇,𝐱 | 𝐱 𝑘 |𝟐𝟐
≤ 𝜌
Average Power Constraint : 𝐄𝐱 𝐱 𝑘𝟐
𝟐|𝐇 𝑘 = 𝐇(𝑡) ≤ 𝜌𝑡
under 𝐄𝐇 𝜌𝑡 ≤ 𝜌
𝐧 𝑘 : 𝑀𝑟 × 1 Complex Gaussian Noise according to 𝐂𝐍(0,1)
𝐲 𝑘 = 𝐇 𝑘 𝐱 𝑘 + 𝐧[𝑘]
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Adaptive Signal Processing Information Theory Group
SU-MA-NB : Rate Maximizing17/22
Adaptive Power Allocation
• 𝐐 𝑘 : Covariance of the Tx. Sig. for each 𝐇[𝑘]
𝐐 𝑘 = arg max𝐐:tr 𝐐 ≤1,𝐐∗=𝐐,𝐐≥0
log2 det(𝐈 + 𝜌𝐇 𝑘 𝐐 𝐇∗ 𝑘 )
• Ergodic Capacity : 𝑅 = 𝐄𝐇[ max𝐐:tr 𝐐 ≤1 ,𝐐∗=𝐐,𝐐≥0
log2 det 𝐈 + 𝜌𝐇𝐐𝐇∗ ]
• s 𝑘 : Channel independent Codeword with 𝐄𝑠 𝑠 𝑘 𝟐 ≤ 1
𝐱 𝑘 = 𝜌 𝐐 𝑘12𝐬[𝑘]
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Adaptive Signal Processing Information Theory Group
Covariance Quantization17/22
Codebook of Possible Cov. Matrices
ℚ = {𝐐𝟏, … , 𝐐𝟐𝑩}
• Rate Maximizing Covariance Selecting
𝑛𝑜𝑝𝑡 𝑘 = arg max1≤𝑛≤2𝐵
log2 det(𝐈 + 𝜌𝐇 𝑘 𝐐𝑛𝐇∗ 𝑘 )
• Maximum Achievable Rate
𝑅ℚ = 𝐄𝐇[max𝐐∈ℚ
log2 det(𝐈 + 𝜌𝐇𝐐𝐇∗)]
• Codebook Generation ℚ based on VC using Lloyd Algorithm
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Adaptive Signal Processing Information Theory Group
Vector Quantization using Lloyd Algorithm17/22
Step 1. Determine { 𝐐𝟏, 𝑹𝟏 , … , 𝐐𝟐𝑩 , 𝑹𝟐𝑩 } for an
initial partition {ℋ𝟏, … , ℋ𝟐𝑩}
Define a distortion measure
14
𝓠∗, 𝓡∗ = arg max𝑄1,𝑅1 ,…,{𝑄
2𝐵 ,𝑅2𝐵}
𝐄𝐇 𝑑 𝐇, 𝑖 𝐇 ∈ ℋ𝑖 Pr[𝐇 ∈ ℋ𝑖]
2𝐵
𝑖=1
= arg max𝑄1,𝑅1 ,…,{𝑄
2𝐵 ,𝑅2𝐵}
𝑅𝑗 ⋅ Pr[𝑅𝑗 < log2 det 𝐈 + 𝐇𝐐𝑗𝐇∗ |𝐇 ∈ ℋ𝑖]
2𝐵
𝑖=1
2𝐵
𝑗=1
⋅ Pr 𝐇 ∈ ℋ𝑖 ⋅ 𝑃𝑖𝑗𝐶𝑆𝐼𝑇
𝓠∗ = {𝐐1∗ , … , 𝐐
2𝐵∗ } 𝓡∗ = {𝑅1
∗, … , 𝑅2𝐵∗ }
𝑑 𝐇, 𝑖 = 𝑅𝑗 ⋅ 1(𝑅𝑗 < log2 det 𝐈 + 𝐇𝐐𝑗𝐇∗ ) ⋅ 𝑃𝑖𝑗
𝐶𝑆𝐼𝑇
2𝐵
𝑖=1
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Adaptive Signal Processing Information Theory Group
Vector Quantization using Lloyd Algorithm17/22
Step 2. Determine partitions {ℋ𝟏, … , ℋ𝟐𝑩} for a
given 𝓠, 𝓡
15
ℋ𝑖∗ = {𝐇 ∈ ℂ𝑀𝑟×𝑀𝑡: 𝑑 𝐇, 𝑖 ≥ 𝑑 𝐇, 𝑘 , ∀𝑖, 𝑘 ∈ 1, … , 2𝐵 , 𝑖 ≠ 𝑘}
ℋ∗ = {ℋ𝟏∗, … , ℋ
𝟐𝑩∗ }
= {𝐇 ∈ ℂ𝑀𝑟×𝑀𝑡: 𝑅𝑗 ⋅ 1[𝑅𝑗 < log2 det 𝐈 + 𝐇𝐐𝑗𝐇∗ ] ⋅ 𝑃𝑖𝑗
𝐶𝑆𝐼𝑇
2𝐵
𝑗=1
≥ 𝑅𝑗 ⋅ 1[𝑅𝑗 < log2 det 𝐈 + 𝐇𝐐𝑗𝐇∗ ] ⋅ 𝑃𝑘𝑗
𝐶𝑆𝐼𝑇
2𝐵
𝑗=1
∀𝑖, 𝑘 ∈ 1, … , 2𝐵 , 𝑖 ≠ 𝑘}
Repeat Step 2 & 3 Until Convergence
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Adaptive Signal Processing Information Theory Group
Beamforming in MISO : Rank One 𝐐18/22
Beamforming Vector
• 𝐟[𝒌] : Channel Dependent Beamforming Vector,
𝐟[𝑘] 2 = 1
• 𝑀𝑡 × 1 MISO Case
• 𝐡 𝑘 : Perfect Channel Column Vector
𝐱 𝑘 = 𝜌𝐟[𝑘]𝑠[𝑘]
𝐟 𝑘 = arg max𝐟: 𝐟 =1
log2(1 + 𝜌 𝐡𝑇𝐟 2)
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Adaptive Signal Processing Information Theory Group
Limited Feedback for Beamforming20/22
1. Antenna Selection
2. Channel Vector Quantization ℋ = {𝐡𝟏, … , 𝐡𝟐𝑩}
17
𝑚𝑜𝑝𝑡 𝑘 = arg max1≤𝑚≤𝑀𝑡
ℎ𝑚 𝑘 2
𝑛𝑜𝑝𝑡 𝑘 = arg max1≤𝑛≤2𝐵
𝐡𝑛∗ 𝐡 𝑘 2
𝐟 𝑘 = arg max𝐟: 𝐟 =1
log2(1 + 𝜌 𝐡𝑛𝑜𝑝𝑡[𝑘]𝑇 𝐟
2)
=𝐡𝑛𝑜𝑝𝑡[𝑘]
𝑇∗
𝐡𝑛𝑜𝑝𝑡 𝑘2
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Adaptive Signal Processing Information Theory Group
Limited Feedback for Beamforming20/22
3. K-Phase Quantization for 𝟐 × 𝟏 MISO
4. Codebook Index within 𝓕 = {𝐟𝟏, … , 𝐟𝟐𝑩}
Grassmannian Line Packing maximizing min. 𝑑(ℱ)
18
𝑛𝑜𝑝𝑡[𝑘] = arg max1≤𝑖≤𝐾
𝐡𝑇 𝑘 𝐟𝒊2
𝐟𝑖 =1
2
1
𝑒𝑗2𝜋𝑖𝐾
𝑑 𝓕 = 1 − max1≤𝑖<𝑗≤2𝐵
𝐟𝑖∗𝐟𝑗
2= min
1≤𝑖<𝑗≤2𝐵sin 𝜃𝑖𝑗
𝓕 ∈ ℂ𝑀𝑡 𝐟𝑖 2 = 1
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Adaptive Signal Processing Information Theory Group
Limited Feedback for Spatial Multiplexing20/22
Linear Precoding for Spatial Multiplexing
• 𝐅 𝑘 : Precoding Matrix, 𝑀𝑡 × 𝑀, 𝐅 𝑘 𝐹2 ≤ 𝑀
• 𝐬[𝑘] : Signal Vector, 𝐄𝐬 𝐬 𝑘 𝐬∗ 𝑘 =1
𝑀𝐈
𝐲 𝑘 = 𝜌𝐇 𝑘 𝐅 𝑘 𝐬 𝑘 + 𝐧[𝑘]
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Adaptive Signal Processing Information Theory Group
Limited Feedback for Spatial Multiplexing20/22
1. Antenna Subset Selection
Choose 𝑀 antenna ports for Power Control or Rate Maximization
2. Codebook 𝓕 = {𝐅𝟏, … , 𝐅𝟐𝑩}
Grassmannian 𝑴-Dim. Line Packing
Householder Reflection Matrix
20
𝐅 𝑘 = 𝑐ℎ𝑜𝑜𝑠𝑒 𝑀 𝑐𝑜𝑙𝑢𝑚𝑛𝑠 [𝐼𝑀𝑡×𝑀𝑡]
log2𝑀𝑡
𝑀 bits
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Adaptive Signal Processing Information Theory Group
Limited Feedback : Space-Time Coding20/22
Received Signal
Limited Feedback
1. Codebook 𝓕 = {𝐅𝟏, … , 𝐅𝟐𝑩}
Grassmannian Subspace Packing
2. Rate Adaptation : Adaptive Constellation
Feedback of Constellation Size ~ SNR
3. Quantized Phase
𝐘𝑀𝑟×𝑀𝑆𝑇𝑘 = 𝜌𝐇 𝑘 𝐅 𝑘 𝐒𝑀×𝑀𝑆𝑇
𝑘 + 𝐍𝑀𝑟×𝑀𝑆𝑇[𝑘]
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter Receiver
… …
Ant. 1
Ant. 2
Ant. 𝑴𝒕
Ant. 1
Ant. 2
Ant. 𝑴𝒓
Feedback Design
𝐇
Limited Feedback 𝐇
𝐅
Codebook Design
Channel
22
Narrowband (NB) Broadband (BB)
Single User (SU) / Multiple User (MU)
Single Antenna (SA) Multiple Antenna (MA)
Narrowband (NB) Broadband (BB)
𝑺 𝐗
𝐍
𝐘
𝐲 𝑣 𝑘 = 𝐇 𝑣 𝑘 𝐱 𝑣 𝑘 +𝐧 𝑣 𝑘
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Adaptive Signal Processing Information Theory Group
SU-MA-BB in Frequency Domain 21/22
Received Signal in Frequency Domain
𝒗 : Subcarrier Index
Subcarrier Power Allocation
𝜌𝑣 : SNR on subcarrier 𝑣
𝐲 𝑣 𝑘 = 𝐇 𝑣 𝑘 𝐱 𝑣 𝑘 +𝐧 𝑣 𝑘
𝐱 𝑣 𝑘 = 𝜌𝑣 𝐅 𝑣 𝑘 𝐬 𝑣[𝑘 ]
23
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Adaptive Signal Processing Information Theory Group
Limited Feedback : SU-MA-BB22/22
Limited Feedback using Interpolation
𝐟𝑗
𝐟𝑖
𝐟𝑘
Interpolated Subcarriers
𝑖 th subcarrier Feedback
(Pilot)
Reported Pilot Feedback
Vectors
Interpolated vectors
24
𝐟 𝑘 =𝑏𝑖𝐟𝑖 + 𝑏𝑗𝐟𝑗
𝑏𝑖𝐟𝑖 + 𝑏𝑗𝐟𝑗 2
𝑏𝑖 , 𝑏𝑗 ≥ 0
𝑏𝑖 + 𝑏𝑗 = 1
𝑓𝑖 2 = 𝑓𝑗 2= 1
𝐰𝑙 𝐰𝑙+1
𝐰 𝑙𝐾 + 𝑘; 𝜃𝑙 =1 − 𝑐𝑘 𝐰𝑙 + 𝑐𝑘𝑒𝑗𝜃𝑙𝐰𝑙+1
1 − 𝑐𝑘 𝐰𝑙 + 𝑐𝑘𝑒𝑗𝜃𝑙𝐰𝑙+1
𝑐𝑘 =𝑘 − 1
𝐾 0 ≤ 𝑘 ≤ 𝐾
𝜃𝑙 :Phase Rotation
𝒘
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter
User 1
…
Ant. 1
Feedback Design
𝐅
Codebook Design
25
Narrowband (NB) Broadband (BB)
Single User (SU) / Multiple User (MU)
Single Antenna (SA) Multiple Antenna (MA)
Narrowband (NB) Broadband (BB)
𝐬𝟏
𝐬𝑈
… User 2
User U
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Adaptive Signal Processing Information Theory Group
Milti-user & Single Transmit Antenna21/22
Resource Scheduling for Multiusers
Ensure larger rate & better reliability
Maximum Throughput ~ Largest Received SNR
Needs Each User Receiver SNR
SNR Limited Feedback
One bit according to predefined threshold SNR
Quantized SNR of Each User
Quantized SNR of Subchannels in FDMA
26
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Adaptive Signal Processing Information Theory Group
OutlineTransmitter
…
Ant. 1
Ant. 2
Ant. 𝑴𝒕
𝐅
Codebook Design
27
Narrowband (NB) Broadband (BB)
Single User (SU) / Multiple User (MU)
Single Antenna (SA) Multiple Antenna (MA)
Narrowband (NB) Broadband (BB)
𝐬𝟏
𝐬𝑈
… Ant. 𝑴𝒓
Receiver 1 …
Ant. 𝟏
Receiver U …
Ant. 𝟏 …
Ant. 𝑴𝒓
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Adaptive Signal Processing Information Theory Group
Milti-user MIMO21/22
Resource Scheduling for Multiusers
Maximizing Sum Rate
Spatial Resource Scheduling
Precoding (𝐅) for Spatial Interference Cancellation
Limited Feedback in MISO
Quantization of 𝐡𝑖[𝑘]
1 Bit Effective SNR or Quantized Effective SNR
28
𝑦𝑖 𝑘 = 𝐡𝑖𝑇 𝑘 𝐱 𝑘 + 𝑛𝑖[𝑘]
𝐱 𝑘 = 𝜌𝐅 𝑘 𝐬[𝑘]
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Adaptive Signal Processing Information Theory Group
Milti-user MIMO21/22
Limited Feedback in MIMO
Quantized Codebook Index based on VQ
Block Diagonalization Information
Quantized Elements of Channel Matrix
Antenna Selection Information
Limited Feedback associated with Relay
1 bit for Relay Selection
Codebook based feedback : Grassmannian or Lloyd Algorithm
29
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Adaptive Signal Processing Information Theory Group
21/22
30
Codebook Based Feedback in Standards
• 3GPP : WCDMA / LTE
• IEEE : WiMAX / WiFi
• 3GPP2 : CDMA
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Adaptive Signal Processing Information Theory Group
Limited Feedback in WCDMA21/22
Adaptive Technique
Open/Closed-loop Transmit Diversity (Tx.D)
𝟐 × 𝟐 MIMO
Limited Feedback for Closed-loop Tx.D
1 bit Phase Adjustment : Equal Gain Combining
0 or 𝜋 Phase Adjustment
4 bits Quantized Index : Amplitude & Phase
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Adaptive Signal Processing Information Theory Group
4 bit Quantization in WCDMA21/22
3 bits Phase & 1 bit Amplitude Quantization
32
Feedback Bits Phase
000 𝜋
001 −3𝜋
4
010 −2𝜋
4
011 −𝜋
4
100 0
101 𝜋
4
110 2𝜋
4
111 3𝜋
4
Feedback Bit 𝑷𝟏 / 𝑷𝟐
0 0.2 / 0.8
1 0.8 / 0.2
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Adaptive Signal Processing Information Theory Group
Limited Feedback in LTE21/22
Adaptive Technique
𝟒 × 𝟒 MIMO (𝟖 × 𝟖 for LTE Advanced)
Transmit Diversity & Spatial Multiplexing
Limited Feedback
Quantized 4 bit CQI Index
2 or 3 bit Differential CQI Feedback in Multiple CQI Reporting
Predefined Precoding Matrix Index (PMI)
PMI based on Householder Reflection Matrix
33
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Adaptive Signal Processing Information Theory Group
PMIs in LTE21/22
For 2 Antenna Ports
For 4 Antenna Ports (16 Possibilities)
A Set of Column Vectors from Householder Reflection Matrix
34
𝐖𝑛 = 𝐈 − 𝐮𝑛𝐮𝑛
𝐻
𝐮𝑛𝐻𝐮𝑛
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Adaptive Signal Processing Information Theory Group
Limited Feedback in IEEE 802-11n21/22
Adaptive Technique
𝟒 × 𝟒 MIMO
Transmit Diversity & Spatial Multiplexing
Limited Feedback per Subcarrier
Quantized Elements of Channel Matrix
A 3 bit Maximum Value
Scaling of Each Real and Imaginary Parts
35
3 + 2 ⋅ 𝑁𝑏 ⋅ 𝑀𝑅 ⋅ 𝑀𝑇 bits
𝑁𝑏 ∈ {4,5,6,8}
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Adaptive Signal Processing Information Theory Group
Limited Feedback in WiMAX21/22
Adaptive Technique
𝟒 × 𝟒 MIMO
Transmit Diversity & Spatial Multiplexing
Limited Feedback
Precoding Matrix
Householder Reflection Matrix
3 bits or 6 bits Indeces
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Adaptive Signal Processing Information Theory Group
PMIs in WiMAX21/22
37
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Adaptive Signal Processing Information Theory Group
Limited Feedback in 3GPP221/22
Adaptive Technique
𝟒 × 𝟒 MIMO
Limited Feedback
Precoding Matrix
Knockdown Codebook
- Identity or Q-level Fourier Matrix
Readymade Precoding Matrix : 64 entries
38
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Adaptive Signal Processing Information Theory Group
PMIs in 3GPP221/22
Q – Level Fourier Matrix Generation
39
𝒬 = {𝐄𝑀0
, 𝐄𝑀1
, … , 𝐄𝑀𝑄−1
}
𝐄𝑀(𝑞)
= 𝑓𝑛𝑚𝑞
= 𝑒𝑗2𝜋𝑛𝑀 (𝑚+
𝑞𝑄)
𝐄4(0)
=1
2
1 11 𝑗
1 1−1 −𝑗
1 −11 −𝑗
1 −1−1 𝑗
𝐄4(1)
=1
2
1 11 + 𝑗
2
−1 + 𝑗
2
1 1−1 − 𝑗
2
1 − 𝑗
2𝑗 −𝑗
−1 + 𝑗
2
1 + 𝑗
2
𝑗 −𝑗1 − 𝑗
2
−1 − 𝑗
2
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Adaptive Signal Processing Information Theory Group
Summary : Limited Feedback21/22
Scalar Quantization
User SNR Qunatization
Subchannelization
On/Off Signaling of User/Antenna/Subchannel Selection
ACK/NACK Signaling
Use AMC Table
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Adaptive Signal Processing Information Theory Group
Summary : Limited Feedback21/22
Vector Quantization
By Lloyd Algorithm
By Grassmannian Line Packing
Beamformaing Vector Quantization
Phase Quantization
Interpollation Vector
41
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Adaptive Signal Processing Information Theory Group
Summary : Limited Feedback21/22
Quantization in Multiuser MIMO
Element Quantization of Channel Vector
Quantization of Effective User SNR
Limited Feedback per Subcarrier in Broadband System
Limited Feedback in Standards
Codebook based Quantization Index
- Householder Reflection Matrix
- Grassmannian Line Packing
- Fourier Matrix
42