Limited Feedback in Wireless Communication Systems

Transcription

1 Limited Feedback in Wireless Communication Systems - Summary of An Overview of Limited Feedback in Wireless Communication Systems Gwanmo Ku May 14, 17, and 21, 2013

2 Outline Transmitter Ant. 1 Channel N Ant. 1 Receiver S F Ant. 2 X H Ant. 2 Y Ant. M t Ant. M r Codebook Design Limited Feedback H Feedback Design Single User (SU) / Multiple User (MU) Single Antenna (SA) Multiple Antenna (MA) Narrowband (NB) Broadband (BB) Narrowband (NB) Broadband (BB) 2

3 Outline n[k] s[k] Transmitter f[k] Ant. 1 Ant. 1 x[k] h[k] Slow fading y[k] Receiver Codebook Design Feedback Design Limited Feedback H Single User (SU) / Multiple User y k = h k x k + n[k] Single Antenna (SA) Multiple Antenna Narrowband (NB) Broadband Narrowband Broadband 3

4 SU - SA - NB with Perfect CSI 12/22 Received Signal y k = h k x k + n[k] Adaptive Power Allocation by Waterfilling x k = ρ(h[k]) s[k] ρ(h) = arg max log 2(1 + ρ h[k] h[k] 2 ) E h k,x[k] x k 2 ρ How to measure Channel State h[k] at the receiver? By Training Sequence from Tx. 4

5 Water-filling L P 1,, P k = Power ν Y j = X j + Z j I X 1,, X k ; Y 1,, Y k k i=1 1 2 log(1 + P i N i ) k 2 j = 0,, k, Z j N(0, N j ), E j=1 X j k i=1 k + λ( P i i=1 P i = ν N i + ν N i + Ref : Elements of Information Theory by Thomas Cover k i=1 1 2 log(1 + P i N i ) P) = P P 4 = λ = 0 2 P i + N i P 12/22 P 1 P 2 P 3 P 5 N 4 N 1 N 2 N 3 N 5 Channel 1 Channel 2 Channel 3 Channel 4 Channel 5 Channel 5

6 Limited Feedback : SU-SA-NB 12/22 1. Quantization of h[k], γ = h k 2 I γ 2. Rate Quantization by Lloyd algorithm Find Quantization Level minimizing Distortion Measure Optimal Rate Partitions associated with Limited feedback 3. On/Off Rate Adaptation = i, γ [γ b i, γ b i+1 ), i = 0,, Q 1 1 bit : On/Off Transmission subject to the channel condition 4. ARQ ACK/NACK Signalling 1 bit : Successful Transmission or Re-transmission Required 6

7 Outline Transmitter s[k] x[k] f[k] Ant. 1 Channel h[k, l] L + 1 Paths n[k] Ant. 1 y[k] Receiver Codebook Design Limited Feedback H Feedback Design Single User (SU) / Multiple User Single Antenna (SA) Multiple Antenna L y k = h k, l x[k l] l=0 + n[k] Narrowband Broadband (BB) Narrowband Broadband 7

8 SU-SA-BB with Perfect CSI 14/22 Received Signal, OFDM Signalling L y k = h k, l x[k l] + n[k] l=0 Post-processing Signal in Frequency Domain y k = diag h[k] x k + n k Subcarrier Power Allocation x k = x 1 [k] x v [k] x N [k] x v [k] = P v s v [k] 8

9 Limited Feedback : SU-SA-BB 12/22 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 N pilot! sets, h min,pilots & h max,pilots 4. Adaptive Modulation and Coding Level Index : Modulation and Coding Scheme ~ SNR 9

10 Outline Transmitter Ant. 1 Channel n[k] Ant. 1 Receiver s[k] F Ant. 2 x[k] H[k] Ant. 2 y[k] Ant. M t Ant. M r Codebook Design Limited Feedback H Feedback Design Single User (SU) / Multiple User y k = H k x k + n[k] Single Antenna Multiple Antenna (MA) Narrowband Broadband Narrowband (NB) Broadband 10

11 SU-MA-NB with Perfect CSI 16/22 Received Signal y k = H k x k + n[k] M t M r MIMO System y k : M r 1 Complex Received Vector H k : M r M t, each entry has flat fading property x k : Transmitted Symbol with Power Constraint E H,x x k 2 2 ρ Average Power Constraint : E x x k 2 2 H k = H(t) ρt under E H ρ t ρ n k : M r 1 Complex Gaussian Noise according to CN(0,1) 11

12 SU-MA-NB : Rate Maximizing 17/22 Adaptive Power Allocation Q k : Covariance of the Tx. Sig. for each H[k] Q k = arg x k = ρ Q k 1 2s[k] max log Q:tr Q 1,Q 2 det(i + ρh k Q H k ) =Q,Q 0 Ergodic Capacity : R = E H [ max log Q:tr Q 1,Q 2 det I + ρhqh ] =Q,Q 0 s k : Channel independent Codeword with E s s k

13 Covariance Quantization 17/22 Codebook of Possible Cov. Matrices Q = {Q 1,, Q 2 B} Rate Maximizing Covariance Selecting n opt k = arg max 1 n 2 B log 2 det(i + ρh k Q n H k ) Maximum Achievable Rate R Q = E H [max Q Q log 2 det(i + ρhqh )] Codebook Generation Q based on VC using Lloyd Algorithm 13

14 Vector Quantization using Lloyd Algorithm 17/22 Step 1. Determine { Q 1, R 1,, Q 2 B, R 2 B } for an initial partition {H 1,, H 2 B} Define a distortion measure Q, R = arg max Q 1,R 1,,{Q 2 B,R 2 B} = arg max Q 1,R 1,,{Q 2 B,R 2 B} Pr H H i 2 B d H, i = R j 1(R j < log 2 det I + HQ j H ) P ij CSIT i=1 P ij CSIT 2 B i=1 2 B E H d H, i H H i Pr[H H i ] 2 B j=1 i=1 R j Pr[R j < log 2 det I + HQ j H H H i ] Q = {Q 1,, Q 2 B} R = {R 1,, R 2 B} 14

15 Vector Quantization using Lloyd Algorithm 17/22 Step 2. Determine partitions {H 1,, H 2 B} for a given Q, R H i = {H C M r M t : d H, i d H, k, i, k 1,, 2 B, i k} 2 B = {H C M r M t : R j 1[R j < log 2 det I + HQ j H ] P ij CSIT j=1 2 B R j 1[R j < log 2 det I + HQ j H CSIT ] P kj j=1 i, k 1,, 2 B, i k} H = {H 1,, H 2 B} Repeat Step 2 & 3 Until Convergence 15

16 Beamforming in MISO : Rank One Q 18/22 Beamforming Vector x k = f[k] : Channel Dependent Beamforming Vector, f[k] 2 = 1 M t 1 MISO Case ρf[k]s[k] f k = arg max f: f =1 log 2(1 + ρ h T f 2 ) h k : Perfect Channel Column Vector 16

17 Limited Feedback for Beamforming 20/22 1. Antenna Selection m opt k = arg max h m k 2 1 m M t 2. Channel Vector Quantization H = {h 1,, h 2 B} n opt k = arg max 1 n 2 B h n h k 2 f k = arg max log 2(1 + ρ h f: f =1 nopt [k] f 2 ) = h T n opt [k] h nopt k 2 T 17

18 Limited Feedback for Beamforming 20/22 3. K-Phase Quantization for 2 1 MISO n opt [k] = arg max 1 i K ht k f i 2 f i = e j2π i K 4. Codebook Index within F = {f 1,, f 2 B} Grassmannian Line Packing maximizing min. d(f) d F = 1 max 1 i<j 2 B f i f j 2 = min 1 i<j 2 B sin θ ij F C M t f i 2 = 1 18

19 Limited Feedback for Spatial Multiplexing 20/22 Linear Precoding for Spatial Multiplexing y k = ρh k F k s k + n[k] F k : Precoding Matrix, M t M, F k F 2 M s[k] : Signal Vector, E s s k s k = 1 M I 19

20 Limited Feedback for Spatial Multiplexing 20/22 1. Antenna Subset Selection log 2 F k = choose M columns [I Mt M t ] M t M bits Choose M antenna ports for Power Control or Rate Maximization 2. Codebook F = {F 1,, F 2 B} Grassmannian M-Dim. Line Packing Householder Reflection Matrix 20

21 Limited Feedback : Space-Time Coding 20/22 Received Signal Y Mr M ST k = ρh k F k S M MST k + N Mr M ST [k] Limited Feedback 1. Codebook F = {F 1,, F 2 B} Grassmannian Subspace Packing 2. Rate Adaptation : Adaptive Constellation Feedback of Constellation Size ~ SNR 3. Quantized Phase 21

22 Outline Transmitter Ant. 1 Channel N Ant. 1 Receiver S F Ant. 2 X H Ant. 2 Y Ant. M t Ant. M r Codebook Design Limited Feedback H Feedback Design Single User (SU) / Multiple User (MU) y v k = H v k x v k +n v k Single Antenna (SA) Multiple Antenna (MA) Narrowband (NB) Broadband (BB) Narrowband (NB) Broadband (BB) 22

23 SU-MA-BB in Frequency Domain 21/22 Received Signal in Frequency Domain y v k = H v k x v k +n v k v : Subcarrier Index Subcarrier Power Allocation x v k = ρ v F v k s v [k] ρ v : SNR on subcarrier v 23

24 Limited Feedback : SU-MA-BB 22/22 Limited Feedback using Interpolation w l w w l+1 Reported Pilot Feedback Vectors f j f k Interpolated Subcarriers w lk + k; θ l = 1 c k w l + c k e jθ lw l+1 1 c k w l + c k e jθ l wl+1 c k = k 1 0 k K K θ l :Phase Rotation f k = Interpolated vectors f i i th subcarrier Feedback (Pilot) b if i + b j f j b i f i + b j f j 2 b i, b j 0 b i + b j = 1 f i 2 = f j 2 = 1 24

25 Outline s 1 s U Transmitter F Codebook Design Ant. 1 User 1 User 2 User U Feedback Design Single User (SU) / Multiple User (MU) Single Antenna (SA) Multiple Antenna (MA) Narrowband (NB) Broadband (BB) Narrowband (NB) Broadband (BB) 25

26 Milti-user & Single Transmit Antenna 21/22 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

27 Outline s 1 Transmitter F Ant. 1 Ant. 2 Ant. 1 Ant. M r Ant. 1 Receiver 1 s U Codebook Design Ant. M t Receiver U Ant. M r Single User (SU) / Multiple User (MU) Single Antenna (SA) Multiple Antenna (MA) Narrowband (NB) Broadband (BB) Narrowband (NB) Broadband (BB) 27

28 Milti-user MIMO 21/22 Resource Scheduling for Multiusers Maximizing Sum Rate Spatial Resource Scheduling Precoding (F) for Spatial Interference Cancellation Limited Feedback in MISO y i k = h i T k x k + n i [k] Quantization of h i [k] 1 Bit Effective SNR or Quantized Effective SNR x k = ρf k s[k] 28

29 Milti-user MIMO 21/22 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

30 21/22 Codebook Based Feedback in Standards 3GPP : WCDMA / LTE IEEE : WiMAX / WiFi 3GPP2 : CDMA 30

31 Limited Feedback in WCDMA 21/22 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 31

32 4 bit Quantization in WCDMA 21/22 3 bits Phase & 1 bit Amplitude Quantization Feedback Bits Phase 000 π 001 3π 4 Feedback Bit P 1 / P / / π π π 4 2π 4 3π 4 32

33 Limited Feedback in LTE 21/22 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

34 PMIs in LTE 21/22 For 2 Antenna Ports For 4 Antenna Ports (16 Possibilities) A Set of Column Vectors from Householder Reflection Matrix W n = I u nu n H u n H u n 34

35 Limited Feedback in IEEE n 21/22 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 N b M R M T bits N b {4,5,6,8} 35

36 Limited Feedback in WiMAX 21/22 Adaptive Technique 4 4 MIMO Transmit Diversity & Spatial Multiplexing Limited Feedback Precoding Matrix Householder Reflection Matrix 3 bits or 6 bits Indeces 36

37 PMIs in WiMAX 21/22 37

38 Limited Feedback in 3GPP2 21/22 Adaptive Technique 4 4 MIMO Limited Feedback Precoding Matrix Knockdown Codebook - Identity or Q-level Fourier Matrix Readymade Precoding Matrix : 64 entries 38

39 PMIs in 3GPP2 21/22 Q Level Fourier Matrix Generation Q = {E M 0, E M 1,, E M Q 1 } E M (q) = fnm q = e j2πn M (m+q Q ) E 4 (0) = j j j j E 4 (1) = j j 2 2 j j 1 + j 1 + j 1 1 j 1 1 j 2 2 j j 1 j 1 j

40 Summary : Limited Feedback 21/22 Scalar Quantization User SNR Qunatization Subchannelization On/Off Signaling of User/Antenna/Subchannel Selection ACK/NACK Signaling Use AMC Table 40

41 Summary : Limited Feedback 21/22 Vector Quantization By Lloyd Algorithm By Grassmannian Line Packing Beamformaing Vector Quantization Phase Quantization Interpollation Vector 41

42 Summary : Limited Feedback 21/22 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