1. Feedback Methods for Multiple-Input Multiple-Output Wireless Systems David J. Love WNCG The University of Texas at Austin March 4, 2004

2. Wireless Networking and Communication Group 2 Outline Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

3. Wireless Networking and Communication Group 3 Wireless Challenges Spectral efficiency Spectrum very expensive $$$ Maximize data rate per bandwidth bits/sec/Hz Quality Wireless links fluctuate Desire SNR to have large mean and low variance Limited transmit power How can we maximize spectral efficiency and quality?

4. Wireless Networking and Communication Group 4 Solution: MIMO Wireless Systems Multiple-input multiple-output (MIMO) using multiple antennas at transmitter and receiver Antennas spaced independent fading Allow space-time signaling Receiver Transmitter

5. Wireless Networking and Communication Group 5 SNR (dB) MIMO Capacity Benefits [Telatar] Multiply Data Rate Multiply throughput $$$ Multiply # users $$$ min(Tx,Rx) antennas Rate Slope 1 by 1 antenna 4.3 b/s/Hz 8 by 8 antennas 32.3 b/s/Hz Capacity 1 by 16 antennas 9 b/s/Hz

6. Wireless Networking and Communication Group 6 Signal Quality Through Diversity Antennas provide diversity advantage [Brennan] Large gains for moderate to high SNR Reduced fading! Better user experience $$$ Signal Power standard with MIMO time 1 antenna 4 th order diversity Diversity = -slope SNR (dB) Error Rate (log scale)

7. Wireless Networking and Communication Group 7 MIMO Systems are Relevant Fixed wireless access 802.16.3 standard (optional) 3G cellular HSDPA – (optional) Local area networks 802.11N Study Group (possibly mandatory) Mobile Broadband Wireless 802.20 Working Group (possibly mandatory --- too early) 4G Lots of discussion

8. Wireless Networking and Communication Group 8 Space-Time Signaling Design in space and time Transmit matrices – transmit one column each transmission Sent over a linear channel time space Assumption: is an i.i.d. complex Gaussian matrix

9. Wireless Networking and Communication Group 9 Role of Channel Knowledge Open-loop MIMO [Tarokh et al] Signal matrix designed independently of channel Most popular MIMO architecture Closed-loop MIMO [Sollenberger],[Telatar],[Raleigh et al] Signal matrix designed as a function of channel Performance benefits

10. Wireless Networking and Communication Group 10 Closed-Loop Performance Benefits Channel capacity fundamentally larger Simplified decoding Reduced error rate Allows multiuser scheduling (transmit to group of best users) SNR (dB) Capacity SNR (dB) Error Rate (log scale) 4b/s/Hz 12 dB

11. Wireless Networking and Communication Group 11 Transmitter Channel Knowledge Fundamental problem: How does the transmitter find out the current channel conditions? Observation: Receiver knows the channel Solution: Use feedback

12. Wireless Networking and Communication Group 12 Solution: Send back feedback [Narula et al],[Heath et al] Feedback channel rate very limited Rate  1.5 kb/s (commonly found in standards, 3GPP, etc) Update  3 to 7 ms (from indoor coherence times) Limited Feedback Problem Feedback amount around 5 to 10 bits

13. Wireless Networking and Communication Group 13 Outline Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

14. Wireless Networking and Communication Group 14 Prior work [Narula et al],[Jongren et al]: Quantize channel Channel quantization fails for MIMO 8x8 MIMO = More than 128 bits of feedback! Singular value structure sensitive to quantization Feedback Design Problem Quantizer

15. Wireless Networking and Communication Group 15 Solution: Limited Feedback Precoding Use open-loop algorithm with linear transformation (precoder) Restrict to Codebook known at transmitter/receiver and fixed Convey codebook index when channel changes bits H Choose F from codebook Update precoder Low-rate feedback path … Open-Loop Space-Time Encoder Receiver … H X F … … FX

16. Wireless Networking and Communication Group 16 Use selection function such that Selection function depends on Underlying open-loop algorithm Performance criterion Solution: Use perfect channel knowledge selection but optimize over codebook Challenge #1: Codeword Selection Channel Realization H Codebook matrix

17. Wireless Networking and Communication Group 17 Challenge #2: Codebook Design Codebook design very important Given: Underlying open-loop algorithm Selection function Goal: Quantize (in some sense) the perfect channel knowledge precoder

18. Wireless Networking and Communication Group 18 Communications Vector Quantization Let Communications Approach: [Love et al] System parameter to maximize Design Objective: Improve system performance Different than traditional vector quantization

19. Wireless Networking and Communication Group 19 Outline Introduction MIMO Background MIMO Signaling Channel adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

20. Wireless Networking and Communication Group 20 Convert MIMO to SISO Beamforming advantages: Error probability improvement Resilience to fading Limited Feedback Beamforming [Love et al] unit vector r Complex number

21. Wireless Networking and Communication Group 21 Nearest neighbor union bound [Cioffi] Instantaneous channel capacity [Cover & Thomas] [Love et al] Challenge #1: Beamformer Selection

22. Wireless Networking and Communication Group 22 Want to maximize on average Average distortion Using sing value decomp & Gaussian random matrix results [James 1964] ( ) where is a uniformly distributed unit vector Challenge #2: Beamformer Codebook channel termcodebook term

23. Wireless Networking and Communication Group 23 Codebook as Subspace Code is a subspace distance – only depends on subspace not vector Codebook is a subspace code Minimum distance [Sloane et al] set of lines

24. Wireless Networking and Communication Group 24 Bounding of Criterion Grassmannian Beamforming Criterion [Love et al]: Design by maximizing Grassmann manifold metric ball volume [Love et al]radius 2

25. Wireless Networking and Communication Group 25 Feedback vs Diversity Advantage Question: How does the feedback amount affect diversity advantage? Diversity Theorem [Love & Heath]: Full diversity advantage if and only if bits of feedback Proof Sketch: 1. Use: Gaussian matrices are isotropically random 2. Bound by selection diversity (known full diversity)

26. Wireless Networking and Communication Group 26 Simulation 3 by 3 QPSK SNR (dB) Error Rate (log scale) 0.6 dB

27. Wireless Networking and Communication Group 27 Beamforming Summary Contribution #1: Framework for beamforming when channel not known a priori at transmitter Codebook of beamforming vectors Relates to codes of Grassmannian lines Contribution #2: New distance bounds on Grassmannian line codes Contribution #3: Characterization of feedback-diversity relationship More info: D. J. Love, R. W. Heath Jr., and T. Strohmer, “Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems,” IEEE Trans. Inf. Th., vol. 49, Oct. 2003. D. J. Love and R. W. Heath Jr., “Necessary and Sufficient Conditions for Full Diversity Order in Correlated Rayleigh Fading Beamforming and Combining Systems,” accepted to IEEE Trans. Wireless Comm., Dec. 2003.

28. Wireless Networking and Communication Group 28 Outline Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

29. Wireless Networking and Communication Group 29 Constructed using orthogonal designs [Alamouti, Tarokh et al] Advantages Simple linear receiver Resilience to fading Do not exist for most antenna combs (complex signals) Performance loss compared to beamforming Orthogonal Space-Time Block Codes (OSTBC)

30. Wireless Networking and Communication Group 30 Solution: Limited Feedback Precoded OSTBC [Love et al] Require Use codebook:

31. Wireless Networking and Communication Group 31 Challenge #1: Codeword Selection Can bound error rate [Tarokh et al] Choose matrix from from as [Love et al] Channel Realization H Codebook matrix

32. Wireless Networking and Communication Group 32 Challenge #2: Codebook Design Minimize loss in channel power Grassmannian Precoding Criterion [Love & Heath]: Maximize minimum chordal distance Think of codebook as a set (or packing) of subspaces Grassmannian subspace packing

33. Wireless Networking and Communication Group 33 Feedback vs Diversity Advantage Question: How does feedback amount affect diversity advantage? Theorem [Love & Heath]: Full diversity advantage if and only if bits of feedback Proof similar to beamforming proof. Precoded OSTBC save at least bits compared to beamforming!

34. Wireless Networking and Communication Group 34 Simulation 8 by 1 Alamouti 16-QAM 9.5dB Open-Loop 16bit channel 8bit lfb precoder Error Rate (log scale) SNR (dB)

35. Wireless Networking and Communication Group 35 Precoded OSTBC Summary Contribution #1: Method for precoded orthogonal space-time block coding when channel not known a priori at transmitter Codebook of precoding matrices Relates to Grassmannian subspace codes with chordal distance Contribution #2: Characterization of feedback-diversity relationship More info: D. J. Love and R. W. Heath Jr., “Limited feedback unitary precoding for orthogonal space time block codes,” accepted to IEEE Trans. Sig. Proc., Dec. 2003. D. J. Love and R. W. Heath Jr., “Diversity performance of precoded orthogonal space-time block codes using limited feedback,” accepted to IEEE Commun. Letters, Dec. 2003.

36. Wireless Networking and Communication Group 36 Outline Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

37. Wireless Networking and Communication Group 37 True “multiple-input” algorithm Advantage: High-rate signaling technique Decode Invert (directly/approx) Disadvantage: Performance very sensitive to channel singular values Spatial Multiplexing [Foschini] { Multiple independent streams

38. Wireless Networking and Communication Group 38 Limited Feedback Precoded SM [Love et al] Assume Again adopt codebook approach

39. Wireless Networking and Communication Group 39 Challenge #1: Codeword Selection Selection functions proposed when known Use unquantized selection functions over MMSE (linear receiver) [Sampath et al], [Scaglione et al] Minimum singular value (linear receiver) [Heath et al] Minimum distance (ML receiver) [Berder et al] Instantaneous capacity [Gore et al] Channel Realization H Codebook matrix

40. Wireless Networking and Communication Group 40 Challenge #2: Distortion Function Min distance, min singular value, MMSE (with trace) [Love et al] MMSE (with det) and capacity [Love et al]

41. Wireless Networking and Communication Group 41 Codebook Criterion Grassmannian Precoding Criterion [Love & Heath]: Maximize Min distance, min singular value, MMSE (with trace) – Projection two-norm distance MMSE (with det) and capacity – Fubini-Study distance

42. Wireless Networking and Communication Group 42 Simulation 4 by 2 2 substream 16-QAM 16bit channel Perfect Channel 6bit lfb precoder 4.5dB Error Rate (log scale) SNR per bit (dB)

43. Wireless Networking and Communication Group 43 Precoded Spatial Multiplexing Summary Contribution #1: Method for precoding spatial multiplexing when channel not known a priori at transmitter Codebook of precoding matrices Relates to Grassmannian subspace codes with projection two- norm/Fubini-Study distance Contribution #2: New bounds on subspace code density More info: D. J. Love and R. W. Heath Jr., “Limited feedback unitary precoding for spatial multiplexing systems,” submitted to IEEE Trans. Inf. Th., July 2003.

44. Wireless Networking and Communication Group 44 Outline Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing Other Areas of Research

45. Wireless Networking and Communication Group 45 Multi-Mode Precoding Fixed rate Adaptively vary number of substreams Yields Full diversity order Rate growth of spatial multiplexing Capacity Ratio >98% >85% SNR (dB) D. J. Love and R. W. Heath Jr., “Multi-Mode Precoding for MIMO Wireless Systems Using Linear Receivers,” submitted to IEEE Transactions on Signal Processing, Jan. 2004.

46. Wireless Networking and Communication Group 46 Space-Time Chase Decoding Decode high rate MIMO signals “costly” Existing decoders difficult to implement Solution([Love et al] with Texas Instruments): Space-time version of classic Chase decoder [Chase] Use linear or successive decoder as “initial bit estimate” Perform ML decoding over set of perturbed bit estimates D. J. Love, S. Hosur, A. Batra, and R. W. Heath Jr., “Space-Time Chase Decoding,” submitted to IEEE Transactions on Wireless Communications, Nov. 2003.

47. Wireless Networking and Communication Group 47 Assorted Areas MIMO channel modeling IEEE 802.11N covariance generation Joint source-channel space-time coding Diversity 4 Diversity 2 Diversity 1 Visually important Visually unimportant …

48. Wireless Networking and Communication Group 48 Future Research Areas Coding theory Subspace codes Binary transcoding Reduced complexity Reed-Solomon UWB & cognitive (or self-aware) wireless Capacity MIMO (???) Multi-user UWB Cross layer optimization (collaborative) Sensor networks Broadcast channel capacity schemes

49. Wireless Networking and Communication Group 49 Conclusions Limited feedback allows closed-loop MIMO Beamforming Precoded OSTBC Precoded spatial multiplexing Diversity order a function of feedback amount Large performance gains available with limited feedback Multi-mode precoding & Efficient decoding for MIMO signals

50. Wireless Networking and Communication Group 50 Beamforming Criterion [Love et al] Differentiation maximize

51. Wireless Networking and Communication Group 51 Precode OSTBC Criterion Let

52. Wireless Networking and Communication Group 52 Precode OSTBC – Cont. [Barg et al] Differentiation maximize

53. Wireless Networking and Communication Group 53 Precode Spat Mult Criterion – Min SV Let Differentiation maximize

54. Wireless Networking and Communication Group 54 Precode Spat Mult Criterion – Capacity Let Differentiation maximize

55. Wireless Networking and Communication Group 55 SM Susceptible to Channel Decreasing Fix Condition number

56. Wireless Networking and Communication Group 56 Vector Quantization Relationship Observation: Problem appears similar to vector quantization (VQ) In VQ, 1. Choose distortion function 2. Minimize distortion function on average VQ distortion chosen to improve fidelity of quantized signal Can we define a distortion function that ties to communication system performance?

57. Wireless Networking and Communication Group 57 Grassmannian Subspace Packing Complex Grassmann manifold set of M-dimensional subspaces in Packing Problem Construct set with maximum minimum distance Distance between subspaces Chordal Projection Two-Norm Fubini-Study Column spaces of codebook matrices represent a set of subspaces in 11 22

58. Wireless Networking and Communication Group 58 Channel Assumptions Flat-fading (single-tap) Antennas widely spaced (channels independent) BW frequency (Hz)

59. Wireless Networking and Communication Group 59 Solution: Limited Feedback Precoding Use codebook Codebook known at transmitter and receiver Convey codebook index when channel changes bits

60. Wireless Networking and Communication Group 60 Communications Vector Quantization Let VQ Approach: Design Objective: Approximate optimal solution Communications Approach: [Love et al] System parameter to maximize Design Objective: Improve system performance

61. Wireless Networking and Communication Group 61 True “multiple-input” algorithm Advantage: High-rate signaling technique Decode Invert (directly/approx) Disadvantage: Performance very sensitive to channel singular values Spatial Multiplexing [Foschini] } Multiple independent streams …

62. Wireless Networking and Communication Group 62 Assorted Areas MIMO channel modeling IEEE 802.11N covariance generation Joint source-channel space-time coding Diversity 4 Diversity 2 Diversity 1 Visually important Visually insignificant …