1. Feedback Benefits in MIMO Communication Systems David J. Love Center for Wireless Systems and Applications School of Electrical and Computer Engineering Purdue University djlove@ecn.purdue.edu

2. CWSA – Purdue University 2 Multiple Antenna Wireless Systems Multiple-input multiple-output (MIMO) using multiple antennas at transmitter and receiver Antennas spaced independent fading Offer improvements in capacity and reliability Receiver Transmitter

3. CWSA – Purdue University 3 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

4. CWSA – Purdue University 4 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 Dramatic performance benefits

5. CWSA – Purdue University 5 Transmitter Channel Knowledge Fundamental problem: How does the transmitter find out the current channel conditions? Observation: Receiver knows the channel Solution: Use feedback

6. CWSA – Purdue University 6 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

7. CWSA – Purdue University 7 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

8. CWSA – Purdue University 8 Convert MIMO to SISO Beamforming advantages: Error probability improvement Resilience to fading Example 1: Limited Feedback Beamforming unit vector r Complex number

9. CWSA – Purdue University 9 Nearest neighbor union bound [Cioffi] Instantaneous channel capacity [Cover & Thomas] [Love et al] Challenge #1: Beamformer Selection

10. CWSA – Purdue University 10 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

11. CWSA – Purdue University 11 Bounding of Criterion Grassmannian Beamforming Criterion [Love et al]: Design by maximizing Grassmann manifold metric ball volume [Love et al]radius 2

12. CWSA – Purdue University 12 Simulation 3 by 3 QPSK SNR (dB) Error Rate (log scale) 0.6 dB

13. CWSA – Purdue University 13 Example 2: Limited Feedback Precoded OSTBC Require Use codebook:

14. CWSA – Purdue University 14 Challenge #1: Codeword Selection Can bound error rate [Tarokh et al] Choose matrix from from as [Love et al] Channel Realization H Codebook matrix

15. CWSA – Purdue University 15 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

16. CWSA – Purdue University 16 Simulation 8 by 1 Alamouti 16-QAM 9.5dB Open-Loop 16bit channel 8bit lfb precoder Error Rate (log scale) SNR (dB)

17. CWSA – Purdue University 17 Example 3:Limited Feedback Precoded Spatial Multiplexing Assume Again adopt codebook approach

18. CWSA – Purdue University 18 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

19. CWSA – Purdue University 19 Challenge #2: Distortion Function Min distance, min singular value, MMSE (with trace) [Love et al] MMSE (with det) and capacity [Love et al]

20. CWSA – Purdue University 20 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

21. CWSA – Purdue University 21 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)

22. CWSA – Purdue University 22 Conclusions Limited feedback allows closed-loop MIMO Beamforming Precoded OSTBC Precoded spatial multiplexing Large performance gains available with limited feedback Limited feedback application IEEE 802.16e IEEE 802.11n

23. CWSA – Purdue University 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. CWSA – Purdue University 24 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.

25. CWSA – Purdue University 25 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

26. CWSA – Purdue University 26 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)

27. CWSA – Purdue University 27 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!

28. CWSA – Purdue University 28 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.

29. CWSA – Purdue University 29 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

30. CWSA – Purdue University 30 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

31. CWSA – Purdue University 31 Limited Feedback Precoded SM [Love et al] Assume Again adopt codebook approach

32. CWSA – Purdue University 32 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

33. CWSA – Purdue University 33 Challenge #2: Distortion Function Min distance, min singular value, MMSE (with trace) [Love et al] MMSE (with det) and capacity [Love et al]

34. CWSA – Purdue University 34 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

35. CWSA – Purdue University 35 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)

36. CWSA – Purdue University 36 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.

37. CWSA – Purdue University 37 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

38. CWSA – Purdue University 38 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.

39. CWSA – Purdue University 39 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.

40. CWSA – Purdue University 40 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 …

41. CWSA – Purdue University 41 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

42. CWSA – Purdue University 42 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

43. CWSA – Purdue University 43 Beamforming Criterion [Love et al] Differentiation maximize

44. CWSA – Purdue University 44 Precode OSTBC Criterion Let

45. CWSA – Purdue University 45 Precode OSTBC – Cont. [Barg et al] Differentiation maximize

46. CWSA – Purdue University 46 Precode Spat Mult Criterion – Min SV Let Differentiation maximize

47. CWSA – Purdue University 47 Precode Spat Mult Criterion – Capacity Let Differentiation maximize

48. CWSA – Purdue University 48 SM Susceptible to Channel Decreasing Fix Condition number

49. CWSA – Purdue University 49 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?

50. CWSA – Purdue University 50 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

51. CWSA – Purdue University 51 Channel Assumptions Flat-fading (single-tap) Antennas widely spaced (channels independent) BW frequency (Hz)

52. CWSA – Purdue University 52 Solution: Limited Feedback Precoding Use codebook Codebook known at transmitter and receiver Convey codebook index when channel changes bits

53. CWSA – Purdue University 53 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

54. CWSA – Purdue University 54 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 …

55. CWSA – Purdue University 55 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 …