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Feedback Methods for Multiple-Input Multiple-Output Wireless Systems. David J. Love WNCG The University of Texas at Austin March 4, 2004. Outline. Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO Limited Feedback Framework Limited Feedback Applications

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Feedback Methods for Multiple-Input Multiple-Output Wireless Systems


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

    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 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. Transmitter • • • 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 • • •

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

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

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

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

    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. Limited Feedback Problem • 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) Feedback amount around 5 to 10 bits

    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. Quantizer Feedback Design Problem • 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

    15. FX X H Open-Loop Space-Time Encoder Receiver F … … … … H Choose F from codebook Low-rate feedback path Update precoder 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

    16. Challenge #1: Codeword Selection Channel Realization H Codebook matrix • 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

    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. Communications Vector Quantization • Let • Communications Approach: [Love et al] System parameter to maximize Design Objective: Improve system performance • Different than traditional vector quantization

    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. Limited Feedback Beamforming[Love et al] unit vector • Convert MIMO to SISO • Beamforming advantages: • Error probability improvement • Resilience to fading Complex number r

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

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

    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. Bounding of Criterion Grassmann manifold radius2 metric ball volume [Love et al] Grassmannian Beamforming Criterion [Love et al]: Design by maximizing

    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. Simulation 3 by 3 QPSK Error Rate (log scale) 0.6 dB SNR (dB)

    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. 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. Orthogonal Space-Time Block Codes (OSTBC) • 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

    30. Solution: Limited Feedback Precoded OSTBC [Love et al] • Require • Use codebook:

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

    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. Precoded OSTBC save at least bits compared to beamforming! 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.

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

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

    38. Limited Feedback Precoded SM[Love et al] • Assume • Again adopt codebook approach

    39. Channel Realization H Codebook matrix 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]

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

    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. 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. Multi-Mode Precoding • Fixed rate • Adaptively vary number of substreams • Yields • Full diversity order • Rate growth of spatial multiplexing >98% Capacity Ratio >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. 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. Visually important Diversity 4 … Diversity 2 Visually unimportant Diversity 1 Assorted Areas • MIMO channel modeling • IEEE 802.11N covariance generation • Joint source-channel space-time coding

    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. 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. Beamforming Criterion • [Love et al] • Differentiation maximize