Precoding Precoding and Interpolation forand Interpolation forSpatial Multiplexing MIMO-OFDMSpatial Multiplexing MIMO-OFDMwith Limited Feedbackwith Limited Feedback

Prof. Robert W. Heath Jr.Joint work with Prof. David Love* and Dr. Jihoon Choi**

Wireless Networking and Communications Group (WNCG)Dept. of Electrical and Computer Engineering

The University of Texas at AustinJuly 30, 2004

* Purdue University ** Samsung Electronics

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OutlineOutline Introduction - Closed-loop MIMO communication Quantized precoding for spatial multiplexing Precoding and interpolation for MIMO-OFDM Simulation results Conclusions and ongoing work

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IntroductionIntroduction

Closed loop vs. open loop MIMO Increased throughput Intelligently share resources among multiple users Simplify decoding algorithms More easily obtain diversity

Main challenge Ensuring the transmitter is informed about the channel

Transmitter Receiver

feedback?

CSI(channel state info)

CSI?

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Linear Linear Precoding Precoding w/ Spatialw/ Spatial Mux Mux

Transmit M < Mt streams Transmit precoder F determined based on H Linear receiver applied to effective channel HF

Transmitter must be informed about H (or F)

SpatialMultiplexing

HF

Detectionand

Decoding

LinearRX

Feedback Channel Estimation &Precoding

… … …Symbols

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BackgroundBackground Prior work on precoding

MMSE precoding [Sampath et. al.][Scaglione et. al] ML based precoding [Berder et. al] Precoding for MIMO-OFDM [Zhou et. al.]

Antenna subset selection (like precoding) Early work [Gore et. al.][Molisch et. al.] With linear receivers [Heath et. al.][Narasimhan]

Limited feedback precoding Quantized precoding [Love & Heath] Multi-mode antenna selection [Heath & Love]

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Precoding Precoding in MIMO-OFDM w/ SMin MIMO-OFDM w/ SM

P/S&

Add CP

IDFT

Feedback of Channel

State Information

IDFT

IDFT

P/S&

Add CP

P/S&

Add CP

RemoveCP&

S/P

DFT

RemoveCP&

S/P

DFT

RemoveCP&

S/P

DFT

VectorDecoder

…… … …

…

Per tone model:Per tone model:

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Problem SummaryProblem Summary

Precoding in MIMO-OFDM requires Feedback requirements ∝ Number of subcarriers

How can we limit the feedback for each matrix? Leverage limited feedback precoding [Love & Heath 2003]

How can we reduce the number of vectors fed back? Exploit correlation between precoding matrices Send back fraction of vectors and use “smart” interpolation

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Limited FeedbackLimited Feedback Precoding Precoding

Consider unitary precoders Restrict F(k) to lie in finite codebook

SpatialMultiplexer

H(k)F(k)

Detectionand

Decoding

LinearRX

… … …

HChoose F(k)

fromcodebook

Updateprecoder

Low-rate feedback path

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Selection of Selection of CodewordsCodewords Choose based on desired performance metric

Example: Mean squared error

Example: Mutual information

Quantized precoder requires finite search

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Selection of CodebookSelection of Codebook Use Grassmannian precoding [Love & Heath]

Codebooks are optimal packings in G(Mt, M) Distance measure depends on precoding criteria

Projection 2-norm for MMSE w/ traceFubini-Study distance for capacity, MMSE w/ determinant

Minimizes bound on avg distor. in Rayleigh channels

Codebooks available athttp://www.ece.utexas.edu/~rheath/research/mimo/lf/

Set of subspaces

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Reducing Feedback w/ ClusteringReducing Feedback w/ Clustering Exploit coherence bandwidth of channel

Use every Kth precoding matrix Use same precoding matrix per cluster (ex K=5)

Disadvantages Performance degradation at cluster boundary

subcarriers

cluster 1 cluster 2 cluster 3 cluster 4

feedback

……

……

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Interpolation of Interpolation of Precoding MtxsPrecoding Mtxs Subsampling & interpolation

Interpolate(?) precoding matrices

subcarriers

feedback

…… …… …………

……

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Interpolation Challenges 1/2Interpolation Challenges 1/2 Problem: Must respect orthogonality constraints

Recall columns of F(k) should be orthogonal

Proposed solution: (inspired by SLERP [Watson ‘83])

Noneuclidean Noneuclidean InterpolationInterpolation

Simple 1st order linear interpolationSimple 1st order linear interpolation

Enforces orthogonal column constraintEnforces orthogonal column constraint

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Interpolation Challenges 2/2Interpolation Challenges 2/2 Problem: Nonuniqueness of precoders

Performance invariant to right x by orthogonal matrix Example: Nonuniqueness results in interpolation problems

Proposed solution: “derotated interpolation”

Ql is a M x M unitary matrix

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Derotation Derotation OptimizationOptimization Optimize rotation over a finite set

Enables limited feedback implementation Use a “uniform” set of unitary matrices

Example: MMSE with trace solves

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Proposed Interpolation AlgorithmProposed Interpolation Algorithm Step 1: Quantize

Step 2: Optimize

Feedback bits required Precoding matrices Derotation matrices

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IEEE 802.11n Example CalculationIEEE 802.11n Example Calculation Parameters

4 TX antennas 2 RX antennas 2 streams 64 tones K=8 (take every 8th precoding mtx)

Use 6-bit codebook [Love & Heath] Use 2-bit codebook

Feedback required 8*6 + 8*2 = 64 bits

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Quantized Quantized BeamformingBeamforming/Interpolation/Interpolation4TX, 2RX, 1 streamsN=64, P=2, K=8, L=6Rayleigh channelMMSE receiverNo coding6 bit precoder codebook F2 bits per phase

Feedback per channelIdeal: 6N=384 bits quantizationSelection diversity: 2N=128 bitsProposed: 6N/K+2N/K=64 bitsClustered: 6N/K = 48 bitsOrthogonal STBC = 0 bits

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Quantized Quantized BeamformingBeamforming/Interpolation/Interpolation4TX, 2RX, 1 streamsN=64, P=2, K=8, L=6Rayleigh channelMMSE receiverRate 1/2 CC w/ interleaving6 bit precoder codebook F2 bits per phase

Feedback per channelIdeal: 6N=384 bits quantizationSelection diversity: 2N=128 bitsProposed: 6N/K+2N/K=64 bitsClustered: 6N/K = 48 bitsOrthogonal STBC = 0 bits

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Quantized Quantized PrecodingPrecoding/Interpolation/Interpolation4TX, 2RX, 2 streamsN=64, P=2, K=8, L=6Rayleigh channelMMSE receiverNo coding6 bit precoder codebook F2 bit rotation codebook Q

Feedback per channel384 bits quantization166 bits antenna selection 64 bits proposed 48 bits clustered

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Mutual Information ComparisonMutual Information Comparison4TX, 2RX, 2 streamsN=64, P=2, K=8, L=6Rayleigh channelMMSE receiverNo coding6 bit precoder codebook F2 bit rotation codebook Q

Feedback per channel384 bits quantization166 bits antenna selection 64 bits proposed 48 bits clustered

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ConclusionsConclusions Limited feedback precoding for MIMO-OFDM

Quantize and decimate precoders Use smart interpolation to fill in gaps Provides good diversity and capacity performance

On-going work Performance in correlated channels Performance with coding and interleaving Better clustering techniques Extensions to multi-mode precoding

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Further ReadingFurther ReadingOverview D. J. Love, R. W. Heath, Jr., W. Santipach, and  M. L. Honig, “What is the Value of Limited

Feedback for MIMO Channels?,” submitted to IEEE Communications Magazine, Oct. 2003.

Narrowband Limited Feedback Techniques 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., ``Limited Feedback Precoding for Spatial Multiplexing Systems,'' in

Proc. of IEEE Global Telecommunications Conf. , San Francisco, CA, Dec. 1-5, 2003; longerversion submitted to IEEE Trans. Inf. Th., July 2003.

D. J. Love  and R. W. Heath, Jr., ``Multi-Mode Precoding Using Linear Receivers for LimitedFeedback MIMO Systems," Proc. of IEEE Int. Conf. on Communications, Paris, France, June 2004;longer version submitted to IEEE Trans. Sig. Proc., December 2003.

Limited Feedback for MIMO-OFDM J. Choi and R. W. Heath Jr. “Interpolation based transmit beamforming for MIMO OFDM with

Limited Feedback” Proc. of IEEE Int. Conf. on Communications, Paris, France, June 2004; longerversion submitted to IEEE Trans. Sig. Proc. Dec. 2003.

J. Choi and  R. W. Heath, Jr., ``Interpolation Based Unitary Precoding for Spatial Multiplexing MIMOOFDM with Limited Feedback,'' to appear in Proc. of IEEE Global Telecommunications Conf. ,Dallas, TX, Nov. 29 - Dec. 3, 2004