Low Rate Feedback MIMO Systems: Code Design

1
Low Rate Feedback MIMO Systems Code Design

• Hamid Jafarkhani
• Electrical Engineering Computer Science
• Center for Pervasive Communications and Computing
• University of California, Irvine

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Outline

• Introduction
• VQ-Based Beamforming
• Transmit Beamforming for Time-Selective Fading
  Channels
• Transmit Beamforming for MIMO-OFDM Wireless
  Systems
• Noisy Feedback Channels
• Conclusions

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Open-loop
Feedback
Close-loop
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Different Types of Feedback in a Close-loop System

• Perfect feedback
• Mean/Covariance feedback
• Average SNR information
• Quantized phase/magnitude feedback
• Quantized direction feedback

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Block Diagram of a Transmit Beamforming System
Bit stream for Ant-1
Input Bits
Encoder
Bit Stream for Ant-2
Receiver
Transmitter
Receiver
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Shortcomings of Channel Feedback from Receiver

• Channel estimation error at the receiver
• Quantization loss
• The delay between estimation time and the time
  that feedback is used
• Noise in the feedback channel

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Channel Feedback Quality

• If the feedback quality drops too low, the
  beamforming scheme should gradually fall back to
  the non-beamformed scheme.
• Perfect Channel Feedback Beamforming
• No Channel Feedback Space-Time Coding
• What shall we do in between?

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Linear beamforming scheme for STBCs
Feedback CSI
STBC Encoder (OSTBC/QSTBC)
Multiply with Beamforming Matrix P
Channel Estimation Linear Proc.
Input Bits
CPC
Decoded Bits
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Advantages and Disadvantages

• Performance improvement through optimal power
  loading
• Complicated implementation (eigen-analysis)
• Beamforming matrix renders high PAPR
• trellis state machine and beamforming scheme
  should be jointly defined

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A Simplified SOSTTC Beamforming Scheme
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CPSTTC System Block Diagram

• Based on the channel phase information, the
  proper inner code is selected
• A standard M-TCM structure is used as the outer
  code

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Rate-Limited FeedbackSystem Block Diagram
Feedback Channel
Codebook
Index
Multiply with Transmit Weight
Select Transmit Weight From Codebook
Base Band Single Data Stream
Input Bits
Dec
Codebook
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VQ-Based Beamforming
A generalized Lloyd algorithm or a Grassmannian
method can be utilized to design the beamformer
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Time-Selective Fading

• Previous work was based on quasi static i.i.d.
  block fading
• Time-Selective Fading Jakes model
• Simplification of Jakes model with AR1

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Beamforming Design for Time-Selective Fading
Channels

• Predictive Vector quantization (PVQ) quantize
  the residue signal instead of the actual channel
  direction
• Successive Beamforming (SBF) the beamforming
  codebook is adjusted based on the transmit weight
  from the previous frames.

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PVQ Beamformer

• Designing VQ for a Gauss-Markov source
• Designing the residue generator and
  reconstruction units
• Designing the optimal predictor
• To min the given distortion (max SNR)

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PVQ Encoder
Complex Householder transformation House(y) is a
unitary matrix with the first column being y
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PVQ Decoder

• Theorem The linear coefficients that accomplish
  the highest predictor SNR is a simple delay unit

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PVQ Beamformer Properties

• Very good performance
• Even better performance is possible by using
  higher order predictors (ARMA)
• Codebook is a function of fading speed and the
  number of antennas
• Convergence of the design algorithm is not
  guaranteed (converges for large N)

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SBF System Block Diagram
Feedback Channel
Delay
Codebook Ct
Index
Multiply with Transmit Weight
Select Transmit Weight From Codebook
Base Band Single Data Stream
Input Bits
Dec
Codebook Ct
Delay
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Successive Beamforming (SBF)

• Codebook is a function of time Ct
• Beamformer has memory
• Synchronized codebook update on both sides
  without extra feedback information
• Flexible implementation No need to have a
  different codebook for a different fading speed

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SBF Codebook Construction

• Proposition At the t th frame, the SBF codebook
  is generated as
• where
• are constant vectors with unit norm e1 1 0
  0T

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Numerical Simulations SNR performance

• Nt 4, 2N16 MISO system
• PVQ beamformer provides best performance
• SBF algorithm is close to PVQ beamformer.
• Both are far better than memoryless Grassmannian
  beamformer

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Numerical Simulation BER performance

• Nt 4, 2N16. WCDMA system parameters
• PVQ beamformer provides best performance.
• SBF algorithm is close to PVQ beamformer.
• Performance gain is larger at slow fading speed
  and smaller SNR.
• Both are better than memoryless Grassmannian
  beamformer.

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Frequency-Selective Fading
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System Model

• Channel taps Exponential power decay
• Doppler shift on L channel taps AR1 fading model

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Existing OFDM Beamformers

• Independent beamforming on each subcarrier using
  memoryless Grassmannian codebook.
• Huge feedback bits Bad performance
• Spherical linear interpolator OFDM beamformer
• Less feedback bits Worse performance

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Our Approach

• Exploit the time domain and frequency domain
  correlations.
• Transmit beamforming based on successive
  beamforming (SBF).

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Time Domain Round Robin SBF
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Frequency Domain Round Robin SBF
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Frequency Domain Cluster SBF
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Numerical Results (IEEE 802.11a)

• TDRSBF and FDRSBF outperform full feedback
  Grassmannian beamformer. (40 bits gt 192 bits,
  only 1dB away from perfect CSI).
• FDRSBF algorithm is affected by channel delay
  spread. Whereas TDRSBF is insensitive to channel
  delay spread.

Hiperlan2 Indoor fading model C (Trms 150ns,
v3m/s)
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Numerical Results (Ergodic Capacity)

• TDRSBF and FDRSBF outperform full feedback
  Grassmannian beamformer (FFGBF). (40 bits gt 192
  bits, 0.5dB from perfect CSI).

Hiperlan2 Indoor fading model A (Trms 150ns,
v3m/s)
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Results

• We have developed beamforming algorithms to
  exploit the mutual correlation in the fading
  channel. The proposed algorithms have very
  limited feedback requirements.
• The TDRSBF algorithm is sensitive to mobile
  Doppler shift. It performs well at slow fading
  scenarios.
• The FDRSBF algorithm is more severely affected by
  channel delay spread rather than mobile Doppler
  shift. It performs better than the TDRSBF
  algorithm at fast fading or small delay spread
  environments.

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Conclusions

• A VQ-based beamformer framework is general enough
  to deal with different scenarios
• We have designed VQ beamformers for
• Time-selective channels
• Frequency-selective channels
• Noisy feedback channels
• Can be combined with space-time coding