A Blind Equalization Technique for Unitary Spacetime Coded Systems

1
A Blind Equalization Technique forUnitary
Space-time Coded Systems
Emre Aktas with Urbashi Mitra
CUBIN Seminar Department of Electrical and
Electronic Engineering The University of
Melbourne
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Challenge

• Wireless multi-path channels introduce
  distortionhigher probability of error
• We need to compensate forthe effect
• Determine the nature of thisdistortion
• Tool channel estimation(explicit or implicit)

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Multi-path Channel

• Delay spread inter-symbol interference
• Channel no longer multiplicative scalar
• Distortion modeled by tapped delay line
  (convolution in discrete time domain)

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Issues in Channel Estimation

• Estimation performance
• Signal processing Mean-squared error
• Communications Probability of bit error
• Pilot signal
• Signal processing, communications, information
  theory approaches
• Numerical complexity at the receiver

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Philosophy

• Use any structure you can find, to
• Improve fidelity (low estimation error)
• Improve tracking (fast estimation)
• Keep an eye on resource use
• Pilot bits (overhead, consumes bandwidth)
• Computational power
• Blind methods Zero overhead!, but
• Tracking worse
• More computational power

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Outline

• Terminology
• Unitary space-time modulation for flat fading
  channel
• New blind equalization method for ISI channel

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Terminology
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Channel Estimation and Equalization

• Channel estimation, followed by equalization
• Determine channel parameters first
• Build equalizer to compensate for the ISI
• Advantage Equalization decoupled, free to choose
  any structure for equalization
• Disadvantage Additional resources (complexity)
  for the equalizer
• Direct equalization (blind or training based)
• Implicit channel estimation
• No additional resource

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Pilot/training-based Estimation

• Transmitter sends a pilot signal known by the
  receiver
• System resources consumed by the pilot signal

time multiplexed
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Blind Estimation

• Primary motivation resources not consumed by the
  pilot
• Issues
• Longer observation durations to converge
• Larger numerical complexity
• Inherent ambiguity (phase ambiguity in SIMO
  channel)
• Example techniques
• Based on second order statistics, subspace
  methodsL. Tong, G. Xu, T. Kailath, IEEE Trans.
  on Info. Theory, March 1994
• Based on higher order statistics, CMAG. J.
  Foschini, ATT Technical Journal, October 1985

DATA
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Semi-blind Estimation

• Combine pilot-based and blind approaches
• Improve pilot-based methods by exploiting the
  data signal
• Example techniques
• ML by modeling data as unknown deterministic or
  GaussianE. de Carvalho, D. Slock, IEEE Veh.
  Tech. Conf. 1998
• Exact ML via EM algorithmJ. L. Bapat Signal
  Processing Magazine, December 1998
• Issue High complexity, especially for parallel
  transmission

time multiplexed
code multiplexed (WCDMA)
PILOT
DATA
DATA
PILOT
DATA
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Blind Equalization for Unitary Coded MIMO

• Information theoretic results promise capacity
  gains via multiple transmit/receive antenna
• E. Telatar, Bell Labs Technical Report, June 1995
• G. Foschini J. Gans, Wireless Personal
  Communications, March 1998
• Intuition Diversity provided by multiple antenna
• Effective signaling required to exploit transmit
  diversitySpace-time modulation

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Space-time Modulation Encoding

Information sequence
Codeword matrix sequence
Matrix constellation
Channel
M number of transmitter antennas N number of
receiver antennasT block length
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Unitary Space-time Constellations

• Unitary definition
• Unitary space-time modulation
• B. Hochwald, T. Marzetta, T. Richardson, W.
  Sweldens, R. Urbanke, IEEE Trans. on Info.
  Theory, September 2000
• Differentially encoded unitary group space-time
  codes
• B. Hughes, IEEE Trans. on Info. Theory, November
  2000
• Easy non-coherent (blind) decoding, but only for
  flat fading

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Generalized Likelihood Ratio Test (GLRT)

• Basic hypothesis testing (which is true?)
• Maximum likelihood detection
• Generalized likelihood detection
• Perform ML estimation of unknown parameter
• Perform ML detection as if estimated parameter
  were true parameter

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Strategy

• Aim Space-time coded system with low complexity
  blind decoding in ISI channel

Use unitary STC available for non-coherent
(blind) decoding in flat fading
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Blind Linear Equalization

• Due to inherent ambiguity in blind MIMO channel
  estimation, best we can do in even noiseless
  channel is

channel
equalizer (to be determined blindly)
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Equalizer Design

• Space-time code structure exploited to form the
  blind equalizer (constant modulus algorithm)
• Standard CMA
• Penalize the deviation of equalizer outputs
  symbols from constant modulus
• Matrix CMA
• Penalize deviation of equalizer output blocks
  from unitary structure
• Adaptive implementation via stochastic gradient
  (low complexity)

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Transient Analysis

• Will the stochastic gradient algorithm always
  converge to desired points?
• Check stationary points
• Analysis of transient behavior of the combined
  channel-equalizer for noiseless channel, G.
  Foschini, ATT Technical Journal, October 1985

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Equalization Non-coherent Detection

• No closed form solution for F in noisy channel
• For scalar CMA we know (no noise) CMA ? ZF
  (noise) CMA ? in vicinity of ZF and MMSE
• Method given channel, obtain pairwise error
  probability for ZF and MMSE
  solutions

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ZF and MMSE Equalizers

• Zero-forcing invert channel
• Total suppression of interference
• Noise enhancement
• MMSE
• Minimize MSE of equalizer output
• Play between noise enhancement and interference

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Conditional Pairwise Error Probability

• Given channel realization, pairwise error
  probability in Gaussian quadratic form, use
  textbook result Proakis

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Effect of Equalizer Delay

• With large number of receive antenna assumption

Maximum energy achieved
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Equalizer for Comparison

• CMA for multi-user signal separation and
  equalization
• C. Papadias A. Paulraj, IEEE Signal Processing
  Letters, June 1997
• Treat each transmit antenna as different user

MU-CMA
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Trajectory of Equalizer
ZF and MMSE
Likelihood corresponding to transmitted codeword
Next largest likelihood
M2, N6, L2, P1, T8, SNR10dB
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Error Rate Performance
non-ideal delay total signal energy is not
captured
d2 ideal delay
Pairwise error probability, by averaging
M2, N8, P2, L2
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Error Rate Performance
d ¹ 2
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Conclusions

• A totally blind equalizer-decoder structure
  proposed for unitary modulation in ISI channels
  (no training, no loss in bandwidth)
• Equalizer is very easy to implement
• Exploited the structure of the unitary codes via
  new matrix CM algorithm
• Stationary point analysis for matrix CMA
• Provided first cut on performance analysis for
  equalized MIMO/STC systems
• Connection between equalizer delay and performance