Dynamic Channel Order Estimation Algorithm

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Dynamic Channel Order Estimation Algorithm by P.
J. Green and D.P. Taylor University of
Canterbury Christchurch, New Zealand
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• TOPICS
• Introduction
• Signal Model
• Dynamic Channel Order Estimation (DYCOE)
  Algorithm
• Simulation Results
• Experimental Test Results
• Conclusions

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INTRODUCTION The Wireless Channel Performance
of a wireless communication link is limited by
the characteristics of the radio channel. The
radio frequency signal arrives from the
transmitter to the receiver via many routes
direct and echoes reflected from natural
artificial objects. These echoes can combine
constructively or destructively (phase dependent)
to cause the signal to fade. In a digital
wireless system, if the echoes arrive at the
receiver in the order of one symbol period or
more, time adjacent symbols will interfere with
each other. Phenomenon is known as inter-symbol
interference (ISI). If the receiver is in motion
(vehicle), Doppler effect will cause the receive
frequency to change, changing the instantaneous
phase of the received signal.
Net effect is high symbol error rate even if the
receive signal strength is high !!
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• The Wireless Channel
• Channel equalization is required to compensate
  for ISI to obtain reliable estimates of the
  transmitted symbols. Viterbi equalizer requires
  channel state information to work properly and
  must be estimated in practice.
• As the channel changes with time, continuous
  estimation of the radio channel is necessary.
• Training sequences known at the receiver are
  periodically sent in the transmitted data (eg.
  17 in a GSM system) to aid the equalizer to
  adaptively adjust its coefficients to compensate
  ISI. (Data Aided Channel Estimation)
• Effective data rate is reduced as training
  symbols cannot be used for information
  transmission.
• Training is reduced or avoided by using blind
  channel estimation methods. The method relies on
  unique statistical properties of the transmitted
  signal.

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• Many blind channel estimation methods assume that
  the order of the channel is known !! In reality,
  it must be estimated.
• If order is underestimated, the Viterbi
  algorithm completely fails.
• If order is overestimated, Viterbi algorithm
  works but computational complexity increases
  exponentially !
• Current channel estimators use algorithms based
  on information theoretic criteria Akaike
  information-theoretic criterion AIC
• Minimum description length MDL
• as the standard first step to estimate the
  channel order.
• They all fail under high SNR or when
  sub-channels are correlated.
• Our new algorithm called the Dynamic Channel
  Order Estimation (DYCOE) algorithm is
• Robust to a wide range of SNR
• Independent of correlation in the received
  channels.

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• The DYCOE Algorithm
• DYCOE works in the spatial context in a SIMO
  system using one transmit antenna to multiple
  receive antennas or in the temporal context in an
  oversampled SISO system
• exploits the robustness of the channel
  estimation algorithm of Karim et al. to the
  over-determination of channel order estimation.
  We call it the Linear Prediction Engine (LPE).
• 3 Inputs Covariance Matrix, estimate of noise
  power and estimate of channel order.
• 1Output A vector with estimate of channel
  coefficients
• assumes that the coefficients of the channel
  estimates have significant power over noise power

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The Signal Model

• In the SIMO system, M is an M-element receive
  antenna array.
• Using matrix notation, the SIMO system can be
  modeled as
• x(k) H s(k) n(k) where
• x(k) M ? 1 Symbol rate received signal vector
• H M ? N Channel matrix H h(0) . h(N-1)
• assume impulse response at each antenna spans N
  symbol periods and constant over time interval
• s(k) N ? 1 Transmitted symbol sequence s(k)
  s(k)..s(k-N1)
• assume complex, zero-mean, unit variance process
• n(k) M ? 1 Noise vector assume zero-mean Gaussian
  process, uncorrelated with transmitted symbols
  and antenna elements.
• The LPE is used to estimate the
  coefficients in H

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The DYCOE AlgorithmFlowchart

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• The DYCOE Algorithm
• Step 1 Computation of covariance matrix
• Q is first set to a value greater than the true
  order N.
• Calculate the autocovariance matrix R. From T
  successive samples of the observations and given
  T gt Q samples of the process xTx(1),, x( T ),
  the Q1 autocovariance coefficients is estimated
  as

• Compute the covariance matrix

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• The DYCOE Algorithm
• Step 2 Eigendecomposition of covariance matrix
• Noise power estimated from the average of M(Q
  1) - (N Q 1) smallest eigenvalues of
  covariance matrix.
• Step 3 Use LPE is used to estimate the channel
  coefficients.
• The first M( Q 1 ) ? 1 vector of HQ
  correspond to true filter coefficients.
• The last M( Q - N ) coefficients are equal to
  the residual noise level.
• Step 4 Calculate the threshold given as

average of M(Q - (Q-1)) coefficients largest
eigenvalue smallest eigenvalue
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• The DYCOE Algorithm
• Step 5 Channel order estimation starts using TH
  and Ninitial 1
• Iteratively increases Ninitial until there are M
  coefficients (residual noise coefficients) below
  TH.
• Step 6 Decision mechanism.
• Counts number of coefficients, Jc below TH.

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The DYCOE Algorithm Step 6 Tracking mechanism

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The DYCOE Algorithm Step 7 A new TH is computed
after every 10th channel order estimate. Summary
The algorithm iteratively increases the
channel order at the start until the
coefficients of the channel estimates fall below
threshold TH set above the noise power. This
happens when the channel order is over-
determined by a factor of 1. The algorithm
continuously tracks/adapt to changing channel
conditions by monitoring the number of
coefficients Jc compared to M.

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Simulation Conditions - 1 100 trials consisting
of 1000 i.i.d sequence of binary variable (-1,1)
with equal probability per trial Noise - i.i.d.
zero mean Gaussian variable 4 variate SIMO model
( One transmitter and 4 receive antennas) True
Channel Order N5 Scenario 2 distinct channels
of which 3 are the same. ( N5 )

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Simulation Results - 1

DYCOE Good channel order estimation performance
over wide SNR range MDL good at only one SNR.
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Simulation Results - 2

Good estimation performance over SNR Most errors
are over-estimations by 1
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Simulation Results - 3

Chaotic performance of the MDL channel estimator
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Algorithm Testing using Smart Antenna Software
RAdio Testing System ( SASRATS ) Platform and
HP11759B RF Channel Simulator Test Frequency
915 MHz ISM band Baud Rate 20 kBaud (50uS
symbol period) 100 trials each consisting of 1000
BPSK signals 1 Transmitter and 2 Receiver SIMO
system (HP11759B limitation)

Phase Adjusters
Power Splitter
Attenuator
RX 1
HP 11759B
TX
RX 2
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P.J. Green and D.P. Taylor, Smart Antenna
Software Radio Test System, Proceedings of the
First IEEE International Workshop on Electronic
Design, Test, and Applications, pg. 68-72, Jan.
2002.
SASRATS Smart Antenna Software RAdio Test System

Smart Antenna Software Radio Test System (SASRATS)
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HP11759B RF Channel Simulator Settings 1 SASRAT
915 MHz transmitter output is split into 2 equal
paths into simulator. 2 outputs into 2 SASRAT
receivers. 2 separate channels with 3
programmable paths per channel True channel order
is 2

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Experiment Results DYCOE algorithm

Perfect estimation performance over 15 35 dB
SNR Most errors are over-estimations by 1 at 5 dB
SNR
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Experiment Results MDL algorithm

Poor estimation performance of MDL algorithm
over all SNRs
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• Conclusions
• DYCOE - a robust channel order estimation
  algorithm which will work over
• wide range of SNRs
• correlated channels
• As DYCOE makes use of the LPE, channel estimates
  are also available after channel order estimate
  is made
• Currently limited to SIMO and oversampled SISO
  channels.

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The Wireless Channel Scenario modelled by means
of the channel impulse response
Different landscape models exist with typical
echo profiles created for Rural, Urban and Hilly
terrain
Transmitted impulse
Channel impulse response
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EXAMPLE EFFECT OF ISI
Path 3
915 MHz BPSK modulation at 20 kBauds
Path 2
TX
RX
Path 1
Channel 1 No ISI
Channel 2 ISI