An Application Of The Divided Difference Filter to Multipath Channel Estimation in CDMA Networks - PowerPoint PPT Presentation

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An Application Of The Divided Difference Filter to Multipath Channel Estimation in CDMA Networks

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An Application Of The Divided Difference Filter to Multipath Channel Estimation in CDMA Networks Zahid Ali, Mohammad Deriche, M. Andan Landolsi – PowerPoint PPT presentation

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Title: An Application Of The Divided Difference Filter to Multipath Channel Estimation in CDMA Networks


1
An Application Of The Divided Difference Filter
to Multipath Channel Estimation in CDMA Networks
  • Zahid Ali, Mohammad Deriche,
  • M. Andan Landolsi
  • King Fahd University of Petroleum and Minerals,
    Dhahran, Saudi Arabia

2
OUTLINE
  • Introduction
  • Overview of DDF Algorithm
  • Channel and Signal Model
  • Application to Channel Estimation with Multipath/
    Multiuser model
  • Simulation Results
  • Conclusion

3
INTRODUCTION
  • Accurate channel parameter estimation for CDMA
    signals is challenging due to
  • Multipath fading
  • Multiple Access interference (MAI)
  • Especially
  • Under near far environment
  • closely spaced multipath

4
INTRODUCTION
  • CDMA multiuser parameter is the problem of
    estimating the states of a system given a set of
    noisy or incomplete measurements

5
  • Advanced Signal Proc. techniques such as
  • Maximum-Likelihood
  • Joint multiuser detection and parametric channel
    estimation approaches
  • Subspace-based approach
  • Kalman filter framework

6
  • Kalman Filtering framework
  • Extended Kalman Filter (EKF) for nonlinear
    estimation and filtering
  • Some Limitations of EKF
  • First order terms of the Taylor series expansion
  • Linearized approximation can be sometimes poor
    undermining the performance
  • Jacobian matrix must exist

7
  • Divided Difference Filter
  • DDF, unlike EKF, is a Sigma Point Filter (SPF)
    where the filter linearizes the nonlinear dynamic
    and measurement functions by using an
    interpolation formula through systematically
    chosen sigma points.
  • DDF consistantly outperforms EKF.
  • No analytic Jacobians or Hessians are calculated.
  • But DDF has same order of computational
    complexity as the EKF

8
  • Channel and Signal Model Asynchronous CDMA system
    model where K users transmit over an M-path
    fading channel. The received baseband signal

complex channel coefficients
mth symbol transmitted by the kth user
spreading waveform used by the kth user
time delay associated with the ith path of the
kth user
Additive White Gaussian Noise (AWGN) of zero mean
and variance
9
  • State-Space Model Representation
  • Unknown channel parameters (path delays
  • and gains) to be estimated are

of
with
  • Dynamic Channel Model

10
  • The scalar measurement model

is a nonlinear function of the state
11
  • DDF Algorithm

Consider a nonlinear function , with
mean and covariance . If the function
is analytic, then the multi-dimensional Taylor
series expansion of a random variable about the
mean is given by the following
12
1. Initialization Step
2. Square Cholesky factorizations


3.State and covariance Propagation
13
4. Observation and Innovation Covariance
Propagation
5. Update
14
Application to Channel Estimation with
Multipath/ Multiuser model
  • No. of users 2, 5, 10
  • No of paths 2 and 3
  • Near far ratio 20 dB

15
Timing epoch estimation
Timing epoch estimation for first arriving path
with a five-user/ three-path channel model (with
1/2-chip path separation)
16
Timing epoch estimation
Timing epoch estimation for second arriving path
with a five-user/ three-path channel model (with
1/2-chip path separation)
17
Timing epoch estimation
Timing epoch estimation for third arriving path
with a five-user/ three-path channel model (with
1/2-chip path separation)
18
Channel Coefficients
MSE of the channel coefficients for first
arriving path with a ten-user/ two-path channel
model
19
DDF vs. EKF
20
UKF vs. DDF
21
CONCLUSION
  • DDF achieves better performance
  • moderate complexity compared to the (linearized)
    EKF
  • DDF is quite robust vis-a-vis near-far
    multiple-access interference
  • Can be applied to track a given signal epoch even
    in the presence of other closely-spaced
    multipaths (within a fraction of a chip).
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