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).