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A New Method for the Identification of a Wiener-Hammerstein Model in a Communication Context

Vincent Corlay

TL;DR

It is obtained that the new method requires reduced-size pilot sequences: the sum of the length of the pilot sequences is approximately the one needed to estimate the convolutional product of the two linear filters with a back-off.

Abstract

We propose a new algorithm to identify a Wiener-Hammerstein system. This model represents a communication channel where two linear filters are separated by a non-linear function modelling an amplifier. The algorithm enables to recover each parameter of the model, namely the two linear filters and the non-linear function. This is to be opposed with estimation algorithms which identify the equivalent Volterra system. The algorithm is composed of three main steps and uses three distinct pilot sequences. The estimation of the parameters is done in the time domain via several instances of the least-square algorithm. However, arguments based on the spectral representation of the signals and filters are used to design the pilot sequences. We also provide an analysis of the proposed algorithm. We estimate, via the theory and simulations, the minimum required size of the pilot sequences to achieve a target mean squared error between the output of the true channel and the output of the estimated model. We obtain that the new method requires reduced-size pilot sequences: The sum of the length of the pilot sequences is approximately the one needed to estimate the convolutional product of the two linear filters with a back-off. A comparison with the Volterra approach is also provided.

A New Method for the Identification of a Wiener-Hammerstein Model in a Communication Context

TL;DR

It is obtained that the new method requires reduced-size pilot sequences: the sum of the length of the pilot sequences is approximately the one needed to estimate the convolutional product of the two linear filters with a back-off.

Abstract

We propose a new algorithm to identify a Wiener-Hammerstein system. This model represents a communication channel where two linear filters are separated by a non-linear function modelling an amplifier. The algorithm enables to recover each parameter of the model, namely the two linear filters and the non-linear function. This is to be opposed with estimation algorithms which identify the equivalent Volterra system. The algorithm is composed of three main steps and uses three distinct pilot sequences. The estimation of the parameters is done in the time domain via several instances of the least-square algorithm. However, arguments based on the spectral representation of the signals and filters are used to design the pilot sequences. We also provide an analysis of the proposed algorithm. We estimate, via the theory and simulations, the minimum required size of the pilot sequences to achieve a target mean squared error between the output of the true channel and the output of the estimated model. We obtain that the new method requires reduced-size pilot sequences: The sum of the length of the pilot sequences is approximately the one needed to estimate the convolutional product of the two linear filters with a back-off. A comparison with the Volterra approach is also provided.
Paper Structure (41 sections, 56 equations, 18 figures, 1 algorithm)

This paper contains 41 sections, 56 equations, 18 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Presentation of the topic and motivations
  3. Main contributions
  4. Estimation of the required total pilot-sequence length and comparison with the benchmark Volterra approach
  5. Organization of the paper
  6. Presentation of the required materials
  7. The Wiener-Hammerstein model
  8. First linear filter
  9. Non-linear function
  10. Second linear filter
  11. Amplifier model and linear filters used for the examples
  12. Equations of the Hammerstein model
  13. The least-square algorithm
  14. The $Q$-values and the NMSE
  15. The $Q$ and $Q'$-values
  16. ...and 26 more sections

Figures (18)

  • Figure 1: The Wiener-Hammerstein model.
  • Figure 2: Non-linear AM/AM model of the amplifier.
  • Figure 3: Amplitude of the frequency response of the linear filters $h$, $g$, and $r$ (denoted by H, G, and R, respectively, on the figure)
  • Figure 4: NMSE as a function of the $Q$-value of the estimated filter.
  • Figure 5: NMSE with the estimated Volterra filter as a function of the predicted $Q$-value of the Volterra filter.
  • ...and 13 more figures