Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Joint Sampling Frequency Offset Estimation and Compensation Algorithms Based on the Farrow Structure

Deijany Rodriguez Linares, Oksana Moryakova, Håkan Johansson

TL;DR

Numerical results for real and complex multisine and bandpass-filtered white noise signals demonstrate accurate estimation and effective compensation over a wide range of operating conditions, confirming the flexibility and efficiency of the proposed approach.

Abstract

This paper presents joint sampling frequency offset (SFO) estimation and compensation algorithms based on the Farrow structure. Unlike conventional approaches that treat estimation and compensation separately, the proposed framework exploits the interpolator structure to enable a low-complexity, fully time-domain solution applicable to arbitrary bandlimited signals, without imposing constraints on the waveform or requiring Fourier transform based processing. The estimation stage can operate on a real-valued component of a complex signal and supports the simultaneous estimation of SFO and sampling time offset, while being inherently robust to other synchronization impairments such as carrier frequency offset. The proposed estimation algorithms rely on two complementary methods, specifically, Newton's method and iterative least-squares formulation. The implementations of the estimators are presented and the overall computational complexity is analyzed, showing that the complexity scales only linearly with the number of samples employed. Numerical results for real and complex multisine and bandpass-filtered white noise signals demonstrate accurate estimation and effective compensation over a wide range of operating conditions, confirming the flexibility and efficiency of the proposed approach. Moreover, the influence of the Farrow structure approximation error on the SFO estimation accuracy is investigated.

Joint Sampling Frequency Offset Estimation and Compensation Algorithms Based on the Farrow Structure

TL;DR

Numerical results for real and complex multisine and bandpass-filtered white noise signals demonstrate accurate estimation and effective compensation over a wide range of operating conditions, confirming the flexibility and efficiency of the proposed approach.

Abstract

This paper presents joint sampling frequency offset (SFO) estimation and compensation algorithms based on the Farrow structure. Unlike conventional approaches that treat estimation and compensation separately, the proposed framework exploits the interpolator structure to enable a low-complexity, fully time-domain solution applicable to arbitrary bandlimited signals, without imposing constraints on the waveform or requiring Fourier transform based processing. The estimation stage can operate on a real-valued component of a complex signal and supports the simultaneous estimation of SFO and sampling time offset, while being inherently robust to other synchronization impairments such as carrier frequency offset. The proposed estimation algorithms rely on two complementary methods, specifically, Newton's method and iterative least-squares formulation. The implementations of the estimators are presented and the overall computational complexity is analyzed, showing that the complexity scales only linearly with the number of samples employed. Numerical results for real and complex multisine and bandpass-filtered white noise signals demonstrate accurate estimation and effective compensation over a wide range of operating conditions, confirming the flexibility and efficiency of the proposed approach. Moreover, the influence of the Farrow structure approximation error on the SFO estimation accuracy is investigated.
Paper Structure (24 sections, 1 theorem, 46 equations, 15 figures, 3 tables)

This paper contains 24 sections, 1 theorem, 46 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline
  4. Problem Statement and Proposed SFO Time-Domain Estimation Utilizing the Farrow Structure
  5. SFO Model
  6. SFO Compensation Using the Farrow Structure
  7. Proposed SFO Estimation Principle Using the Farrow Structure
  8. Proposed SFO Estimator Using Newton's Method
  9. Low-Complexity Implementation
  10. Time-Index and Time-Index-Squared Weighted Sum Computations Based on Cascaded Accumulators
  11. Implementation Complexity
  12. Number of Samples Used for Estimation
  13. Proposed SFO Estimator Using An Iterative Least-Squares Algorithm
  14. Low-Complexity Implementation
  15. Numerical Examples
  16. ...and 9 more sections

Key Result

Theorem 1

$\mathbf{Q}=\mathbf{A}^\top \mathbf{A}$ is invertible if there exist at least two sample indices $n_a \neq n_b$ such that $u_1(n_a) \neq 0$ and $u_1(n_b) \neq 0$ for any integer $n_a, n_b\in[0, N-1]$.

Figures (15)

  • Figure 1: Variable-fractional-delay filter based on the Farrow structure.
  • Figure 2: Implementation of the SFO compensator (highlighted with the gray rectangular) and computations of the elements in \ref{['eq:Hessian']} and \ref{['eq:gradient']} required for the SFO estimator using the Newton based algorithm.
  • Figure 3: Implementation of the SFO compensator (highlighted with the gray rectangular) and computations to obtain the elements in \ref{['eq:Q']} and \ref{['eq:c']} required for the SFO estimator using the ILS algorithm.
  • Figure 4: Example \ref{['ex:multisine']}: Importance of jointly estimating (SFO and STO). Amplitude spectrum before and after compensation for a multisine signal.
  • Figure 5: Example \ref{['ex:mcperformance']}: Convergence analysis. SFO and STO precision against iteration count.
  • ...and 10 more figures

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3: Finite-step convergence for the one-branch case
  • Remark 4
  • Remark 5
  • proof