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Timing Recovery and Sequence Detection for Integrate-and-Fire Time Encoding Receivers

Neil Irwin Bernardo

TL;DR

A joint timing recovery and data detection framework for integrate-and-fire time encoding receivers is presented, and the log-likelihood function is derived to capture the dependence between firing times, symbol timing offset, and transmitted sequence, leading to a maximum likelihood formulation for joint timing estimation and sequence detection.

Abstract

Recent advances in neuromorphic signal processing have introduced time encoding machines as a promising alternative to conventional uniform sampling for low-power communication receivers. In this paradigm, analog signals are converted into event timings by an integrate-and-fire circuit, allowing information to be represented through spike times rather than amplitude samples. While event-driven sampling eliminates the need for a fixed-rate clock, receivers equipped with integrate-and-fire time encoding machines, called time encoding receivers, often assume perfect symbol synchronization, leaving the problem of symbol timing recovery unresolved. This paper presents a joint timing recovery and data detection framework for integrate-and-fire time encoding receivers. The log-likelihood function is derived to capture the dependence between firing times, symbol timing offset, and transmitted sequence, leading to a maximum likelihood formulation for joint timing estimation and sequence detection. A practical two-stage receiver is developed, consisting of a timing recovery algorithm followed by a zero-forcing detector. Simulation results demonstrate accurate symbol timing offset estimation and improved symbol error rate performance compared to existing time encoding receivers.

Timing Recovery and Sequence Detection for Integrate-and-Fire Time Encoding Receivers

TL;DR

A joint timing recovery and data detection framework for integrate-and-fire time encoding receivers is presented, and the log-likelihood function is derived to capture the dependence between firing times, symbol timing offset, and transmitted sequence, leading to a maximum likelihood formulation for joint timing estimation and sequence detection.

Abstract

Recent advances in neuromorphic signal processing have introduced time encoding machines as a promising alternative to conventional uniform sampling for low-power communication receivers. In this paradigm, analog signals are converted into event timings by an integrate-and-fire circuit, allowing information to be represented through spike times rather than amplitude samples. While event-driven sampling eliminates the need for a fixed-rate clock, receivers equipped with integrate-and-fire time encoding machines, called time encoding receivers, often assume perfect symbol synchronization, leaving the problem of symbol timing recovery unresolved. This paper presents a joint timing recovery and data detection framework for integrate-and-fire time encoding receivers. The log-likelihood function is derived to capture the dependence between firing times, symbol timing offset, and transmitted sequence, leading to a maximum likelihood formulation for joint timing estimation and sequence detection. A practical two-stage receiver is developed, consisting of a timing recovery algorithm followed by a zero-forcing detector. Simulation results demonstrate accurate symbol timing offset estimation and improved symbol error rate performance compared to existing time encoding receivers.
Paper Structure (9 sections, 1 theorem, 22 equations, 3 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 22 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Architecture
  3. Time Encoding Receiver Algorithms
  4. Log-likelihood for Joint ML Estimation
  5. Timing Recovery Phase
  6. Data Detection Phase
  7. Numerical Results
  8. Conclusion
  9. Proof of Proposition \ref{['proposition:log_likelihood']}

Key Result

Proposition 1

Consider the observed firing time vector $\mathbf{t} = [t_0,\cdots, t_K]^T$ and the known pilot sequence vector $\mathbf{s}_{\mathrm{p}} = [s_{0}^{(\mathrm{p})},\cdots, s_{L_{\mathrm{p}}-1}^{(\mathrm{p})}]^T$ available at the time encoding receiver. Let $\mathbf{s}_{\mathrm{d}} = [s_{0}^{(\mathrm{d} where the $k$-th element of $\mathbf{y}\in\mathbb{R}^{K\times 1}$ is the $k$-th row and $(l+1)$-th

Figures (3)

  • Figure 1: System diagram of the proposed integrate-and-fire time encoding receiver.
  • Figure 2: NMSE (in dB) vs. SNR (in dB) of the proposed timing recovery for the integrate-and-fire time encoding receiver under different operating modes ($b = 1.50$ and $b = 4.50$) and different effective pilot lengths ($\tilde{L}_{\mathrm{p}} = 3$, $\tilde{L}_{\mathrm{p}} = 6$, and $\tilde{L}_{\mathrm{p}} = 9$).
  • Figure 3: Symbol Error Rate vs. SNR (in dB) of the proposed ZF-based sequence detection for the integrate-and-fire time encoding receiver under different operating modes ($b = 1.50$ and $b = 4.50$). Superimposed in the plot is the ZF receiver presented in Bernardo2025SIPS.

Theorems & Definitions (2)

  • Proposition 1
  • proof