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Message-Passing Receiver for OCDM over Multi-Lag Multi-Doppler Channels

Yun Liu, Fei Ji, Miaowen Wen, Hua Qing

TL;DR

The paper tackles symbol detection for OCDM in doubly selective channels with multiple lags and Doppler shifts (MLMD). It derives a closed-form Fresnel-domain channel matrix $\mathbf{H}_{\mathrm{eff}} = \mathbf{\Phi} \mathbf{H} \mathbf{\Phi}^H$ and shows a sparse, complexity-reduced approximation that preserves the essential path effects. A message-passing detector operating on the Fresnel-domain factor graph exploits this sparsity to iteratively estimate the transmitted symbols, achieving BER gains over MMSE-based receivers. The results demonstrate robust performance improvements in both under-spread terrestrial vehicular channels and overspread underwater acoustic channels, highlighting OCDM’s potential for full diversity in high-mobility scenarios.

Abstract

As a new candidate waveform for the next generation wireless communications, orthogonal chirp division multiplexing (OCDM) has attracted growing attention for its ability to achieve full diversity in uncoded transmission, and its robustness to narrow-band interference or impulsive noise. Under high mobility channels with multiple lags and multiple Doppler-shifts (MLMD), the signal suffers doubly selective (DS) fadings in time and frequency domain, and data symbols modulated on orthogonal chirps are interfered by each other. To address the problem of symbol detection of OCDM over MLMD channel, under the assumption that path attenuation factors, delays, and Doppler shifts of the channel are available, we first derive the closed-form channel matrix in Fresnel domain, and then propose a low-complexity method to approximate it as a sparse matrix. Based on the approximated Fresnel-domain channel, we propose a message passing (MP) based detector to estimate the transmit symbols iteratively. Finally, under two MLMD channels (an underspread channel for terrestrial vehicular communication, and an overspread channel for narrow-band underwater acoustic communications), Monte Carlo simulation results and analysis are provided to validate its advantages as a promising detector for OCDM.

Message-Passing Receiver for OCDM over Multi-Lag Multi-Doppler Channels

TL;DR

The paper tackles symbol detection for OCDM in doubly selective channels with multiple lags and Doppler shifts (MLMD). It derives a closed-form Fresnel-domain channel matrix and shows a sparse, complexity-reduced approximation that preserves the essential path effects. A message-passing detector operating on the Fresnel-domain factor graph exploits this sparsity to iteratively estimate the transmitted symbols, achieving BER gains over MMSE-based receivers. The results demonstrate robust performance improvements in both under-spread terrestrial vehicular channels and overspread underwater acoustic channels, highlighting OCDM’s potential for full diversity in high-mobility scenarios.

Abstract

As a new candidate waveform for the next generation wireless communications, orthogonal chirp division multiplexing (OCDM) has attracted growing attention for its ability to achieve full diversity in uncoded transmission, and its robustness to narrow-band interference or impulsive noise. Under high mobility channels with multiple lags and multiple Doppler-shifts (MLMD), the signal suffers doubly selective (DS) fadings in time and frequency domain, and data symbols modulated on orthogonal chirps are interfered by each other. To address the problem of symbol detection of OCDM over MLMD channel, under the assumption that path attenuation factors, delays, and Doppler shifts of the channel are available, we first derive the closed-form channel matrix in Fresnel domain, and then propose a low-complexity method to approximate it as a sparse matrix. Based on the approximated Fresnel-domain channel, we propose a message passing (MP) based detector to estimate the transmit symbols iteratively. Finally, under two MLMD channels (an underspread channel for terrestrial vehicular communication, and an overspread channel for narrow-band underwater acoustic communications), Monte Carlo simulation results and analysis are provided to validate its advantages as a promising detector for OCDM.
Paper Structure (14 sections, 2 theorems, 73 equations, 10 figures, 4 tables, 1 algorithm)

This paper contains 14 sections, 2 theorems, 73 equations, 10 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. OCDM Modulation
  4. Channel Model
  5. Input-output Relation
  6. General expression of the chirp-domain channel matrix
  7. Complexity-reduced computation of the chirp-domain channel matrix
  8. Message Passing Based Detector
  9. Simulation results and discussion
  10. Conclusion
  11. Proof of Lemma \ref{['lemma1']}
  12. Proof of Lemma \ref{['lemma2']}
  13. The case $k$ being a positive integer
  14. The case $k$ being a negative integer

Key Result

Lemma 1

For a given length-$N$ vector, the operation of Doppler shift after a cyclic shift can be realized by a cyclic shift after a Doppler shift. More specifically, the relation of the operation matrices can be expressed as

Figures (10)

  • Figure 1: Waveforms of a set of orthogonal chirps defined in (\ref{['eqn_def_chirp']}) when $N=16$. (a) the real part of $\psi _m\left( t \right)$, (b) the imaginary part of $\psi _m\left( t \right)$.
  • Figure 2: The block diagram of OCDM transmitter.
  • Figure 3: Linear time variant channel with multiple lags and multiple Doppler-shifts.
  • Figure 4: The chirp-domain input-output relation of an OCDM system of 8 orthogonal chirps, while the channel has 2 logical paths, with chirp-shifts 0 and 2 respectively.
  • Figure 5: Messages in factor graph: (a) massages sent from an observation node to $L$ variable nodes, (b) massages got by an variable node from $L$ observation nods, (c) messages sent from an variable node to $L$ observation nodes, (d) messages got by an observation node from $L$ variable nodes.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2