Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generalized Orthogonal Chirp Division Multiplexing in Doubly Selective Channels

Yun Liu, Hao Zhao, Huazhen Yao, Zeng Hu, Yinming Cui, Dehuan Wan

TL;DR

This work introduces a novel unitary transform called the generalized discrete Fresnel transform (GDFnT) and proposes a new waveform based on this transform, named generalized OCDM (GOCDM), which achieves better PAPR performance than OCDM without compromising bit error rate (BER) performance.

Abstract

In recent years, orthogonal chirp division modulation (OCDM) has gained attention as a robust communication waveform due to its strong resistance to both time-domain and frequency-domain interference. However, similar to orthogonal frequency division multiplexing (OFDM), OCDM suffers from a high peak-to-average power ratio (PAPR), resulting in increased hardware costs and reduced energy efficiency of the transmitter's power amplifiers. In this work, we introduce a novel unitary transform called the Generalized Discrete Fresnel Transform (GDFnT) and propose a new waveform based on this transform, named Generalized Orthogonal Chirp Division Modulation (GOCDM). In GOCDM, data symbols from the constellation diagram are independently placed in the Generalized Fresnel (GF) domain. We derive the GF-domain channel matrix for the GOCDM system under time-frequency doubly selective channels and leverages the sparsity of the GF-domain channel matrix to design an iterative receiver based on the message-passing algorithm. Simulation results demonstrate that GOCDM achieves better PAPR performance than OCDM without compromising bit error rate (BER) performance.

Generalized Orthogonal Chirp Division Multiplexing in Doubly Selective Channels

TL;DR

This work introduces a novel unitary transform called the generalized discrete Fresnel transform (GDFnT) and proposes a new waveform based on this transform, named generalized OCDM (GOCDM), which achieves better PAPR performance than OCDM without compromising bit error rate (BER) performance.

Abstract

In recent years, orthogonal chirp division modulation (OCDM) has gained attention as a robust communication waveform due to its strong resistance to both time-domain and frequency-domain interference. However, similar to orthogonal frequency division multiplexing (OFDM), OCDM suffers from a high peak-to-average power ratio (PAPR), resulting in increased hardware costs and reduced energy efficiency of the transmitter's power amplifiers. In this work, we introduce a novel unitary transform called the Generalized Discrete Fresnel Transform (GDFnT) and propose a new waveform based on this transform, named Generalized Orthogonal Chirp Division Modulation (GOCDM). In GOCDM, data symbols from the constellation diagram are independently placed in the Generalized Fresnel (GF) domain. We derive the GF-domain channel matrix for the GOCDM system under time-frequency doubly selective channels and leverages the sparsity of the GF-domain channel matrix to design an iterative receiver based on the message-passing algorithm. Simulation results demonstrate that GOCDM achieves better PAPR performance than OCDM without compromising bit error rate (BER) performance.
Paper Structure (12 sections, 1 theorem, 74 equations, 6 figures, 4 tables, 1 algorithm)

This paper contains 12 sections, 1 theorem, 74 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Generalized Discrete Fresnel Transform
  3. System Model
  4. GOCDM Modulation
  5. Channel Model
  6. Input-output Relation
  7. General Expression of the GF-domain Channel Matrix
  8. Complexity-reduced Computation of the GF-domain Channel Matrix
  9. Message Passing Based Detector
  10. Simulation results and discussion
  11. Conclusion
  12. Proof of Lemma \ref{['Lemma_1']}

Key Result

Lemma 1

Matrices $\mathbf{\Phi }_{M,N}^{\mathcal{H}}$ and $\mathbf{\Pi }$ satisfy the commutative property of multiplication, i.e., $\mathbf{\Pi \Theta }_{M,N}^{H}\,\,=\,\,\mathbf{\Theta }_{M,N}^{H}\mathbf{\Pi }.$

Figures (6)

  • Figure 1: The block diagram of GOCDM transmitter.
  • Figure 2: The LTV channel with multiple lags and multiple Doppler shifts.
  • Figure 3: Messages in the factor graph: (a) messages sent from a variable node to $L$ observation nodes, (b) messages got by an observation node from $L$ variable nodes, (c) messages sent from an observation node to $L$ variable nodes, (d) messages got by a variable node from $L$ observation nodes.
  • Figure 4: Comparison of the PAPR among GOCDM, OCDM and OFDM signals, where the number of orthogonal chirps in the OCDM symbols is N = 128, while GOCDM is configured with MN = 128. 4-QAM constellations are used in both systems.
  • Figure 5: BER performance comparison for GOCDM, OCDM and OFDM in UWA mobile channels, where the number of orthogonal subchannels in OCDM (or OFDM) is set to be N = 128, while GOCDM is configured with MN = 128. 4-QAM constellations are used in all systems.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Lemma 1