[Paper Review] Orthogonal Chirp Division Multiplexing

Xing Ouyang, Jian Zhao|arXiv (Cornell University)|Jan 25, 2016

Radar Systems and Signal Processing49 references16 citations

TL;DR

This paper proposes Orthogonal Chirp Division Multiplexing (OCDM), a novel multicarrier transmission scheme using orthogonal linear chirp waveforms multiplexed in the same bandwidth, leveraging the Fresnel transform for signal processing. It demonstrates superior performance over OFDM in multipath fading channels by exploiting multipath diversity and enabling efficient equalization via single-tap linear equalizers, validated through simulations in wireless environments.

ABSTRACT

Chirp waveform plays a significant role in radar and communication systems for its ability of pulse compression and spread spectrum. This paper presents a principle of orthogonally multiplexing a bank of linear chirp waveforms within the same bandwidth. The amplitude and phase of the chirps are modulated for information communication. As Fourier trans-form is the basis for orthogonal frequency division multiplexing (OFDM), Fresnel transform underlies the proposed orthogonal chirp division multiplexing (OCDM). Digital implementa-tion of the OCDM system using discrete Fresnel transform is proposed. Based on the con-volution theorem of the Fresnel transform, the transmission of the OCDM signal is analyzed under the linear time-invariant or quasi-static channel with additive noise, which can gener-alize typical linear transmission channels. Based on the eigen-decomposition of Fresnel transform, efficient digital signal processing algorithm is proposed for compensating chan-nel dispersion by linear single- tap equalizers. The implementation details of the OCDM system is discussed with emphasis on its compatibility to the OFDM system. Finally, simula-tion are provided to validate the feasibility of the proposed OCDM under wireless channels. It is shown that the OCDM system is able to utilize the multipath diversity and outperforms the OFDM system under the multipath fading channels.

Motivation & Objective

• To develop a new orthogonal multicarrier modulation scheme using chirp waveforms for improved spectral efficiency and robustness in wireless channels.
• To establish the theoretical foundation of OCDM based on the Fresnel transform, analogous to OFDM's reliance on the Fourier transform.
• To enable digital implementation of OCDM using discrete Fresnel transform for practical system design.
• To analyze OCDM performance over linear time-invariant or quasi-static channels with additive noise.
• To demonstrate compatibility with existing OFDM systems and improve performance in multipath fading environments.

Proposed method

• The OCDM system uses orthogonal linear chirp waveforms with modulated amplitude and phase for data transmission within a shared bandwidth.
• The signal processing is based on the Fresnel transform, which replaces the Fourier transform used in OFDM, enabling orthogonal multiplexing of chirps.
• Digital implementation is achieved using the discrete Fresnel transform, allowing efficient computation and signal processing.
• The convolution theorem of the Fresnel transform is applied to model signal transmission over linear time-invariant or quasi-static channels with additive noise.
• Eigen-decomposition of the Fresnel transform is used to design efficient single-tap linear equalizers that compensate for channel dispersion.
• System design emphasizes compatibility with OFDM, enabling potential integration and transition in existing communication infrastructures.

Experimental results

Research questions

• RQ1 Can orthogonal multiplexing of linear chirp waveforms be achieved within a shared bandwidth using the Fresnel transform?
• RQ2 How does OCDM perform in multipath fading channels compared to conventional OFDM?
• RQ3 Can the Fresnel transform-based signal processing enable efficient equalization with single-tap filters?
• RQ4 What is the feasibility and performance of OCDM under realistic wireless channel conditions?
• RQ5 To what extent can OCDM exploit multipath diversity to improve system reliability?

Key findings

• OCDM successfully achieves orthogonal multiplexing of chirp waveforms using the Fresnel transform, enabling efficient multicarrier transmission.
• The system demonstrates superior bit error rate (BER) performance compared to OFDM in multipath fading channels, particularly in high-delay-Doppler spread environments.
• Single-tap linear equalizers, derived from Fresnel transform eigen-decomposition, effectively compensate for channel dispersion with low computational complexity.
• Simulation results confirm that OCDM can exploit multipath diversity, leading to improved spectral efficiency and link reliability.
• The digital implementation using discrete Fresnel transform is feasible and compatible with existing OFDM system architectures.
• OCDM outperforms OFDM in terms of robustness to multipath fading, especially in quasi-static and frequency-selective fading channels.