Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels

Area of Science:

• Electrical Engineering
• Signal Processing
• Telecommunications

Background:

• Orthogonal Chirp Division Multiplexing (OCDM) enhances Orthogonal Frequency Division Multiplexing (OFDM) in frequency-selective channels using chirp subcarriers.
• Doubly selective channels lack efficient low-complexity equalization algorithms for OCDM systems.
• Standard OCDM incurs storage overhead due to varying phase matrices in modulation.

Purpose of the Study:

• Introduce Uniform Phase-Orthogonal Chirp Division Multiplexing (UP-OCDM) for high-speed communication over doubly selective channels.
• Reduce modulation storage requirements through uniform phase matrices.
• Develop low-complexity equalization algorithms tailored for UP-OCDM systems.

Main Methods:

• UP-OCDM utilizes uniform phase matrices, reducing storage overhead.
• The circulant nature of UP-OCDM's transform matrix is mathematically proven.
• Special structures of channel matrices in UP-OCDM over doubly selective channels are identified: approximate band matrix and a sum of diagonal/circulant matrices.
• Two low-complexity equalization algorithms are developed based on block LDL H factorization and iterative matrix inversion.

Main Results:

• UP-OCDM demonstrates reduced storage requirements compared to conventional OCDM.
• The transform matrix of UP-OCDM is confirmed to be circulant.
• Channel matrices in UP-OCDM exhibit exploitable structures for equalization.
• Numerical simulations validate the performance of UP-OCDM and its proposed equalizers.
• UP-OCDM and OCDM show similar Bit Error Rate (BER) performance in doubly selective channels, outperforming OFDM.
• Proposed UP-OCDM equalizers achieve better BER than their OFDM counterparts.

Conclusions:

• UP-OCDM is an effective modulation scheme for high-speed communication over doubly selective channels.
• The proposed low-complexity equalization algorithms significantly improve UP-OCDM system performance.
• UP-OCDM presents a viable alternative to OFDM and OCDM, offering advantages in storage and equalization efficiency.