Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels
Abstract
:1. Introduction
2. System Model
2.1. Signal Model of UP-OCDM
- (1)
- Multiplying the symbol vector by the phase matrix ,
- (2)
- Performing IFFT algorithm,
- (3)
- Multiplying the same phase matrix .
2.2. Circulant Structure of the Transform Matrix
2.3. Transmission Model over Doubly Selective Channels
3. Low Complexity Equalizers for UP-OCDM Under Doubly Selective Channels
3.1. MMSE Block Equalizer
3.2. Band MMSE Block Equalizer
3.2.1. Band MMSE Equalization Algorithm
- (1)
- Performing FFT algorithm on the received signal to obtain ;
- (2)
- Constructing the banded matrices and . Performing the LDL factorization to obtain the diagonal matrix and the triangular matrix ;
- (3)
- Solving the system by solving firstly the lower-triangular system , secondly the diagonal system , and finally the upper-triangular system ;
- (4)
- Obtaining the estimate of symbol vector by .
Algorithm 1 band LDL factorization algorithm |
|
3.2.2. Computational Complexity
3.3. Iterative LSQR Block Equalizer
3.3.1. Iterative LSQR Block Equalization Algorithm
- (1)
- Computing the diagonal matrices with the BEM coefficients;
- (2)
- Multiplying by the diagonal matrix ;
- (3)
- Solving (23) by LSQR algorithm to obtain the symbol vector ;
3.3.2. Compational Complexity
4. Numerical Simulations
4.1. Performance with MMSE Equalizer
4.2. Performance with Band MMSE Block Equalization
4.3. Performance with Iterative LSQR Equalization
4.4. Performance Comparison of Proposed Equalization Algorithms
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
OCDM | Orthogonal Chirp Division Multiplexing |
UP-OCDM | Uniform Phase-Orthogonal Chirp Division Multiplexing |
OFDM | Orthogonal Frequency Division Multiplexing |
FrFT | fractional Fourier transform |
UAC | Underwater Acoustic Commmunication |
BEM | Basis Expansion Mode |
MMSE | Minimum Mean Square Error |
ISI | intersymbol interference |
AWGN | Additive White Gaussian Noise |
CIR | Channel Frequency Response |
ICI | Intercarrier Interference |
CM | Complex Multiplications |
CA | Complex Additions |
BER | Bit Error Rate |
WSSUS | Wide Sense Stationary Uncorrelated Scattering |
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Algorithm | MMSE Equalization | Band MMSE Equalization | Iterative LSQR Equalization |
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Complexity |
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Wang, X.; Jiang, Z.; Shen, X.-H. Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels. Sensors 2020, 20, 3125. https://doi.org/10.3390/s20113125
Wang X, Jiang Z, Shen X-H. Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels. Sensors. 2020; 20(11):3125. https://doi.org/10.3390/s20113125
Chicago/Turabian StyleWang, Xin, Zhe Jiang, and Xiao-Hong Shen. 2020. "Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels" Sensors 20, no. 11: 3125. https://doi.org/10.3390/s20113125
APA StyleWang, X., Jiang, Z., & Shen, X.-H. (2020). Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels. Sensors, 20(11), 3125. https://doi.org/10.3390/s20113125