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Optimal Joint Design of Hermitian Transform Matrix and Corresponding Mask Coefficients for Multi-Digital Demodulation Systems

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Abstract

Nowadays, signals are transmitted using different digital modulation systems according to different channel conditions. Different digital modulation systems transmit signals using different frequency bands. To demodulate the signals and decode the corresponding digital symbols, different filters with different frequency bands are employed. This paper explores the possibility of performing the digital demodulation in a general energy preserved transform domain instead of in the conventional frequency domain. In particular, instead of performing the multiplication in the frequency domain for performing the conventional filtering, this paper proposes to perform the multiplication in an optimal Hermitian transform domain for performing the optimal mask operation. The joint design of the Hermitian transform matrix and the corresponding mask coefficients is formulated as a least squares optimization problem subject to the Hermitian condition. This is actually a complex-valued quadratic matrix equality constrained least squares optimization problem. A condition on an optimal solution is derived via a singular value decomposition approach. Based on the derived condition, an iterative approach is proposed for finding the solution of the optimization problem. Computer numerical simulation results show that our proposed approach outperforms the conventional filtering approach.

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Acknowledgements

This work was supported partly by the National Nature Science Foundation of China (No. 61372173), the Guangdong Higher Education Engineering Technology Research Center for Big Data on Manufacturing Knowledge Patent (No. 501130144), the Hundred People Plan from the Guangdong University of Technology, the Young Thousand People Plan from the Ministry of Education of China and the Pearl Scholarship from the Guangdong Province.

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Authors and Affiliations

  1. School of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China

    Xiao-Zhi Zhang, Bingo Wing-Kuen Ling, Meilin Wang, Yu Zheng & Chuqi Yang

  2. Engineering Research Center, University of South China, Hengyang, 421001, China

    Xiao-Zhi Zhang

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  1. Xiao-Zhi Zhang
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  2. Bingo Wing-Kuen Ling
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  3. Meilin Wang
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  4. Yu Zheng
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  5. Chuqi Yang
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Correspondence to Bingo Wing-Kuen Ling.

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Zhang, XZ., Ling, B.WK., Wang, M. et al. Optimal Joint Design of Hermitian Transform Matrix and Corresponding Mask Coefficients for Multi-Digital Demodulation Systems. Circuits Syst Signal Process 36, 3243–3264 (2017). https://doi.org/10.1007/s00034-016-0450-0

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