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Polynomial Expansion-Based MMSE Channel Estimation and Precoding for Massive MIMO-GFDM Systems

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Abstract

In this paper, low-complexity channel estimators and precoders are proposed for massive multiple-input multiple-output generalized frequency division multiplexing (MIMO-GFDM) systems. In order to combat the effect of non-orthogonality in GFDM, interference-free pilots are used in frequency-domain minimum mean square error (MMSE) channel estimation. Polynomial expansion is used to approximately compute the matrix inverses in the conventional MMSE estimation and precoding, consequently reducing the cubic computational complexity to square order. The degree of the matrix polynomial can be properly selected to get a required trade-off between complexity and estimation/precoding performance. Different weights can be assigned to the terms in the polynomial expansion and be optimized to achieve a minimal mean square error (MSE). Derived limits on the MSE of the proposed estimators can predict their performance in the high \(E_s/N_0\) region. Then, we derive a Cramér-Rao lower bound (CRLB) and use it as a benchmark for the estimators. In addition, the related computational complexity and the impacts of the polynomial degree are also investigated. Numerical results show the accuracy of the proposed channel estimators and precoders.

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Acknowledgements

The authors would like to thank the China Scholarship Council for its funding support for the work.

Funding

Yanpeng Wang received a scholarship from the China Scholarship Council (Grant No. 201608130110).

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Laval University, Quebec City, Quebec, G1V 0A6, Canada

    Yanpeng Wang & Paul Fortier

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  1. Yanpeng Wang
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Contributions

YW and PF: jointly conceived the fundamental idea of this work. YW: developed the methodology, conducted related simulations, and wrote the paper. PF: provided critical guidance on the methodology and simulations and revised the paper.

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Correspondence to Yanpeng Wang.

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Wang, Y., Fortier, P. Polynomial Expansion-Based MMSE Channel Estimation and Precoding for Massive MIMO-GFDM Systems. Wireless Pers Commun 128, 109–129 (2023). https://doi.org/10.1007/s11277-022-09943-0

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