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Union Bound on the Bit Error Rate for MIMO-GFDM Systems

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Abstract

In this paper, a union bound on the bit error rate (BER) for multiple input multiple output generalized frequency division multiplexing (MIMO-GFDM) systems is derived based on exact pairwise error probabilities. The moment-generating function is used to calculate the exact pairwise error probability under the assumption that a maximum likelihood detector is used at the receiver. A realistic multipath MIMO channel environment is investigated in which the spatial correlation between antennas and the channel estimation errors are included. The Kronecker model and an additive model are used to describe the spatial correlation and channel estimation errors, respectively. The impacts of the spatial correlation and the channel estimation errors on the derived bound are investigated. The performances of MIMO-GFDM systems using different modulation techniques are also examined. Numerical calculations of the union bound and computer-based Monte-Carlo simulations of BER are carried out to verify the derived bound. Numerical results show that the derived union bound is a tight upper bound on the BER for MIMO-GFDM systems in a reasonable \(E_s/N_0\) region.

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Acknowledgements

The authors would like to thank the China Scholarship Council and the Natural Sciences and Engineering Research Council of Canada for their funding support for the work.

Funding

Yanpeng Wang received a scholarship from the China Scholarship Council. Paul Fortier received funds from the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

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

    Yanpeng Wang & Paul Fortier

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  1. Yanpeng Wang
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  2. Paul Fortier
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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. Union Bound on the Bit Error Rate for MIMO-GFDM Systems. Wireless Pers Commun 123, 1825–1839 (2022). https://doi.org/10.1007/s11277-021-09215-3

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