Least squares decoding in binomial frequency division multiplexing

This paper proposes a method that can reduce the complexity of a system matrix by analyzing the characteristics of a pseudoinverse matrix to receive a binomial frequency division multiplexing (BFDM) signal and decode it using the least squares (LS) method. The system matrix of BFDM can be expressed...

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Bibliographic Details
Published inETRI journal Vol. 45; no. 2; pp. 277 - 290
Main Authors Kim, Myungsup, Jung, Jiwon, Kim, Ki‐Man
Format Journal Article
LanguageEnglish
Published Electronics and Telecommunications Research Institute (ETRI) 01.04.2023
Subjects
binomial
cyclic
decoder
decomposition
division
frequency
multiplexing
OFDM
orthogonal
precoder
singular
spectrum
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Summary:This paper proposes a method that can reduce the complexity of a system matrix by analyzing the characteristics of a pseudoinverse matrix to receive a binomial frequency division multiplexing (BFDM) signal and decode it using the least squares (LS) method. The system matrix of BFDM can be expressed as a band matrix, and as this matrix contains many zeros, its amount of calculation when generating a transmission signal is quite small. The LS solution can be obtained by multiplying the received signal by the pseudoinverse matrix of the system matrix. The singular value decomposition of the system matrix indicates that the pseudoinverse matrix is a band matrix. The signal‐to‐interference ratio is obtained from their eigenvalues. Meanwhile, entries that do not contribute to signal generation are erased to enhance calculation efficiency. We decode the received signal using the pseudoinverse matrix and the removed pseudoinverse matrix to obtain the bit error rate performance and to analyze the difference.
ISSN:1225-6463
2233-7326
DOI:10.4218/etrij.2021-0456