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Random Frequency Division Multiplexing.
Entropy (Basel)
December 2024
The School of Electric Engineering and Intelligentization, Dongguan University of Technology, Dongguan 523808, China.
In this paper, we propose a random frequency division multiplexing (RFDM) method for multicarrier modulation in mobile time-varying channels. Inspired by compressed sensing (CS) technology which use a sensing matrix (with far fewer rows than columns) to sample and compress the original sparse signal simultaneously, while there are many reconstruction algorithms that can recover the original high-dimensional signal from a small number of measurements at the receiver. The approach choose the classic sensing matrix of CS-Gaussian random matrix to compress the signal.
View Article and Find Full Text PDFNon-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties.
Phys Rev E
October 2024
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico.
Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of N×N real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i-j| View Article and Find Full Text PDF
Optimized Tail Bounds for Random Matrix Series.
Entropy (Basel)
July 2024
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China.
Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.
View Article and Find Full Text PDFCoupled unidirectional chaotic microwave graphs.
Phys Rev E
July 2024
Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland.
We experimentally investigate the undirected open microwave network Γ with internal absorption composed of two coupled directed halves, unidirectional networks Γ_{+} and Γ_{-}, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network Γ is measured and the spectral statistics and the elastic enhancement factor of the network are evaluated. The comparison of the number of experimental resonances with the theoretical one predicted by the Weyl's law shows that within the experimental resolution the resonances are doubly degenerate.
View Article and Find Full Text PDFNorms of structured random matrices.
Math Ann
April 2023
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
For , let be a random matrix, a real deterministic matrix, and the corresponding structured random matrix. We study the expected operator norm of considered as a random operator between and for . We prove optimal bounds up to logarithmic terms when the underlying random matrix has i.
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