• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.19-26
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• 2013

In this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of $4{\times}4$ and $8{\times}8$ Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.9
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• pp.21-29
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• 2014

Due to enormous number of user and limited memory space, the memory saving is become an important issue for big data service these days. In the large scaled multiple-input multiple-output (MIMO) system, the Teoplitz channel can play the significance rule to improve the performance as well as power efficiency. In this paper, we propose a Toeplitz channel decomposition based on matrix vectorization. Here we use Toeplitz matrix to the channel for large scaled MIMO system. And we show that the Toeplitz Jacket matrices are decomposed to Cooley-Tukey sparse matrices like fast Fourier transform (FFT).