• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.93-101
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• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9A
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• pp.1339-1345
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• 1999

In this paper we propose the digital information hiding technique by which we use the combination of random sequence and Hadamard matrix to hide multiple information. The prior work used only one random sequence multiplied by information signal to lower the energy level of information signal and thus it is difficult for a third party to detect the information signal or jam it. But because we have to use the orthogonal code for hiding key in order to hide multiple information in the same digital image, only the use of random sequence that are not uncorrelated has some problems in the information hiding scheme. Thus we present a new information hiding scheme that can be used in hiding multiple information by the use of random sequence that spreads the energy level of the data to be hidden and Hadamard matrix that makes the random sequence uncorrelated.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.451-461
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• 2023

In this paper, we study the fixed point property for generalized asymptotically nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.11
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• pp.1539-1548
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• 2016

Beamforming technique at the ground station is known to be effective in obtaining coverage extension or SNR gain for communication with unmanned aerial vehicle (UAV). When a UAV moves, periodic beam tracking is necessary to maintain beam gain. In order to track beams for multiple UAVs, the ground station needs to receive different preamble sequences from multiple UAVs. In this paper, a preamble sequence design technique is proposed for beam tracking in a GMSK-based communication system with multiple UAVs. Hadamard sequence is considered for the design of preamble sequence due to its ideal cross-correlation property. A preamble sequence appropriate for a GMSK communication system with multiple UAVs is proposed after analyzing the properties of received signal in a GMSK system with the input of Hadamard sequence.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.549-570
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• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.889-896
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• 2006

The crest factor distribution of orthogonal frequency division multiplexing (OFDM) symbol sequences is evaluated and it is shown that OFDM symbol sequences with a short period are expected to have a high crest factor. The crest factor relationship between two input symbol sequences, Hamming distance D apart is also derived. Using these two results, we propose two criteria for a phase sequence set of the selected mapping (SLM) scheme and suggest the rows of the cyclic Hadamard matrix constructed from an m-sequence as the near optimal phase sequence set of the SLM scheme.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.233-236
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• 2001

Orthogonal freqency division multiplexing (OFDM) is an attractive technique for achieving high-bit-rate wireless data transmission. However, the potentially large peak-to-average power ratio (PAPR) has limited its application; An OFDM signal with the large PAPR can cause power degradation (In-band distortion) and spectral spreading (Out-of-band distortion) by being clipped passing through a power amplifier. Thus, we propose the combining algorithm of Hadamard transform and phase shift, which is ascribed to the relation between the correlation of the IFFT input sequence function and PAPR. Extensive computer simulations show that the combining algorithm is an effective technique to reduce PAPR.

• East Asian mathematical journal
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• v.36 no.1
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• pp.61-71
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• 2020

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension Theorem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP instead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.2A
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• pp.116-123
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• 2002

The jacket matrix is based on the Walsh-Hadamard matrix and an extension of it. While elements of the Walsh-Hadamard matrix are +1, or -1, those of the Jacket matrix are ${\pm}$1 and ${\pm}$$\omega$, which is $\omega$, which is ${\pm}$j and ${\pm}$2$\sub$n/. This matrix has weights in the center part of the matrix and its size is 1/4 of Hadamard matrix, and it has also two parts, sigh and weight. In this paper, instead of the conventional Jacket matrix where the weight is imposed by force, a simple Jacket sequence generation method is proposed. The Jacket sequence is generated by AND and Exclusive-OR operations between the binary indices bits of row and those of column. The weight is imposed on the element by when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by jacket sequence using row and column binary index bits. Using Distributed Arithmetic (DA), we present a VLSI architecture of the Fast Jacket transform is presented. The Jacket matrix is able to be applied to cryptography, the information theory and complex spreading jacket QPSK modulation for WCDMA.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.119-125
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• 2015

In this paper, we introduce a Hadamard matrix interstream transmission based blind channel estimation for multi-cells multiple-input and multiple-output (MIMO) networks. The proposed scheme is based on a network with mobile stations (MS) which are deployed with multi cells. We assume that the MS have the signals from both cells. The signal from near cell are considered as desired signal and the signals from the other cells are interference signal. Since the channel is blind, so that we transmit Hadamard matrix pattern pilot stream to estimate the channel; that gives easier and fast channel estimation for large scale MIMO channel. The computation of Hadamard based system takes only complex additions, and thus the complexity of which is much lower than the scheme with Fourier transform since complex multiplications are not needed. The numerical analysis will give perfection of proposed channel estimation.