• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.939-955
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• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.9
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• pp.1-8
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• 2010

A digital phase wrapping modulation (DPM) open-loop polar transmitter can be efficiently applied to a wideband orthogonal frequency division multiplexing (OFDM) communication system by converting in-phase and quadrature signals to envelope and phase signals and then employing the signal mapping process. This mapping process is very similar to quantization in a general communication system, and when taking into account the error that appears during mapping process, one can replace the coordinates rotation digital computer (CORDIC) algorithm in the coordinate conversion part with the Taylor series approximation method. In this paper, we investigate the application of the Taylor series approximation to the cartesian to polar coordinate conversion part of a DPM polar transmitter for wideband OFDM systems. The conventional approach relies on the CORDIC algorithm. To achieve efficient application, we perform computer simulation to measure mean square error (MSE) of the both approaches and find the minimum approximation order for the Taylor series approximation compatible to allowable error of the CORDIC algorithm in terms of hardware design. Furthermore, comparing the processing speeds of the both approaches in the implementation with FPGA reveals that the Taylor series approximation with lower order improves the processing speed in the coordinate conversion part.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.6B
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• pp.1024-1031
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• 1999

In order to transmit high-speed wide band signals efficiently in multipath fading environments, M-ary QAM signalling combined with OFDM transmission technique is applied. In this paper, the effect of synchronization error caused by carrier frequency offset and SER(Symbol Error Rate) performance of OFDM-16QAM and OFDM-64QAM are theoretically analyzed. Our result shows that as the number of sub-carrier in OFDM system increases the frequency-offset caused inter-channel interference(ICI) increases significantly, and that an error floor occurs even at high SNR of OFDM system. For OFDM-64QAM, the error floor occurs at SER=1$\times$10-7 when a normalized frequency-offset is 0.001, in which the SNR degradation is much greater than that of OFDM-16QAM. From this study the maximum allowable frequency-offset of OFDM-16QAM and OFDM-64QAM systems can be determined to meet the specific SER requirement.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.9C
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• pp.810-819
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• 2007

The I/Q unbalance which is generated by non-ideal components such as a $90^{\circ}$ phase shifter and I/Q filters is an inevitable physical phenomenon and leads to performance degradation when we implement a coherent two-dimensional (2-D) modulation/demodulation system. This paper provides an exact and general expression for the SEP(symbol error probability) of DVB-S2 system with I/Q phase and amplitude unbalance over AWGN channel. Coordinate rotation and shift techniques used to redefine a received signal are key mathematical tools. In conclusion, the derived result is expressed as a linear combination of the 2-D Gaussian Q-functions.

• ETRI Journal
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• v.36 no.2
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• pp.206-213
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• 2014

This paper presents a novel 90 GHz band 16-quadrature amplitude modulation (16-QAM) orthogonal frequency-division multiplexing (OFDM) communication system. The system can deliver 6 Gbps through six channels with a bandwidth of 3 GHz. Each channel occupies 500 MHz and delivers 1 Gbps using 16-QAM OFDM. To implement the system, a low-noise amplifier and an RF up/down conversion fourth-harmonically pumped mixer are implemented using a $0.1-{\mu}m$ gallium arsenide pseudomorphic high-electron-mobility transistor process. A polarization-division duplex architecture is used for full-duplex communication. In a digital modem, OFDM with 256-point fast Fourier transform and (255, 239) Reed-Solomon forward error correction codecs are used. The modem can compensate for a carrier-frequency offset of up to 50 ppm and a symbol rate offset of up to 1 ppm. Experiment results show that the system can achieve a bit error rate of $10^{-5}$ at a signal-to-noise ratio of about 19.8 dB.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.6
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• pp.80-86
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• 2001

This paper proposes a precision displacement measuring method of detecting fringe movement of interferograms with a nanometric resolution. It is well known that the laser interferometer plays a useful and essential role in scientific and industrial application, but they have such error sources as an unequal gain of detectors, imbalanced beams, and lack of quadrature. These error sources degrade the accuracy of the interferometer. However, the fringe movement of interferograms has little relation with these error sources. In order to investigate performance of the proposed method. analysis and simulation were executed over random noise and wavefront distorion. Results of the simulation show that the proposed method is robust against these errors. Experiment was implemented to verify this method.

• Journal of Communications and Networks
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• v.18 no.5
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• pp.677-687
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• 2016

Multi-way relay networks (MWRNs) allow multiple users to exchange information with each other through a single relay terminal. MWRNs are often incorporated with capacity achieving lattice codes to enable the benefits of high-rate signal constellations to be extracted. In this paper, we analytically characterize the symbol error rate (SER) performance of a functional decode and forward (FDF) MWRN in the presence of channel estimation errors. Considering M-ary quadrature amplitude modulation (QAM) with square constellations as an important special case of lattice codes, we obtain asymptotic expressions for the average SER for a user in FDF MWRN. The accuracy of the analysis at high signal-to-noise ratio is validated by comparison with the simulation results. The analysis shows that when a user decodes other users with better channel conditions than itself, the decoding user experiences better error performance. The analytical results allow system designers to accurately assess the non-trivial impact of channel estimation errors and the users' channel conditions on the SER performance of a FDF MWRN with M-QAM modulation.

• ETRI Journal
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• v.34 no.5
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• pp.649-654
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• 2012

This paper presents a novel 16-quadrature-amplitude-modulation (QAM) E-band communication system. The system can deliver 10 Gbps through eight channels with a bandwidth of 5 GHz (71-76 GHz/81-86 GHz). Each channel occupies 390 MHz and delivers 1.25 Gbps using a 16-QAM. Thus, this system can achieve a bandwidth efficiency of 3.2 bit/s/Hz. To implement the system, a driver amplifier and an RF up-/down-conversion mixer are implemented using a $0.1{\mu}m$ gallium arsenide pseudomorphic high-electron-mobility transistor (GaAs pHEMT) process. A single-IF architecture is chosen for the RF receiver. In the digital modem, 24 square root raised cosine filters and four (255, 239) Reed-Solomon forward error correction codecs are used in parallel. The modem can compensate for a carrier-frequency offset of up to 50 ppm and a symbol rate offset of up to 1 ppm. Experiment results show that the system can achieve a bit error rate of $10^{-5}$ at a signal-to-noise ratio of about 21.5 dB.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11C
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• pp.1070-1076
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• 2003

This paper presents and analyses the exact and general closed-form expression for the average bit error probability of M-ary square quadrature amplitude modulation (QAM) for maximal ratio combining (MRC) diversity reception in frequency-nonselective Nakagami-m fading. An L-branch Maximal ratio combining diversity technique with independent or correlated fading cases is considered. Numerical results demonstrate the error performance improvement by employing with the use of MRC diversity reception. The new expressions presented here can offer a convenient way to evaluate the performance of an arbitrary square M-W square QAM with an MRC diversity combiner for various cases of practical interest.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.21 no.7
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• pp.761-768
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• 2010

This paper presents an effective method to achieve the wideband waveform for high resolution SAR(Synthetic Aperture Radar) using the frequency multiplication technique. And also this paper analyzes the root causes for the spectral regrowth due to 3rd-order intermodulation in chirp bandwidth expansion scheme using quadrature modulator and frequency multipliers. The amplitude and phase imbalance requirement are defined based on the simulation results in terms of quadrature channel imbalance. This minimizes the degradation of range resolution, peak sidelobe ratio and integrated sidelobe ratio. The wideband chirp generator using the frequency multiplier and memory map scheme was manufactured and the compensation technique was presented to reduce the spectral regrowth of SAR waveform by minimizing the amplitude and phase imbalance. After I and Q channel imbalance adjustment, the carrier level reduces －28.7 dBm to －53.4 dBm. Chirp signal with 150 MHz bandwidth at S-band expands to 600 MHz bandwidth at X-band. The sidelobe levels are reduced by about 8 to 9 dB by compensating the amplitude balance between I and Q channels.