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Several Modulation in Direct-Sequence Spectrum-Spread Systems
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作者 Wang Yi, Zhao Ming, Zhang Zhongpei & Yao Yan State Key Lab. on Microwave & Digital Communication, Tsinghua University, Beijing 100084, P.R.China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2002年第1期53-58,共6页
Performances of BPSK, balanced quaternary modulation, dual quaternary modulation and complex quaternary modulation in direct sequence spectrum spread (DS SS) system are discussed in this paper. Based on the crit... Performances of BPSK, balanced quaternary modulation, dual quaternary modulation and complex quaternary modulation in direct sequence spectrum spread (DS SS) system are discussed in this paper. Based on the criterion the power of original signal is the same, it is shown that complex quaternary modulation has the best performance, and dual quaternary modulation degrades 2dB. Moreover, the frequency efficient of the two modulations is 2bit/Hz. Balanced quaternary has the same performance as BPSK with frequency efficient 1bit/Hz. 展开更多
关键词 MODULATION direct sequence spectrum spread Frequency efficient.
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High-Sensitivity Acquisition of Ultrahigh Dynamic Direct Sequence Spread Spectrum Signals in Space Communications 被引量:2
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作者 徐颖 袁洪 《China Communications》 SCIE CSCD 2013年第10期26-36,共11页
According to the requirements of the high-sensitivity acquisition of Direct Sequence Spread Spectrum(DSSS) signals under ultrahigh dynamic environments in space communications, a three-dimensional joint search of the ... According to the requirements of the high-sensitivity acquisition of Direct Sequence Spread Spectrum(DSSS) signals under ultrahigh dynamic environments in space communications, a three-dimensional joint search of the phase of Pseudo-Noise-code(PN-code),Doppler frequency and its rate-of-change is presented to achieve high sensitivity in sensing high-frequency dynamics. By eliminating the correlation peak loss caused by ultrahigh Doppler frequency and its rate-of-change offset,the proposed method improves the acquisition sensitivity by increasing the non-coherent accumulation time. The validity of the algorithm is proved by theoretical analysis and simulation results. It is shown that signals with a carrier- to-noise ratio as low as 39 dBHz can be captured with high performance when the Doppler frequency is up to ±1 MHz and its rate-of-change is up to ±200 kHz/s. 展开更多
关键词 direct sequence spread spectrum signals space communications ACQUISITION high sensitivity ultrahigh dynamic
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Research on Estimator and Testing Acquisition Schemes in Direct Sequence Spectrum Spreading Systems 被引量:1
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作者 陈岩 黄其华 +1 位作者 安建平 罗伟雄 《Journal of Beijing Institute of Technology》 EI CAS 2004年第1期5-9,共5页
Serveral methods for the pararrel acquisition of a PN sequence in a baseband direct sequence spread spectrum system are investigated. Four different kinds of schemes are considered: the optimal estimation scheme, the ... Serveral methods for the pararrel acquisition of a PN sequence in a baseband direct sequence spread spectrum system are investigated. Four different kinds of schemes are considered: the optimal estimation scheme, the locally optimal estimation scheme, the optimal testing searches and the locally optimal testing scheme. In the four kinds of parallel acquisition schemes, the expressions for the probability of error are given and compared with the actual error probabilities obtained via Monte Carlo simulation. We also outline a technique that can be suboptimal because of a large amount of hardware and computation when using the parallel acquisition schemes. 展开更多
关键词 direct sequence spectrum spreading systems parallel acquisition SYNCHRONIZATION
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Ultra-wideband direct-sequence design approach for multiple narrowb and interference suppression 被引量:1
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作者 Huibin Xu Junjun Guo Xingjun Shi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2013年第3期365-371,共7页
A novel direct sequence (DS) design method for suppressing the narrowband interference in DS spread spectrum ultra-wideband receivers is proposed. The method has low computational complexity and can be easily implem... A novel direct sequence (DS) design method for suppressing the narrowband interference in DS spread spectrum ultra-wideband receivers is proposed. The method has low computational complexity and can be easily implemented in practical systems. Simulation results prove that the proposed method is effective to suppress the narrowband interference. Therefore, the integrity of both the ultra-wide bandwidth and the narrowband systems can be highly enhanced. 展开更多
关键词 bit error rate (BER) narrowband interference Rayleigh-Ritz direct sequence (DS).
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New Acquisition Algorithm for Direct Sequence Spread Spectrum Signals 被引量:1
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作者 王永庆 吴嗣亮 《Journal of Beijing Institute of Technology》 EI CAS 2009年第4期468-472,共5页
Aiming at improving acquisition performance for direct sequence spread spectrum (DSSS) signals, a new acquisition algorithm based on fast Fourier transform (FFT) is proposed. The code phases are parallel searched ... Aiming at improving acquisition performance for direct sequence spread spectrum (DSSS) signals, a new acquisition algorithm based on fast Fourier transform (FFT) is proposed. The code phases are parallel searched throughout the Doppler frequency domain. Since the influence of Doppler frequency errors on peak-to- average ratios of correlation power shows a pattern similar to the sinc function, it is our belief that by judging on peak-to-average ratios for different Doppler frequency errors false alarm probabilities should be lowered. Analyses have supported the underlying principle of this new algorithm. Simulation results have also indicated that the new algorithm can effectively improve the acquisition performance for DSSS signals. 展开更多
关键词 direct sequence spread spectrum (DSSS) ACQUISITION false alarm probability
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Low complexity method for spreading sequence estimation of DSSS signal in non-cooperative communication systems 被引量:10
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作者 Chang Liang Wang Fuping Wang Zanji 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第1期41-49,共9页
It is a necessary step to estimate the spreading sequence of direct sequence spread spectrum (DSSS) signal for blind despreading and demodulation in non-cooperative communications. Two innovative and effective detec... It is a necessary step to estimate the spreading sequence of direct sequence spread spectrum (DSSS) signal for blind despreading and demodulation in non-cooperative communications. Two innovative and effective detection statistics are proposed to implement the synchronization and spreading sequence estimation procedure. The proposed algorithm also has a low computational complexity with only linear additions and modifications. Theoretical analysis and simulation results show that the algorithm performs quite well in low SNR environment, and is much better than all the existing typical algorithms with a comprehensive consideration both in performance and computational complexity. 展开更多
关键词 direct sequence spread spectrum detection statistic low complexity.
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Fast method for spreading sequence estimation of DSSS signal based on maximum likelihood function 被引量:12
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作者 Yanhua Peng Bin Tang Ming Lv 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第6期948-953,共6页
To estimate the spreading sequence of the direct sequence spread spectrum (DSSS) signal, a fast algorithm based on maximum likelihood function is proposed, and the theoretical derivation of the algorithm is provided. ... To estimate the spreading sequence of the direct sequence spread spectrum (DSSS) signal, a fast algorithm based on maximum likelihood function is proposed, and the theoretical derivation of the algorithm is provided. By simplifying the objective function of maximum likelihood estimation, the algorithm can realize sequence synchronization and sequence estimation via adaptive iteration and sliding window. Since it avoids the correlation matrix computation, the algorithm significantly reduces the storage requirement and the computation complexity. Simulations show that it is a fast convergent algorithm, and can perform well in low signal to noise ratio (SNR). 展开更多
关键词 direct sequence spread spectrum (DSSS) signal spreading sequence maximum likelihood estimation (MLE).
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Approach to blind estimation of the PN sequence in DS-SS signals with residual carrier 被引量:8
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作者 Tianqi Zhang Shaosheng Dai +2 位作者 Guoning Ma Wei Zhang Pu Miao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第1期1-8,共8页
This paper presents an approach of singular value de- composition plus digital phase lock loop to solve the difficult problem of blind pseudo-noise (PN) sequence estimation in low signal to noise ratios (SNR) dire... This paper presents an approach of singular value de- composition plus digital phase lock loop to solve the difficult problem of blind pseudo-noise (PN) sequence estimation in low signal to noise ratios (SNR) direct sequence spread spectrum (DS-SS) signals with residual carrier. This approach needs some given parameters, such as the period and code rate of PN sequence. The received signal is firstly sampled and divided into non-overlapping signal vectors according to a temporal window, whose duration is two periods of PN sequence. An autocorrelation matrix is then computed and accumulated by those signal vectors one by one. The PN sequence with residual carrier can be estimated by the principal eigenvector of the autocorrelation matrix. Further more, a digital phase lock loop is used to process the estimated PN sequence, it estimates and tracks the residual carrier and removes the residual carrier in the end. Theory analysis and computer simulation results show that this approach can effectively realize the PN sequence blind estimation from the input DS-SS signals with residual carrier in lower SNR. 展开更多
关键词 direct sequence spread spectrum (DS-SS) signal pseudo-noise (PN) sequence blind estimation singular value de-composition digital phase lock loop residual carrier.
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Neural network approach to blindestimation of PN spreading sequence in lower SNR DS/SS signals 被引量:6
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作者 Zhang Tianqi Lin Xiaokang Zhou Zhengzhong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第4期756-760,共5页
An approach based on discrete Karhunen-Loeve transformation of the DS/SS signals is proposed to estimate PN sequence in lower S/N ratio DS/SS signals. Characteristics of self-organization and principle components extr... An approach based on discrete Karhunen-Loeve transformation of the DS/SS signals is proposed to estimate PN sequence in lower S/N ratio DS/SS signals. Characteristics of self-organization and principle components extraction of unsupervised neural networks are exploited adequately. Theoretical analysis and experimental results are provided to show that this approach can work well on the lower S/N ratio input signals. 展开更多
关键词 discrete Karhunen-Loeve transformation neural networks direct sequence spread spectrum (DS/SS) signal PN sequence.
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A Neural Network Approach to Blind Estimation of PN Spreading Sequence in DS/SS Signals 被引量:1
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作者 张天麒 周正中 《Journal of Electronic Science and Technology of China》 2004年第2期1-6,共6页
In this paper, a new approach is proposed to estimate pseudo noise(PN) sequence in the lower SNR DS/SS signals blindly. This method utilizes the characteristics of self-organization, principal components analysis and ... In this paper, a new approach is proposed to estimate pseudo noise(PN) sequence in the lower SNR DS/SS signals blindly. This method utilizes the characteristics of self-organization, principal components analysis and extraction of unsupervised neural networks adequately, in addition to its higher-speed operation ability, successfully solve the difficult problem about PN sequence blind estimation. The theoretic analysis and experimental results show that this approach can work very well on lower SNR input signals. 展开更多
关键词 neural networks direct sequence spread spectrum signal PN sequence
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Non-Supervised Learning for Spread Spectrum Signal Pseudo-Noise Sequence Acquisition
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作者 Hao Cheng Na Yu Tai-Jun Wang 《Journal of Electronic Science and Technology》 CAS CSCD 2015年第1期83-86,共4页
An idea of estimating the direct sequence spread spectrum(DSSS) signal pseudo-noise(PN) sequence is presented. Without the apriority knowledge about the DSSS signal in the non-cooperation condition, we propose a s... An idea of estimating the direct sequence spread spectrum(DSSS) signal pseudo-noise(PN) sequence is presented. Without the apriority knowledge about the DSSS signal in the non-cooperation condition, we propose a self-organizing feature map(SOFM) neural network algorithm to detect and identify the PN sequence. A non-supervised learning algorithm is proposed according the Kohonen rule in SOFM. The blind algorithm can also estimate the PN sequence in a low signal-to-noise(SNR) and computer simulation demonstrates that the algorithm is effective. Compared with the traditional correlation algorithm based on slip-correlation, the proposed algorithm's bit error rate(BER) and complexity are lower. 展开更多
关键词 Blind estimation direct sequence spread spectrum signal non-supervised learning pseudo-noise sequence
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Reconfigurable Intelligent Surface-Based Hybrid Phase and Code Modulation for Symbiotic Radio
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作者 Song Bai Qiang Li Donghong Cai 《China Communications》 SCIE CSCD 2023年第10期30-42,共13页
Reconfigurable intelligent surface(RIS)-assisted symbiotic radio is a spectrum-and energy-efficient communication paradigm,in which an RIS performs passive beamforming to enhance active transmission,while using the el... Reconfigurable intelligent surface(RIS)-assisted symbiotic radio is a spectrum-and energy-efficient communication paradigm,in which an RIS performs passive beamforming to enhance active transmission,while using the electromagnetic waves from the active transmission for additional information transfer(i.e.,passive transmission).In this paper,a hybrid RIS-based modulation,termed hybrid phase and code modulation(HPCM),is proposed to improve the reliability of RIS-assisted symbiotic radio.In RIS-HPCM,the RIS simultaneously performs direct sequence spread spectrum and passive beamforming on incident signals.Moreover,both the spreading code and phase offset are exploited to carry the RIS’s own information.A low-complexity detector is designed,in which the receiver first detects the spreading codes and then demodulates the constellation symbols.We analyze the bit error rate(BER)performance of RIS-HPCM over Rician fading channels.BER upper bounds and approximate BER expressions are derived in closed-form for maximum-likelihood and low-complexity detectors,respectively.Simulation results in terms of BER verify the analysis and show the superiority of RIS-HPCM over the existing RIS-based modulation. 展开更多
关键词 reconfigurable intelligent surface symbiotic radio index modulation direct sequence spread spectrum performance analysis
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Direct RNA sequencing in plants:Practical applications and future perspectives
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作者 Xi-Tong Zhu Pablo Sanz-Jimenez +2 位作者 Xiao-Tong Ning Muhammad Tahir ul Qamar Ling-Ling Chen 《Plant Communications》 SCIE CSCD 2024年第11期54-71,共18页
The transcriptome serves as a bridge that links genomic variation to phenotypic diversity.A vast number of studies using next-generation RNA sequencing(RNA-seq)over the last 2 decades have emphasized the essential rol... The transcriptome serves as a bridge that links genomic variation to phenotypic diversity.A vast number of studies using next-generation RNA sequencing(RNA-seq)over the last 2 decades have emphasized the essential roles of the plant transcriptome in response to developmental and environmental conditions,providing numerous insights into the dynamic changes,evolutionary traces,and elaborate regulation of the plant transcriptome.With substantial improvement in accuracy and throughput,direct RNA sequencing(DRS)has emerged as a new and powerful sequencing platform for precise detection of native and full-length transcripts,overcoming many limitations such as read length and PCR bias that are inherent to short-read RNA-seq.Here,we review recent advances in dissecting the complexity and diversity of plant transcriptomes using DRS as the main technological approach,covering many aspects of RNA metabolism,including novel isoforms,poly(A)tails,and RNA modification,and we propose a comprehensive workflow for processing of plant DRS data.Many challenges to the application of DRS in plants,such as the need for machine learning tools tailored to plant transcriptomes,remain to be overcome,and together we outline future biological questions that can be addressed by DRS,such as allele-specific RNA modification.This technology provides convenient support on which the connection of distinct RNA features is tightly built,sustainably refining our understanding of the biological functions of the plant transcriptome. 展开更多
关键词 direct RNA sequencing novel isoforms fusion transcripts poly(A)tail RNA modifications
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NanoTrans:an integrated computational framework for comprehensive transcriptome analysis with nanopore direct RNA sequencing
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作者 Ludong Yang Xinxin Zhang +3 位作者 Fan Wang Li Zhang Jing Li Jia-Xing Yue 《Journal of Genetics and Genomics》 SCIE CAS 2024年第11期1300-1309,共10页
Nanopore direct RNA sequencing(DRS)provides the direct access to native RNA strands with full-length information,shedding light on rich qualitative and quantitative properties of gene expression profiles.Here with Nan... Nanopore direct RNA sequencing(DRS)provides the direct access to native RNA strands with full-length information,shedding light on rich qualitative and quantitative properties of gene expression profiles.Here with NanoTrans,we present an integrated computational framework that comprehensively covers all major DRS-based application scopes,including isoform clustering and quantification,poly(A)tail length estimation,RNA modification profiling,and fusion gene detection.In addition to its merit in providing such a streamlined one-stop solution,NanoTrans also shines in its workflow-orientated modular design,batch processing capability,all-in-one tabular and graphic report output,as well as automatic installation and configuration supports.Finally,by applying NanoTrans to real DRS datasets of yeast,Arabidopsis,as well as human embryonic kidney and cancer cell lines,we further demonstrate its utility,effectiveness,and efficacy across a wide range of DRS-based application settings. 展开更多
关键词 direct RNA sequencing Nanopore Transcriptome Long reads DRS
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Multi-access performance of DS UWB systemunder indoor dense multi-path channel
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作者 樊祥宁 倪剑强 毕光国 《Journal of Southeast University(English Edition)》 EI CAS 2005年第4期393-397,共5页
The performance of multi-user code to direct spreading bi-phase shift keying (DS-BPSK) direct impulse ultra wideband (UWB) systems under indoor multi-user and multi-path environment is analyzed and simulated. The ... The performance of multi-user code to direct spreading bi-phase shift keying (DS-BPSK) direct impulse ultra wideband (UWB) systems under indoor multi-user and multi-path environment is analyzed and simulated. The system output signals with Rake receiver are derived, then a simple and practical code selection scheme is given; i. e., with a large occupation to empty ratio of the repeating pulses, directly choosing those random or pseudo-random user codes with enough length and good co-relative orthogonal features will make the performance of DS-BPSK approximate the optimum and, so there is no need to carefully design the code or its type. The system multi-access performances are simulated using Gold sequence and PN codes as multi-user codes under CMI-CM4 multi-path channels. Simulation results prove that the proposed scheme is feasible. 展开更多
关键词 ultra wideband multi-access MULTI-PATH Gold code direct sequence RAKE
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Concatenated Trellis Coding and CPM for DS/SSMA Communications in Rayleigh Fading Channel
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作者 仰枫帆 梁树雄 毕光国 《Journal of Southeast University(English Edition)》 EI CAS 1999年第1期9-16,共8页
In this paper, direct sequence spread spectrum multiple access (DS/SSMA) communication system employing serially concatenated trellis coded modulation (TCM) and continuous phase modulation (CPM) over flat Rayleigh fa... In this paper, direct sequence spread spectrum multiple access (DS/SSMA) communication system employing serially concatenated trellis coded modulation (TCM) and continuous phase modulation (CPM) over flat Rayleigh fading channel are presented. The performance of this concatenated TCM/CPM DS/SSMA system is exploited by the theoretical analysis and numerical simulations. The results demonstrate that significant improvements in error probability of this DS/SSMA system over the system with single TCM or CPM of different modulation indices can be achieved under the same conditions. 展开更多
关键词 concatenated TCM/CPM direct sequence spread spectrum multiple access Rayleigh fading channel
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Study on Fast Acquisition of Hybrid DS/FHSS 被引量:3
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作者 张波 邵定蓉 Tarek S.ELHABIAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第2期161-165,共5页
In hybrid Direct Sequence/Frequency Hopping Spread Spectrum (DS/FH SS) system, the fast acquisition is a key technique. A combined fast scanning and waiting method for FH acquisition is introduced, and a neural netw... In hybrid Direct Sequence/Frequency Hopping Spread Spectrum (DS/FH SS) system, the fast acquisition is a key technique. A combined fast scanning and waiting method for FH acquisition is introduced, and a neural network for DS acquisition is presented also. Using these two methods, the fast acquisition of the hybrid DS/FH SS system can be realized. 展开更多
关键词 spread spectrum ACQUISITION frequency identification neural network direct sequence/ lrequency hopping
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Regulations of m^(6)A methylation on tomato fruit chilling injury 被引量:4
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作者 Chunmei Bai Minghuan Fang +8 位作者 Baiqiang Zhai Lili Ma Anzhen Fu Lipu Gao Xiaohong Kou Demei Meng Qing Wang Shufang Zheng Jinhua Zuo 《Horticultural Plant Journal》 SCIE CSCD 2021年第5期434-442,共9页
Tomato fruit are sensitive to chilling injury(CI)during cold storage.Several factors have been discovered to be involved in chilling injury of tomato fruit.Plant hormones play an important regulatory role,however,the ... Tomato fruit are sensitive to chilling injury(CI)during cold storage.Several factors have been discovered to be involved in chilling injury of tomato fruit.Plant hormones play an important regulatory role,however,the relationship between chilling injury and N6-methyladenosine(m^(6)A)methylation of transcripts in plant hormone pathways has not been reported yet.In order to clarify the complex regulatory mechanism of m^(6)A methylation on chilling injury in tomato fruit,Nanopore direct RNA sequencing was employed.A large number of enzymes and transcription factors were found to be involved in the regulation process of fruit chilling injury,which were associated with plant hormone,such as 1-aminocyclopropane 1-carboxylate synthase(ACS),aspartate aminotransferase(AST),auxin response factor(ARF2),ethylene response factor 2(ERF2),gibberellin 20-oxidase-3(GA20ox)and jasmonic acid(JA).By conjoint analysis of the differential expression transcripts related to chilling injury andm^(6)Amethylation differential expression transcripts 41 differential expression transcripts were identified involved in chilling injury including 1-aminocyclopropane-1-carboxylate oxidase(ACO)and pectinesterase(PE)were down-regulated and heat shock cognate 70 kD protein 2(cpHSC70),HSP70-binding protein(HspBP)and salicylic acid-binding protein 2(SABP2)were up-regulated.Our results will provide a deeper understanding for chilling injury regulatory mechanism and post-harvest cold storage of tomato fruit. 展开更多
关键词 m^(6)A methylation Chilling injury Plant hormone Nanopore direct RNA sequencing Tomato fruit
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An underwater acoustic direct sequence spread spectrum communication system using dual spread spectrum code 被引量:2
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作者 Lan-jun LIU Jian-fen LI +4 位作者 Lin ZHOU Peng ZHAI Hao ZHAO Jiu-cai JIN Zhi-chao LV 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2018年第8期972-983,共12页
With the goal of achieving high stability and reliability to support underwater point-to-point communications and code division multiple access(CDMA) based underwater networks, a direct sequence spread spectrum based ... With the goal of achieving high stability and reliability to support underwater point-to-point communications and code division multiple access(CDMA) based underwater networks, a direct sequence spread spectrum based underwater acoustic communication system using dual spread spectrum code is proposed. To solve the contradictions between the information data rate and the accuracy of Doppler estimation, channel estimation, and frame synchronization, a data frame structure based on dual spread spectrum code is designed. A long spread spectrum code is used as the training sequence, which can be used for data frame detection and synchronization, Doppler estimation, and channel estimation. A short spread spectrum code is used to modulate the effective information data. A delay cross-correlation algorithm is used for Doppler estimation, and a correlation algorithm is used for channel estimation. For underwater networking, each user is assigned a different pair of spread spectrum codes. Simulation results show that the system has a good anti-multipath, anti-interference, and anti-Doppler performance, the bit error rate can be smaller than 10^(-6) when the signal-to-noise ratio is larger than-10 dB, the data rate can be as high as 355 bits/s, and the system can be used in the downlink of CDMA based networks. 展开更多
关键词 Underwater acoustic communication direct sequence spread spectrum Doppler estimation and compensation Channel estimation and equalization Gold code Single carrier Code division multiple access
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Novel LFM Jammer Suppression Algorithm for DSSS in FRFT Domain 被引量:2
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作者 Jining Feng Xiaobo Yang Jun Wang 《Journal of Beijing Institute of Technology》 EI CAS 2019年第4期783-789,共7页
A novel algorithm is proposed to resolve the defects in the traditional linear frequency modulation(LFM)jamming suppression algorithm in the fractional Fourier transform(FRFT)domain.The traditional LFM jamming suppres... A novel algorithm is proposed to resolve the defects in the traditional linear frequency modulation(LFM)jamming suppression algorithm in the fractional Fourier transform(FRFT)domain.The traditional LFM jamming suppression algorithm in the FRFT domain has some defects.For example,the exact threshold is difficult to set and both the signal-to-noise ratio(SNR)loss and spectrum leakage are serious in strong jamming-to-signal ratio(JSR)situations.Windowing,overlapping and inverse windowing techniques are used in the FRFT domain to reduce the spectrum leakage and the SNR loss.Under the condition that only the direct sequence spread spectrum(DSSS)signal and white Gaussian noise are present,the amplitude of the received signal after FRFT is assumed to be Rayleigh distributed.Based on the distribution characteristic,hypothesis testing is used to suppress the jamming spectrum using the algorithm.Simulation results show that the performance of proposed algorithm is better than that of the conventional algorithms,especially in a strong jamming and multi component LFM jamming environment. 展开更多
关键词 direct sequence spread spectrum(DSSS) fractional Fourier transform(FRFT) linear frequency modulation(LFM)jamming inverse windowed
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