Autocorrelation Sequence Research Articles

A Reflection Measurement System With High Accuracy Using Binary Coded Signals

The measurement of the electromagnetic reflection characteristics of a device under test (DUT) is of interest in a large variety of applications. For this task, the established low-cost approach of using pulse-shaped excitation signals is more and more replaced by employing continuous binary coded excitation signals. The reason behind this is that reflection measurement systems with continuous signals offer a larger signal-to-noise ratio (SNR), which allows for a larger dynamic range compared to pulsed systems for the same measurement time. However, a correlator is needed to access the impulse response function (IRF) of the DUT. In this contribution, a reflection measurement system is presented using a hybrid correlation approach. In the latter, the correlation is performed using a combination of a hardware and a software correlator. The hardware of the developed measurement system has been optimized to achieve a high dynamic range and a high measurement accuracy. A demonstrator system has been realized using the so-called almost perfect auto-correlation sequences (APASs) with a chip clock of 5Gchips/s. With the optimized hardware, a dynamic range of 82 dB has been achieved. The measurement accuracy has been validated by means of distance measurements versus a high accuracy laser reference system achieving a maximum error of 25 ${\mu }\text{m}$ . Furthermore, the measured reflection coefficient of a low-pass filter has been compared with the results obtained with a vector network analyzer (VNA).

Photon Counting LIDAR Based on True Random Coding.

In this paper, a true random coding photon counting LIDAR is described, in which a Gm-APD (Geiger mode avalanche photodiode) acts as the true random sequence signal generator. The true random coding method not only improves the anti-crosstalk capability of the system, but also greatly reduces the 1-bit missed detection caused by the limited Gm-APD count rate. The experiment verifies the feasibility of the true random sequence used in a photon counting LIDAR ranging system, and a simple and intuitive evaluation model of true random sequence autocorrelation is proposed. Finally, the influence of system parameters (mean echo photon number, mean pulse count density, sequence length, mean noise count) on detection probability is explored. In general, this paper proves that the true random code photon counting LIDAR is an effective target detection method, and provides a new idea for the research of an anti-crosstalk LIDAR system.

Prony-Type Polynomials and Their Common Zeros

The problem of hidden periodicity of a bivariate exponential sum $ {f({\bf n})=\sum_{j=1}^{N}a_j\exp{(-\mathrm{i}\langle{\bm \omega}_j, {\bf n}\rangle)}}, $ where $a_1,\dots,a_N \in \mathbb{C}\backslash\{0\}$ and ${\bf n}\in \mathbb{Z}^2$, is to recover frequency vectors ${\bm \omega}_1, \dots, {\bm \omega}_N \in [0,2\pi)^2$ using finitely many {samples of $f$.} Recently, this problem has received a lot of attention, and different approaches have been proposed to obtain its solution. For example, \cite{KunisProny} relies on the kernel basis analysis of the multilevel Toeplitz matrix of moments of $f$. In \cite{CuytProny2}, the exponential analysis has been considered as a Pad\'e approximation problem. In contrast to the previous method, the algorithms developed in \cite{BDAR,Cuyt} use sampling of $f$ along several lines in the hyperplane to obtain the univariate analog of the problem, which can be solved by classical one-dimensional approaches. Nevertheless, the stability of numerical solutions in the case of noise corruption still has a lot of open questions, especially when the number of parameters increases. Inspired by the one-dimensional approach developed in \cite{FMPrestin}, we propose to use the method of Prony-type polynomials, where the elements ${\bm \omega}_1, \dots, {\bm \omega}_N $ can be recovered due to a set of common zeros of the monic bivariate polynomial of an appropriate multi-degree. The use of Cantor pairing functions allows us to express bivariate Prony-type polynomials in terms of determinants and to find their exact algebraic representation. With respect to the number of samples the method of Prony-type polynomials is situated between the methods proposed in \cite{KunisProny, Cuyt}. Although the method of Prony-type polynomials requires more samples than \cite{Cuyt}, numerical computations show that the algorithm behaves more stable with regard to noisy data. Besides, combining the method of Prony-type polynomials with an autocorrelation sequence allows the improvement of the stability of the method in general.

Enhanced performance of PS-256QAM-OFDM for optical access network

In this paper, to increase communication capacity and improve receiver sensitivity for optical access networks, probabilistically-shaped orthogonal frequency division multiplexing (PS-OFDM) assisted by constant amplitude zero autocorrelation sequence (CAZAC) is investigated in cost-effective intensity-modulation and direct-detection (IM-DD) system. Since 256-QAM is adopted in PS-OFDM, it can significantly improve spectral efficiency and shaping gain Moreover, we compared the probability shaping scheme with the traditional scheme in the terms of receiver sensitivity and achievable information rate (AIR). Experimental results demonstrate that the performance of probabilistically-shaped OFDM scheme outperforms the traditional OFDM scheme. At the same rate of 6.0 bits/QAM symbol, 2.0-dB performance improvement in both receiver sensitivity and AIR can be achieved employing probabilistic shaping assisted by CAZAC precoding. Meanwhile, a 2.45-Gbit/s/λ capacity increase can be achieved with the proposed scheme. In addition, a 30.61-Gbit/s/λ PS-256QAM-OFDM can achieve 20km single-mode fiber (SMF) transmission at BER below 10−6.

Multichannel maximum-entropy method for the Wigner-Ville distribution

The Wigner-Ville distribution is a powerful technique for the time-frequency spectral analysis of nonstationary seismic data. However, the Wigner-Ville distribution suffers from cross-term interference between different wave components in seismic data. To mitigate cross-term interference, we have developed a multichannel maximum-entropy method (MEM) to modify the Wigner-Ville kernel. The method is related to the conventional maximum-entropy spectral analysis (MESA) algorithm because both algorithms use Burg’s reflection coefficients for the calculation of the prediction-error filter (PEF). The MESA algorithm works on the standard autocorrelation sequence, but it does not work for the Wigner-Ville kernel, which is an instantaneous autocorrelation sequence. Our multichannel MEM algorithm uses the PEF to modify any single Wigner-Ville kernel sequence by exploiting multiple Wigner-Ville kernel sequences simultaneously. This multichannel implementation is capable of robustly determining the reflection coefficient and a minimum-phased PEF for the Wigner-Ville kernel sequence. The Wigner-Ville distribution and the multichannel MEM algorithm in conjunction with each other in turn can produce a high-resolution time-frequency spectrum by mitigating the cross-term interferences and suppressing the spurious energy in the spectrum.

A Hybrid Chaotic Encryption Scheme for Wireless Body Area Networks

Wireless body area network is a low-power and high-security wireless communication protocol specially used in the medical environment. It requires a highly secure encryption algorithm to ensure that information related to a patient’s vital signs cannot be accessed by an attacker. In this article, a security scheme based on chaotic mapping for WBAN is proposed. This algorithm makes use of the hybrid chaotic system obtained by the combination of Logistic and Tent mapping as the sequence generator, which can select the effective precision according to the importance of the transmitted information to ensure the reasonable allocation of computing resources, including floating-point encryption, fixed-point 32-bit encryption, fixed-point 24-bit encryption, and fixed-point 16-bit encryption. In the randomness test of the sequence, it can be seen that the sequence autocorrelation coefficient generated by the combined chaotic system is close to 0 and has a flat power spectrum. At the same time, the sequences produced by the floating-point system and 32-bit fixed-point system have passed the NIST test, which proves that combined chaos overcomes the influence of sequence length and finite precision. Experimental analysis and performance comparison show that the proposed encryption algorithm has sufficient security to resist common attacks.

Shared-Autocorrelation Binary Codes Found by Exhaustive Search

Binary code negation and reversal are known to leave the autocorrelation sequence (ACS) unchanged. However, for some code lengths, there exist “shared-autocorrelation” code pairs for which the mechanism behind shared autocorrelation is not so simple. In this paper, exhaustive search is used to find representatives for all such code pairs for lengths 2 to 39. The resulting code pairs are used to discover code structures associated with the shared autocorrelation property. Some of the code pairs discovered exhibit either Golay skew-symmetry or are found to be Kronecker products of smaller shared-autocorrelation pairs. All four-code sets (or quads) for length $N\leq 36$ having the shared- $\rm ACS$ property were also found.

Computationally Efficient Algorithm for Estimating the Frequency of Signals at the Output of a Channel with White Gaussian Noise and Narrowband Interference

Abstract—A computationally efficient algorithm is proposed for estimating the frequency of a quasi-harmonic signal in the presence of narrowband interference based on iterative calculation of the autocorrelation sequence. A feature of the algorithm is the use of an additional filtering procedure that improves its stability. Simulation results have confirmed the proximity of the estimates obtained to the theoretical boundaries.

Performance Enhancement of Probabilistically Shaped OFDM Enabled by Precoding Technique in an IM-DD System

Probabilistically shaped orthogonal frequency-division multiplexing (PS-OFDM) signal is proposed and experimentally demonstrated in a low-cost intensity-modulation and direct-detection (IM-DD) system for optical access networks. The concatenation of constant composition distribution matcher (CCDM) and low-density parity-check (LDPC) code sequentially implements probabilistic amplitude shaping (PAS) and channel coding. Thanks to the precoding scheme, all data subcarriers can be treated equally by one optimized probabilistic distribution. Experimental results demonstrate that constant amplitude zero autocorrelation sequence (CAZAC) precoding can offer optimal performance compared to orthogonal circulant transform (OCT) precoding and discrete Fourier transform spread (DFT-spread) in terms of increasing generalized mutual information (GMI) and reducing PAPR. Moreover, probabilistically-shaped 64-QAM OFDM signal can provide shaping gains of 1.04/0.94/0.64 dB at 4.0/3.6/3.0 bits/QAM symbol compared to traditional 64-QAM OFDM signal. Meanwhile, compared to traditional 16-QAM OFDM, it can offer shaping gains of 1.64/0.64 dB at 3.6/3.0 bits/QAM symbol. In addition, net data rate ranging from 32.66 to 43.55-Gb/s over 20-km single mode fiber (SMF) can be achieved by only adjusting the probabilistic distribution.

Generalized CAZA sequences

ABSTRACTConstant amplitude zero auto-correlation (CAZA) sequences and periodic sequences have been widely used as preambles for synchronization and channel estimation in the literature. In this paper, we first construct generalized CAZA (GCAZA) sequences in the time domain. Then, their Cramer-Rao bounds containing no matrix inversion for the purpose of joint carrier frequency offset and channel impulse response estimation are derived. The properties of auto-correlation and the discrete Fourier transform of a GCAZA are then presented analytically. The latter also explains the relationship between the conventional frequency-domain CAZA and the proposed time-domain GCAZA. Finally, we conduct numerical simulations and compare the results with existing sequences in the literature for fading channels.

Relation Between Autocorrelation Sequence and Average Shortest-Path Length in a Time Serie to Network Mapping

An invertible mapping between time series and networks was recently proposed. It can be used as a tool to figure out properties of the mapped time series. In the present work we use controlled artificial signals to numerically investigate how correlation properties of time series are mapped in the topological measures of associated networks. More specifically, we employ filtered uniform white noise and analyse how the autocorrelation sequence influences the average shortest-path length.

Modified CAZAC Sequence Based Timing Synchronization Scheme for OFDM System

Several classical timing synchronization schemes for OFDM systems have been proposed based on the correlation between identical parts of OFDM symbol. These schemes show poor performance due to the presence of plateau and significant side lobe. In this paper we design a new OFDM symbol based on a constant amplitude zero auto correlation sequence and proposed a modified timing metric for time synchronization. The performance of the proposed timing synchronization scheme is better than the classical techniques.

An Anti-Interference Synchronization for OFDM Systems Based on Scrambling Sequence

To improve the performance of the synchronization in OFDM systems in the presence of interference, a new synchronization algorithm based on scrambling sequence is proposed in this paper, which redesigns the training sequence with the constant amplitude zero auto-correlation (CAZAC) sequence and an extra scrambling operation. Compared with the traditional scrambling sequence-based algorithm, the simulations carried out both in AWGN and COST 207 4-path rural area (RA) channel show that the proposed synchronization algorithm can still maintain the sharper correlation peak, and achieve accurate symbol timing estimation and carrier frequency offset (CFO) estimation in the interference environment, with a lower out-of-band energy of the spectrum due to a new scrambling sequence. Furthermore, owing to the particularity of the component elements from the scrambling sequence, a low complexity implementation structure is presented here to realize the correlation function of the proposed algorithm with fewer hardware resources.

Poetic speech melody: A crucial link between music and language.

Research on the music-language interface has extensively investigated similarities and differences of poetic and musical meter, but largely disregarded melody. Using a measure of melodic structure in music––autocorrelations of sound sequences consisting of discrete pitch and duration values––, we show that individual poems feature distinct and text-driven pitch and duration contours, just like songs and other pieces of music. We conceptualize these recurrent melodic contours as an additional, hitherto unnoticed dimension of parallelistic patterning. Poetic speech melodies are higher order units beyond the level of individual syntactic phrases, and also beyond the levels of individual sentences and verse lines. Importantly, auto-correlation scores for pitch and duration recurrences across stanzas are predictive of how melodious naive listeners perceive the respective poems to be, and how likely these poems were to be set to music by professional composers. Experimentally removing classical parallelistic features characteristic of prototypical poems (rhyme, meter, and others) led to decreased autocorrelation scores of pitches, independent of spoken renditions, along with reduced ratings for perceived melodiousness. This suggests that the higher order parallelistic feature of poetic melody strongly interacts with the other parallelistic patterns of poems. Our discovery of a genuine poetic speech melody has great potential for deepening the understanding of the music-language interface.

Characterizing the coordination of speech production and breathing

A robust, positive correlation between inhalation depth and subsequent utterance length in read speech has been interpreted as an anticipatory effect. Since anticipatory posturing of the respiratory system during phrase preparation has important theoretical implications, the present study was designed to rigorously test the effect. Healthy college-aged participants learned by rote a passage with equal numbers of short and long sentences, which were randomized to create a zero (lag-1) autocorrelation sequence that controlled for priming effects. Rote learning was used to control for visual cues to utterance length. Multiple repetitions of the passage produced by six speakers were acoustically segmented into pause-speech intervals for preliminary analyses, with pause intervals coded for breath intake or no intake. Analyses on data that retained the experimental structure indicated a strong effect of preceding utterance length on the presence/absence of breath intake, but no effect of subsequent utterance length. Analyses of breath pause durations indicated only significant negative correlations with utterance length, and no relation between intake duration and utterance length. Together, the results suggest only an effect of physiological recovery on speech breathing under conditions that better approximate spontaneous production than in previous studies. [Work supported in part by NIH award number R01HD087452.]

A MB-CAZAC precoding combined with 128/64/32/16-QAM modulation for OFDM-VLC system

In this paper, multi-band constant amplitude zero autocorrelation sequence (MB-CAZAC) precoding combined with the 128/64/32/16-quadrature amplitude modulation (QAM) technology is proposed and experimentally demonstrated in the orthogonal frequency-division multiplexing-based visible light communication (OFDM-VLC) system. By using the MB-CAZAC precoding, it can equalize the uneven signal-to-noise ratio (SNR) and reduce the PAPR compared with the traditional OFDM system. The experimental results show that the 128/64/32/16-QAM MB-CAZAC precoding outperforms the traditional scheme at different data rates for OFDM-VLC system. The spectral efficiency (SE) of the proposed scheme is up to 5.28 b/s/Hz. Meanwhile, it can be successfully transmitted 50-cm free-space at the bit error rate (BER) of 3.82×10−4.

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data

BackgroundFunctional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. New methodA widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. ResultWe have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Comparison with existing methodsOur method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. ConclusionsIn this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis.

Timing and Integer Frequency Offset Estimation for DLMT System over Time-Varying Rayleigh Fading Channel

In this paper, we study the timing and integer carrier frequency offset (ICFO) estimation problem for dynamic lattice multicarrier transmission (DLMT) system over time-varying Rayleigh fading channel. Firstly, a novel preamble structure based on two constant amplitude zero auto-correlation (CAZAC) sequences is designed for DLMT system. Then, by using the designed dual-CAZAC preamble, a discrete cross ambiguity function (DCAF) based timing and ICFO estimation algorithm is proposed. Simulation results show that the proposed DCAF based timing and ICFO estimation algorithm can mitigate the impact of time-varying multipath Rayleigh fading channel and outperforms traditional estimators on the correct estimation probability performance.

A Novel CAZAC Sequence Based Timing Synchronization Scheme for OFDM System

Several classical timing synchronization schemes have been proposed for the timing synchronization in OFDM systems based on the correlation between identical parts of OFDM symbol. These schemes show poor performance due to the presence of plateau and significant side lobe. In this paper we present a timing synchronization schemes with timing metric based on a Constant Amplitude Zero Auto Correlation (CAZAC) sequence. The performance of the proposed timing synchronization scheme is better than the classical techniques

An integrative time-varying frequency detection and channel sounding method for dynamic plasma sheath

The plasma sheath-surrounded hypersonic vehicle is a dynamic and time-varying medium and it is almost impossible to calculate time-varying physical parameters directly. The in-fight detection of the time-varying degree is important to understand the dynamic nature of the physical parameters and their effect on re-entry communication. In this paper, a constant envelope zero autocorrelation (CAZAC) sequence based on time-varying frequency detection and channel sounding method is proposed to detect the plasma sheath electronic density time-varying property and wireless channel characteristic. The proposed method utilizes the CAZAC sequence, which has excellent autocorrelation and spread gain characteristics, to realize dynamic time-varying detection/channel sounding under low signal-to-noise ratio in the plasma sheath environment. Theoretical simulation under a typical time-varying radio channel shows that the proposed method is capable of detecting time-variation frequency up to 200 kHz and can trace the channel amplitude and phase in the time domain well under –10 dB. Experimental results conducted in the RF modulation discharge plasma device verified the time variation detection ability in practical dynamic plasma sheath. Meanwhile, nonlinear phenomenon of dynamic plasma sheath on communication signal is observed thorough channel sounding result.