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Pursley and Sarwate established a lower bound on a combined measure of autocorrelation and crosscorrelation for a pair $(f,g)$ of binary sequences (i.e., sequences with terms in {−1, 1}). If $f$ is a nonzero sequence, then its autocorrelation demerit factor, $\text {ADF}(f)$ , is the sum of the squared magnitudes of the aperiodic autocorrelation values over all nonzero shifts for the sequence obtained by normalizing $f$ to have unit Euclidean norm. If $(f,g)$ is a pair of nonzero sequences, then their crosscorrelation demerit factor, $\text {CDF}(f,g)$ , is the sum of the squared magnitudes of the aperiodic crosscorrelation values over all shifts for the sequences obtained by normalizing both $f$ and $g$ to have unit Euclidean norm. Pursley and Sarwate showed that for binary sequences, the sum of $\text {CDF}(f,g)$ and the geometric mean of $\text {ADF}(f)$ and $\text {ADF}{(g)}$ must be at least 1. For randomly selected pairs of long binary sequences, this quantity is typically around 2. In this paper, we show that Pursley and Sarwate’s bound is met for binary sequences precisely when $(f,g)$ is a Golay complementary pair. We also prove a generalization of this result for sequences whose terms are arbitrary complex numbers. We investigate constructions that produce infinite families of Golay complementary pairs, and compute the asymptotic values of autocorrelation and crosscorrelation demerit factors for such families. [ABSTRACT FROM AUTHOR]

A near-field source localization method is proposed for 2-D direction-of-arrival (DOA) and range estimation based on a symmetrical cross array. It first employs the conjugate symmetry property of signal autocorrelation for different time delays to construct a conjugate augmented spatial–temporal cross-correlation matrix, then the extended steering vector is decoupled to avoid the usual multidimensional search based on the properties of the Khatri–Rao product, and finally three 1-D MUSIC-type searches are employed to obtain the results. The proposed method can realize automatic pairing of multiple parameters associated with each source and it also works in the underdetermined case. Furthermore, the stochastic Cramer–Rao lower bound with different time delays is derived. Compared with two existing methods, simulation results demonstrate that the proposed method provides satisfactory estimation performance for both the DOA and range parameters at low signal-to-noise ratio and with a small number of snapshots. [ABSTRACT FROM AUTHOR]

In this paper, we provide the left and right Parseval relations over the quaternions. Moreover, we construct a new infinite family of sequences almost over $Q_{8} $ with period $p$ by a generalization of Legendre mapping, where $p\equiv 1 \pmod {8}$ is prime and the sequences have ideal autocorrelation. The sequences are symmetric when $p\equiv 1 \pmod {16}$ , and antisymmetric when $p\equiv 9 \pmod {16} $. [ABSTRACT FROM AUTHOR]

Using elementary properties of primitive multiplicative characters we derive the autocorrelation of a unimodular $M$ -ary character-based sequence of length $pq$ , where $p$ and $q$ are distinct odd primes. Subsequently: (1) we identify three new sets of twin-prime quadriphase sequences with the largest autocorrelation sidelobe magnitude equal to $\sqrt {5}$ or 3, (2) we show that the smallest maximum autocorrelation sidelobe magnitude of an $M$ -ary character-based sequence, when $4|M$ , either decreases with $M$ and tends to 2, when $6\nmid M$ , or is equal to 2, when $6|M$ , and (3), we show that the smallest maximum autocorrelation sidelobe magnitude of a full-alphabet $M$ -ary character-based sequence, where $M>2$ , is greater or equal to $\sqrt {3}$ , and, in particular, is equal to $\sqrt {3}$ for the sextic phase sequence. [ABSTRACT FROM AUTHOR]

Sequences with low aperiodic autocorrelation and crosscorrelation are used in communications and remote sensing. Golay and Shapiro independently devised a recursive construction that produces families of complementary pairs of binary sequences. In the simplest case, the construction produces the Rudin–Shapiro sequences, and in general it produces what we call Golay–Rudin–Shapiro sequences. Calculations by Littlewood show that the Rudin–Shapiro sequences have low mean square autocorrelation. A sequence’s peak sidelobe level is its largest magnitude of autocorrelation over all nonzero shifts. Høholdt, Jensen, and Justesen showed that there is some undetermined positive constant $A$ such that the peak sidelobe level of a Rudin–Shapiro sequence of length $2^{n}$ is bounded above by $A(1.842626\ldots)^{n}$ , where $1.842626\ldots $ is the positive real root of $X^{4}-3 X-6$. We show that the peak sidelobe level is bounded above by $5(1.658967\ldots)^{n-4}$ , where $1.658967\ldots $ is the real root of $X^{3}+X^{2}-2 X-4$. Any exponential bound with lower base will fail to be true for almost all $n$ , and any bound with the same base but a lower constant prefactor will fail to be true for at least one $n$. We provide a similar bound on the peak crosscorrelation (largest magnitude of crosscorrelation over all shifts) between the sequences in each Rudin–Shapiro pair. The methods that we use generalize to all families of complementary pairs produced by the Golay–Rudin–Shapiro recursion, for which we obtain bounds on the peak sidelobe level and peak crosscorrelation with the same exponential growth rate as we obtain for the original Rudin–Shapiro sequences. [ABSTRACT FROM AUTHOR]

Noise modeling in power line communications has recently drawn the attention of researchers. However, when characterizing the noise process in narrowband communications, previous works have only focused on small-scale phenomena involving fine-grained details. Nevertheless, the communication link's reliability is also affected by long-term noise phenomena that might affect transfer rates at higher layers as well. This paper addresses the problem of long-term noise characterization for narrowband power line communications and provides a statistical analysis of the long-term trends affecting the noise levels. We present a statistical description of the noise process in the time and frequency domains based on real field measurements in the FCC band (10 kHz–490 kHz). The collected data comprises more than 1.8 billion samples taken from three different locations over a time period of approximately ten days. The noise samples have been statistically analyzed by considering stationarity, autocorrelation, and independence. Although our results—being unprecedented—are interesting per se, they improve the noise pattern knowledge, thus paving the way for the design and implementation of more robust PLC protocols. [ABSTRACT FROM AUTHOR]

Under actual working conditions, the initial faults of rolling bearings are difficult to be predicted effectively because of the lack of prior fault knowledge, weak fault information, and strong noise interference. How to enhance the fault characteristics while removing the vibration signal noise of rolling bearings has become the key challenge to the field of early fault diagnosis of rolling bearings. Based on the above problems, a rolling bearing initial fault diagnosis model based on second-order cyclic autocorrelation (Soca) and deep auto-encoder (AE) combined with transfer learning (TL) was proposed to improve the overall performance of rolling bearing fault identification. First, the Soca is used to estimate the second-order cyclic statistics of the vibration signal, which can better highlight the periodic pulse characteristics of rolling bearings and suppress random noise to a certain extent. After that, the dataset containing the valuable health state information of the rolling bearing is input into the denoising and contraction auto-encoder (DCAE). The advantages of denoising AEs (DAEs) and contraction AEs are fully utilized to extract the initial fault characteristics of rolling bearings. Finally, the balanced distribution adaptation (BDA) is used to reduce the distribution difference and class spacing of the transferable features extracted from the original datasets and the target datasets, and the initial fault diagnosis of the target rolling bearing is diagnosed according to the feature knowledge of the source rolling bearing. In three experimental datasets, six TL experiments were carried out to verify that the Soca-Denoising auto-encoder, Contraction auto-encoder and Transfer learning (DCT) model can effectively enhance the initial fault characteristics of rolling bearings, and has higher diagnostic accuracy and robustness compared with the existing initial fault diagnosis methods of rolling bearings. This method has a good application prospect in the field of early fault diagnosis of rolling bearings. [ABSTRACT FROM AUTHOR]

We consider the sparse phase retrieval problem of recovering a sparse signal $\mathbf {x}$ in $\mathbb {R}^d$ from intensity-only measurements in dimension $d \geq 2$. Sparse phase retrieval can often be equivalently formulated as the problem of recovering a signal from its autocorrelation, which is in turn directly related to the combinatorial problem of recovering a set from its pairwise differences. In one spatial dimension, this problem is well studied and known as the turnpike problem. In this work, we present MISTR (Multidimensional Intersection Sparse supporT Recovery), an algorithm which exploits this formulation to recover the support of a multidimensional signal from magnitude-only measurements. MISTR takes advantage of the structure of multiple dimensions to provably achieve the same accuracy as the best one-dimensional algorithms in dramatically less time. We prove theoretically that MISTR correctly recovers the support of signals distributed as a Gaussian point process with high probability as long as sparsity is at most $\mathcal {O}(n^{d\theta })$ for any $\theta < 1/2$ , where $n^d$ represents pixel size in a fixed image window. In the case that magnitude measurements are corrupted by noise, we provide a thresholding scheme with theoretical guarantees for sparsity at most $\mathcal {O}(n^{d\theta })$ for $\theta < 1/4$ that obviates the need for MISTR to explicitly handle noisy autocorrelation data. Detailed and reproducible numerical experiments demonstrate the effectiveness of our algorithm, showing that in practice MISTR enjoys time complexity which is nearly linear in the size of the input. [ABSTRACT FROM AUTHOR]

This letter studies the impact of auto-correlation of stochastic processes on the dynamic response of power systems. The frequency spectrum of the trajectories of the state variables of the system is utilized as a metric to evaluate this impact. Simulation results indicate that the auto-correlation have a direct impact on the amplitude of the dominant electro-mechanical modes of the system. Results also show that, for a wide range of the values of the auto-correlation, the impact of stochastic processes on system dynamics is local, affects differently each area of the system and, in some cases, can lead to instability and voltage collapse. [ABSTRACT FROM AUTHOR]

Monitoring of winding faults is of great significance for the assessment of the transformer maintenance status. In this study, the time series analysis is combined with frequency response analysis (FRA) for better interpretation and analysis of FRA results. Here, healthy baseline residual data are modeled using the time series analysis for faults detection of the transformer winding. Different statistical software, such as R 4.0.2 and ITSM2000, are used to analyze measured data. To detect the transformer’s winding faults, various analyses, such as the autocorrelation and partial autocorrelation functions plot, the Box–Pierce test, the Ljung–Box test, the McLeod–Li test, the turning points test, the Wallis and Moore phase–frequency test, and the Jarque–Bera test, and the order of minimum corrected Akaike’s information criteria are used. The simulation results show that the suggested method is able to classify and discriminate mechanical and electrical faults of the transformer’s winding with good accuracy. [ABSTRACT FROM AUTHOR]

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums at each of the non-zero time-shifts within a certain region, called the zero correlation zone (ZCZ). ZCPs are categorised into two types: Type-I ZCPs and Type-II ZCPs. Type-I ZCPs have the ZCZ around the in-phase position and Type-II ZCPs have the ZCZ around the end-shift position. Till now only a few constructions of Type-II ZCPs are reported in the literature, and all have lengths of the form 2m ± 1 or N + 1 where N = 2a 10b 26c and a, b, c are non-negative integers. In this paper, we propose a recursive construction of ZCPs based on concatenation of sequences. Inspired by Turyn’s construction of Golay complementary pairs, we also propose a construction of Type-II ZCPs from known ones. The proposed constructions can generate optimal Type-II ZCPs with new flexible parameters and Z-optimal Type-II ZCPs with any odd length. In addition, we give upper bounds for the PMEPR of the proposed ZCPs. It turns out that our constructions lead to ZCPs with low PMEPR. [ABSTRACT FROM AUTHOR]

We develop sparse array receive beamformer design methods achieving maximum signal-to-interference plus noise ratio for wideband sources and jammers. Both tapped delay line filtering and the DFT realizations to wideband array processing are considered. The array sparsity stems from the limited number of available radio frequency (RF) transmission chains that switch between the sensors, thereby configuring different arrays at different times. The sparse array configuration design problem is formulated as a quadratically constraint quadratic program and solved by using semidefinite relaxation. A computationally viable approach through successive convex relaxation is also pursued. In order to realize an implementable design, in presence of missing autocorrelation lags, we propose parameter-free block Toeplitz matrix completion to estimate the received data correlation matrix across the entire array aperture. It is shown that the optimum wideband sparse array effectively utilizes the array aperture and provides considerable performance improvement over suboptimal array topologies. [ABSTRACT FROM AUTHOR]

Remote sensing opens opportunities to assess spatial patterns on ecological data for a wide range of ecosystems. This information can be used to more effectively design sampling strategies for fieldwork, either to capture the maximum spatial dependence related to the ecological data or to completely avoid it. The sampling design and the autocorrelation observed in the field will determine whether there is a need to use a spatial model to predict ecological data accurately. In this article, we show the effects of different sampling designs on predictions of a plant trait, as an example of an ecological variable, using a set of simulated hyperspectral data with an increasing range of spatial autocorrelation. Our findings show that when the sample is designed to estimate population parameters such as mean and variance, a random design is appropriate even where there is strong spatial autocorrelation. However, in remote sensing applications, the aim is usually to predict characteristics of unsampled locations using spectral information. In this case, regular sampling is a more appropriated design. Sampling based on close pairs of points and clustered over a regular design may improve the accuracy of the training model, but this design generalizes poorly. The use of spatially explicit models improves the prediction accuracy significantly in landscapes with strong spatial dependence. However, such models have low generalization capacities to extrapolate to other landscapes with different spatial patterns. When the combination of design and size results in sample distances similar to the range of the spatial dependence in the field, it increases predictions uncertainty. [ABSTRACT FROM AUTHOR]

Stochastic electromagnetic fields caused by the data transferring signals along the printed circuit boards are potentially harmful interference sources for modern digital electronic devices. The characterization of the near-field electromagnetic emissions from the electronic device in time domain was implemented by real-time digital oscilloscope in conjunction with the sequential scanning system of the near-field probes. Excluding of the periodic sample mean function reveals the hidden cyclostationarity of the data transferring process measured by the near-field scanning system. In this article, the quantitative autocorrelation analysis of the hidden cyclostationary properties of the random nonperiodic data sequences is presented. The time-domain evolution of the autocovariance cross sections estimated at each scanning point were exploited for spatial-time localization of the transmission line. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated time-frequency rate distribution (TFRD) technique, i.e., coherently integrated trilinear autocorrelation function (CITAF), for the detection and parameter estimation of quadratic frequency modulated (QFM) signal embedded in white Gaussian noise. The basic idea is to design a trilinear autocorrelation function (TAF) enabling a coherent integration of the signal energy in both of the time and lag-time domains. Theoretical analysis and numerical simulations show that this new method has a lower signal to noise ratio (SNR) threshold and higher estimation accuracy in comparison with several state-of-the-art algorithms. Furthermore, the coherently integrated nonuniform TAF (CINTAF) is briefly introduced. [ABSTRACT FROM AUTHOR]

With the advancement of GPS and remote sensing technologies, large amounts of geospatial data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data samples with explanatory features and targeted responses (categorical or continuous) at a set of locations, the spatial prediction problem aims to learn a model that can predict the response variable based on explanatory features. The problem is important with broad applications in earth science, urban informatics, geosocial media analytics, and public health, but is challenging due to the unique characteristics of spatial data, including spatial autocorrelation, heterogeneity, limited ground truth, and multiple scales and resolutions. This paper provides a systematic review on principles and methods in spatial prediction. We provide a taxonomy of methods categorized by the key challenge they address. For each method, we introduce its underlying assumption, theoretical foundation, and discuss its advantages and disadvantages. We also discuss spatiotemporal extensions of methods. Our goal is to help interdisciplinary domain scientists choose techniques to solve their problems, and more importantly, to help data mining researchers to understand the main principles and methods in spatial prediction and identify future research opportunities. [ABSTRACT FROM AUTHOR]

Coded orthogonal frequency-division multiplexing (COFDM) is a popular modulation technique for wireless communication that guarantees reliable transmission of data over noisy wireless channels. However, a major disadvantage in implementing it is its resulting high peak to average power ratio (PAPR). Including forward error correction (FEC) in the orthogonal frequency division multiplexing (OFDM) system enables the avoidance of transmission errors. Nevertheless, the selected code may impact the value of PAPR. The objective of this paper is to analyze the impact of FEC on the PAPR for the COFDM system based on the autocorrelation of the signal, before the inverse fast Fourier transform (IFFT) block in the COFDM system, the evaluation of the complementary cumulative distribution function (CCDF) of PAPR, and the bit error rate (BER). The autocorrelation of the COFDM system is calculated based on a Markov chain model. From the results, we can reach a conclusion on the characteristics we need to consider in order to choose the codes relating to the PAPR performance in the COFDM system. [ABSTRACT FROM AUTHOR]

In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH sequence, so the study of the partial Hamming correlation of FH sequence is particularly important. If an FH sequence or an FH sequence set has an optimal partial Hamming correlation with respect to the partial Hamming correlation bound for all length of correlation window, then the FH sequence or the FH sequence set is said to be strictly optimal. In this paper, we first prove that there is no strictly optimal FH sequence set of family size $M$ and sequence length $N$ over a frequency slot set of size $q$ with respect to the partial Hamming correlation bound derived by Niu et al. when $N>{q^{2}}/{M}$ and $q\geq 2$ , and that by Cai et al. when $N>{q^{2}}/{M}$ and $q\geq {2N}/({N-2})$. Furthermore, we define a special partition-type difference packing (DP) called $[N,\nabla,H_{a}^{l}]$ PDP and give several classes of $[N,\nabla,H_{a}^{l}]$ PDPs. Then, we present a new construction of strictly optimal FH sequences. By choosing different PDPs, the FH sequences constructed can give new and flexible parameters. By utilizing this construction method recursively, we can obtain new $[N,\nabla,H_{a}^{l}]$ PDPs, which lead to infinitely many classes of strictly optimal FH sequences with new parameters. Moreover, based upon an $[N,\nabla,H_{a}^{l}]$ PDP, we present a construction of strictly optimal FH sequence sets. By preceding construction method and recursive construction, we can also obtain infinite classes of strictly optimal FH sequence sets which can give new and flexible parameters. [ABSTRACT FROM AUTHOR]

This paper presents a novel autocorrelation-based algorithm that uses statistical knowledge to detect orthogonal frequency division multiplexing signals in channels where frequency offset is present. The algorithm may be viewed as a significant improvement over other types of autocorrelation algorithms that appear in literature that lead to false alarm due to the hardware impairment of frequency offset. The algorithm works by making an unbiased estimate of the square of an autocorrelation coefficient and from that deduces an appropriate probability density function for the phase angle of the complex test statistic and thereby palliating the effect of phase distortion introduced by the frequency offset. It is shown that the algorithm presented in this paper can be implemented on a testbed, as well as overcome simulations that have been specifically designed to have worst case frequency offset phase distortion conditions. [ABSTRACT FROM AUTHOR]

Continuous phase modulation (CPM) plays an important role in wireless communications due to its constant envelope signal property and tight spectrum confinement capability. Although CPM has been studied for many years, CPM training waveforms having autocorrelations with zero sidelobes have not been reported before, to the best of our knowledge. Existing works on the CPM system design mostly assume that the channel fading coefficients are eitherperfectlyknown at the receiver or estimated using random CPM training waveforms. In this correspondence paper, we propose a novel class of CPM training waveforms displaying autocorrelation sidelobes close to zero. The key idea of our construction is to apply differential encoding to Golay complementary pair having perfect aperiodic autocorrelation sum properties. [ABSTRACT FROM AUTHOR]

Zero correlation zone (ZCZ) sequence sets and Golay complementary sets (GCSs) have different correlation properties and hence have different engineering applications. A number of constructions of ZCZ sequence sets and GCSs have been proposed, respectively, in the literature. In addition, some ZCZ sequence sets can be constructed from mutually orthogonal GCSs. In this paper, the relationship between GCSs and ZCZ sets is discovered further. We propose a new type of sequence sets which are ZCZ sequence sets and also GCSs. They are called the Golay-ZCZ sequence sets in this paper. Therefore, they have low peak-to-average power ratios when employed in OFDM systems due to the good autocorrelation properties of GCSs. Besides, the Golay-ZCZ sets possess zero autocorrelations and cross-correlations within their ZCZ and hence have the potential application to synchronization. Furthermore, a construction of Golay-ZCZ sequence family with flexible set sizes, various sequence lengths, and large ZCZ widths is proposed in this paper. [ABSTRACT FROM AUTHOR]

We examine Fourier transforms of real-valued stationary time series from the point of view of the statistical propriety. Processes with a large dynamic range spectrum have transforms that are very significantly improper for some frequencies; the real and imaginary parts can be highly correlated, and the periodogram will not have the standard chi-square distribution at these frequencies, nor have two degrees of freedom. Use of a taper reduces impropriety to just frequencies close to zero and Nyquist only, and frequency ranges where the propriety breaks down can be quite accurately and easily predicted by half the autocorrelation width of $|H*H(2f)|,$ denoted by $c,$ where $H(f)$ is the Fourier transform of the taper and $*$ denotes convolution. For vector time series we derive an improved distributional approximation for minus twice the log of the generalized likelihood ratio test statistic for testing for propriety of the Fourier transform at any frequency, and compare frequency range cutoffs for propriety determined by the hypothesis test with those determined by $c.$ [ABSTRACT FROM AUTHOR]

Eigen-based algorithms are very effective and stable in signal combining. However, the major problem is the heavy computational cost. In this paper, a fast signal combining algorithm is proposed by using signum polarization and Collatz–Wielandt iteration methods. Simulation results indicate that this algorithm can significantly reduce the computational complexity and has good combining performance. [ABSTRACT FROM AUTHOR]

Collective inference has attracted considerable attention in the last decade, where the response variables within a group of instances are correlated and should be inferred collectively, instead of independently. Previous works on collective inference mainly focus on exploiting the autocorrelation among instances in a static network during the inference process. There are also approaches on time series prediction, which mainly exploit the autocorrelation within an instance at different time points during the inference process. However, in many real-world applications, the response variables of related instances can co-evolve over time and their evolutions are not following a static correlation across time, but are following an internal life cycle. In this paper, we study the problem of collective evolution inference, where the goal is to predict the values of the response variables for a group of related instances at the end of their life cycles. This problem is extremely important for various applications, e.g., predicting fund-raising results in crowd-funding and predicting gene-expression levels in bioinformatics. This problem is also highly challenging because different instances in the network can co-evolve over time and they can be at different stages of their life cycles and thus have different evolving patterns. Moreover, the instances in collective evolution inference problems are usually connected through heterogeneous information networks (HINs for short), which involve complex relationships among the instances interconnected by multiple types of links. We propose an approach, called NetCycle+, by incorporating information from both the correlation among related instances and their life cycles. Furthermore, in order to study the deep dependencies between nodes in the network, we extend the graph convolution model into our algorithm. We compared our approach with existing methods of collective inference and time series analysis on two real-world networks. The results demonstrate that our proposed approach can improve the inference performance by considering the autocorrelation through networks and the life cycles of the instances. [ABSTRACT FROM AUTHOR]

Hu introduced a simple method to compute the 2-adic complexity of any periodic binary sequence with ideal two-level autocorrelation. We extend this approach to some other sequences. First, we provide a substantially shorter proof of the maximality of the 2-adic complexity of the Legendre sequence of period $N\equiv 1\bmod 4$ first proved by Xiong et al. Then, we show that the 2-adic complexity of the two-prime generator of period $pq$ with two odd primes $p\ne q$ attains the maximum if $(q+1)/4\le p\le 4q-1$. This result was only known for twin primes $q=p+2$ before. For arbitrary odd primes $p\ne q$ , we can still prove that the 2-adic complexity of the two-prime generator is close to its period. [ABSTRACT FROM AUTHOR]

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation. [ABSTRACT FROM AUTHOR]

Optical fiber signals with high power exhibit spectral broadening that seems to limit capacity. To study spectral broadening, the autocorrelation function of the output signal given the input signal is derived for a simplified fiber model that has zero dispersion, distributed optical amplification (OA), and idealized spatial noise processes. The autocorrelation function is used to upper bound the output power of bandlimited or time-resolution limited receivers, and thereby to bound spectral broadening and the capacity of receivers with thermal noise. The output power scales at most as the square-root of the launch power, and thus capacity scales at most as one-half the logarithm of the launch power. The propagating signal bandwidth scales at least as the square-root of the launch power. However, in practice the OA bandwidth should exceed the signal bandwidth to compensate attenuation. Hence, there is a launch power threshold beyond which the fiber model loses practical relevance. Nevertheless, for the mathematical model an upper bound on capacity is developed when the OA bandwidth scales as the square-root of the launch power, in which case capacity scales at most as the inverse fourth root of the launch power. [ABSTRACT FROM AUTHOR]

Several new constructions of 3-D optical orthogonal codes are presented here. In each case, the codes have ideal OFF-peak autocorrelation \mathbf \lambda a = 0 , and in all, but one case a cross correlation of \mathbf \lambda c = 1 . All codes produced are optimal with respect to the applicable Johnson bound either presented or developed here. Thus, on one hand the codes are as large as possible, and on the other, the bound(s) are shown to be tight. All codes are constructed by using a particular automorphism (a singer cycle) of PG(k, q), the finite projective geometry of dimension $k $ over the field of order q, or by using an affine analogue in $AG(k, q) $ . [ABSTRACT FROM AUTHOR]

Diffuse scattering (DS), mostly caused by macroscopically rough surfaces, can be modeled by an effective roughness (ER) approach. In the ER approach, the object surface is divided into tiles, and the DS field amplitude associated with each tile is given. Assuming that the transmit antenna (or emitted field) is fixed and the phases associated with different tiles are independent, this paper proposes a phase evolution model based on the relative spatial locations of the receive antenna (Rx) to each tile. The proposed model contains two parts: the deterministic part that depends on the variation of the distance from Rx to tile center, and the correlated random part that depends on the variation of the angle between the Rx and the normal vector of tile. The correlation of the tile field phases resulting from the angular variation is modeled by the exponentially damped cosine correlation function. The proposed phase evolution model is evaluated by being applied to the ER approach to predict the DS component of radio channel transfer function (CTF). The predicted DS-CTF is compared with the reference (simulated data by physical optics and measured data in well-controlled environment) in terms of the spatial autocorrelation as well as the spatial Doppler spectrum. [ABSTRACT FROM PUBLISHER]

A novel microwave radiometric technique, wideband autocorrelation radiometry (WiBAR), is introduced. The radiometer offers a direct method to remotely measure the microwave propagation time difference of multipath microwave emission from low-loss layered surfaces, such as a dry snowpack and a freshwater lake icepack. The microwave propagation time difference through the pack yields a measure of its vertical extent; thus, this technique provides a direct measurement of depth. It is also a low-power sensing method, since there is no transmitter. We present a simple geophysical forward model for the multipath interference phenomenon and derive the system requirements needed to design a WiBAR instrument. An X-band instrument fabricated from commercial-off-the-shelf (COTS) components measured the thickness of the freshwater lake ice at the University of Michigan Biological Station. Ice thickness retrieval is demonstrated from nadir to 59°. The WiBAR was able to directly measure the lake icepack thickness of about 36 cm with an accuracy of 2 cm over this range of incidence angles. [ABSTRACT FROM AUTHOR]

The complexity properties of the chaotic signals generated by a chaotic semiconductor laser (SL) with double time delays are quantified numerically. A modified complexity quantifier, mean permutation entropy (MPE), based on information theory, is applied to fully characterize the chaotic complexity. The autocorrelation time (ACT) is also employed as a supplement quantifier. The numerical analyses of the MPE and the ACT have been performed extensively, and the effects of feedback rate, bias current, feedback delays, and linewidth enhancement factor are examined. The parameter regions leading to high chaotic complexity are identified successfully by the MPE. Besides, we also successfully quantify the chaotic complexity of the SL with three time delays. Hence, such information-theory-based MPE is an effective and universal complexity quantifier for a chaotic SL with multiple time delays, which is interesting and valuable for chaos communication systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the maximum absolute value \Delta f in the autocorrelation spectrum (not considering the zero point) of a function f . In an even number of variables n , bent functions possess the highest nonlinearity with \Delta f = 0 . The long standing open question (for two decades) in this area is to obtain a theoretical construction of balanced functions with \Delta f < 2^{n/2} . So far, there are only a few examples of such functions for n = 10, 14 , but no general construction technique is known. In this paper, we mathematically construct an infinite class of balanced Boolean functions on n variables having absolute indicator strictly lesser than \delta n = 2^{n/2}-2^{(({n+6})/{4})} , nonlinearity strictly greater than \rho n = 2^{n-1} - 2^{n/2} + 2^{n/2-3} - 5\cdot 2^{(({n-2})/{4})} and algebraic degree n-1 , where n\equiv 2 \pmod 4 and n\geq 46 . While the bound n \geq 46 is required for proving the generic result, our construction starts from n = 18 and nonlinearity > 2^n-1 - 2^n/2 for n = 18, 22 , and 26. [ABSTRACT FROM PUBLISHER]

Bit retrieval is the problem of reconstructing a periodic binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval. [ABSTRACT FROM PUBLISHER]

Defining a sound shift operator for graph signals, similar to the shift operator in classical signal processing, is a crucial problem in graph signal processing (GSP), since almost all operations, such as filtering, transformation, prediction, are directly related to the graph shift operator. We define a set of energy-preserving shift operators that satisfy many properties similar to their counterparts in classical signal processing, but are different from the shift operators defined in the literature, such as the graph adjacency matrix and Laplacian matrix based shift operators, which modify the energy of a graph signal. We decouple the graph structure represented by eigengraphs and the eigenvalues of the adjacency matrix or the Laplacian matrix. We show that the adjacency matrix of a graph is indeed a linear shift invariant (LSI) graph filter with respect to the defined shift operator. We further define autocorrelation and cross-correlation functions of signals on the graph, enabling us to obtain the solution to the optimal filtering on graphs, i.e., the corresponding Wiener filtering on graphs and the efficient spectra analysis and frequency domain filtering in parallel with those in classical signal processing. This new shift operator based GSP framework enables the signal analysis along a correlation structure defined by a graph shift manifold as opposed to classical signal processing operating on the assumption of the correlation structure with a linear time shift manifold. Several illustrative simulations are presented to validate the performance of the designed optimal LSI filters. [ABSTRACT FROM PUBLISHER]

This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level. The problem is formulated as a biobjective Pareto optimization forcing either a continuous or a discrete phase constraint at the design stage. An iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and NP-hard in general. Each iteration of the devised method requires the solution of a nonconvex min–max problem. It is handled either through a novel bisection or an FFT-based method respectively for the continuous and the discrete phase constraint. Additionally, a heuristic approach to initialize the procedures employing the $l_p$-norm minimization technique is proposed. Simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase/binary case. [ABSTRACT FROM PUBLISHER]

A new binary frequency-shift keying (BFSK) waveform is suggested for continuous wave radar. It provides ideal periodic autocorrelation (PAC) when processed by a matched filter, and perfect periodic cross-correlation (PCC) when processed by a mismatched filter. Ideal PAC implies a uniform sidelobe level, whose ratio to the PAC peak is equal to the inverse of the code length. Perfect PCC implies zero sidelobes. BFSK is relatively spectrum efficient. Design details and processing issues are discussed. [ABSTRACT FROM PUBLISHER]

Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared with a random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation values (for each sequence in the pair) and significantly lower mean square crosscorrelation values. If we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation, and if we define demerit factor as the reciprocal of merit factor, then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1. Our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1, and at the same time, the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 (which also indicates better than average performance). The sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters, such as maximal linear recursive sequences (m-sequences) and Legendre sequences. In this paper, exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters. Data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length. [ABSTRACT FROM PUBLISHER]

While plane-wave imaging can improve the performance of power Doppler by enabling much longer ensembles than systems using focused beams, the long-ensemble averaging of the zero-lag autocorrelation R(0) estimates does not directly decrease the mean noise level, but only decreases its variance. Spatial variation of the noise due to the time-gain compensation and the received beamforming aperture ultimately limits sensitivity. In this paper, we demonstrate that the performance of power Doppler imaging can be improved by leveraging the higher lags of the autocorrelation [e.g., R(1), R(2),…] instead of the signal power (R(0)). As noise is completely uncorrelated from pulse-to-pulse while the flow signal remains correlated significantly longer, weak signals just above the noise floor can be made visible through the reduction of the noise floor. Finally, as coherence decreases proportionally with respect to velocity, we demonstrate how signal coherence can be targeted to separate flows of different velocities. For instance, we show how long-time-range coherence of microbubble contrast-enhanced flow specifically isolates slow capillary perfusion (as opposed to conduit flow). [ABSTRACT FROM AUTHOR]

Quad-phase codes of a given length can be grouped into equivalence classes based on operations preserving autocorrelation peak sidelobe level, or “PSL -preserving operators.” The task of enumerating these equivalence classes is facilitated by establishing a relationship with the problem of enumerating equivalence classes of 2\times N binary grids with respect to a pair of binary grid symmetries. We show this connection by a one-to-one mapping between even-length quad-phase codes and 2\times N binary grids. When N is even, this mapping allows the known enumeration of 2\times N , or roughly 1 quadrillion codes). One of the devices used to narrow the search space while achieving an exhaustive search is to seed the search with the equivalence class representatives of length N=6. The optimal PSL for length-25 quad-phase codes is determined to be 2, achieved by the codes in a single size-32 equivalence class. For length 26, the optimal PSL is found to be \sqrt5, achieved by 604\,480 codes belonging to 9445 equivalence classes of size 64. [ABSTRACT FROM AUTHOR]

A complementary set of $K$ binary $\pm 1$ codes of length $N$ has the useful property that the sum of the autocorrelation sequences of the codes has only one nonvanishing element, its size-$KN$ peak. The $N\times K$ matrix whose columns are the codes of a binary complementary set, arranged in order, is the code set's complementary code matrix (CCM). One might ask for which $K$ and $N$ such matrices exist. A simple necessary condition for the existence of an $N\times K$ CCM is introduced, involving the sum of the squares of the imbalance values of the codes in the set (the imbalance of a binary $\pm 1$ code being the difference between the number of 1 and number of $-1$s in the code). The one-to-one relationship between binary CCMs and binary complementary code sets allows the necessary condition for the $N\times K$ CCM existence to extend to a necessary condition for sets of $K$ complementary code sets of length $N$. We examine the sum-of-squares condition for the separate cases of $N$ even and $N$ odd. The odd case is especially interesting, since representations in terms of sums of squares of odd integers are equivalent to representations as sums of triangular numbers, a subject of recent research in Number Theory. Furthermore, we exhibit a refinement of the existence condition in terms of the imbalance values of pairs of interlaced subcodes. This refinement is new, to the best of our knowledge. Finally, we investigate whether odd-length complementary code sets exist for $K>2$, unlike the Golay case of $K=2$ where odd-length sets cannot exist. We easily find, by computer search, a four-code set of length 15, suggesting that these are likely not uncommon. [ABSTRACT FROM AUTHOR]

A low-frequency noise (LFN) analysis technique is introduced, based on the autocorrelation of the LFN spectra in terms of frequency, biasing, and temperature. This technique reveals information about the mechanisms behind 1/ f noise that is difficult to obtain otherwise. These correlation analyses provide strong evidence that the LFN of both nMOS and pMOS transistors is mainly composed of the superposition of thermally activated random telegraph signals (RTSs). The methodology enables quantification and validation of old and new LFN models, and, therefore, helps to clarify the relation between RTS and 1/ f that is still frequently debated in the literature. [ABSTRACT FROM PUBLISHER]

The product of the scanned responses of two colinear interleaved arrays estimates the spatial power spectral density of the received signal. This estimate has mathematical structure similar to the classical periodogram and hence is called the generalized periodogram. The generalized periodogram includes sparse arrays such as coprime arrays and two level nested arrays. This paper derives the analytical expected value of the generalized periodogram output for any signal. The generalized periodogram expected value is the convolution of the true spectral density with a windowing function. This result reveals that the expected product spectrum is not guaranteed to be positive definite. The paper also derives the covariance function of the generalized periodogram for a white Gaussian process. Finally, the paper illustrates the implicit equivalence between the product spectrum and estimation of the correlation function from the products of appropriately spaced pairs of sensors. [ABSTRACT FROM PUBLISHER]

This paper introduces a novel method to improve the Time of Arrival (ToA) estimation resolution for a fixed available bandwidth in the presence of unknown multipath frequency selective (MPFS) channels. Here, the maximum rising level detector technique is proposed which utilizes oversampling and multiple correlation paths to evaluate with high resolution the path corresponding to the maximum rising level of matched filters output. However, employing such technique demands for transmission of waveform that creates a very high rising level at autocorrelation center. This paper proposes an efficient technique to design proper waveforms (very high rising level at autocorrelation center) via minimization of weighted integrated sidelobe level, exploiting the trust-region algorithm. The performance of the proposed technique is evaluated via simulations of the ToA mean square error, and compared with the state-of-the-art approaches considering the same bandwidth, and Cramer–Rao lower bound as benchmark. Simulations confirm that the ToA resolution is improved as the number of correlation paths increases and verify the feasibility of the proposed technique compared with the available approaches for the MPFS channels. [ABSTRACT FROM PUBLISHER]

Generalized spatial modulation (GSM) is an extended architecture to the spatial modulation multiple antenna system. The GSM system uses multiple activated transmit antennas to further exploit the system transmission capacity. In this paper, we consider the GSM systems with channel diagonalization (CD-) transmitter pre-coder (TPC), channel inversion TPC, and without TPC. For each TPC scheme, the pairwise activated antenna detection discriminant and closed-form antenna detection pairwise error probability (PEP) of the GSM system are derived. We use the antenna detection PEP to calculate the analytical antenna detection symbol error rate union bound and the mutual information lower bound. We use asymptotic methods to analyze antenna detection diversity and coding gains of GSM system with or without TPC when the signal-to-noise ratio is high. Together with complexity analysis on the pre-coders and antenna detectors, we discover the CD-TPC trades the antenna detection performance for complexity reduction, while the CD-TPC scheme achieves a balance between the performance and complexity. This paper introduces methods to the performance evaluation of the GSM system, and provides a guideline for the GSM system design such as antenna configuration and TPC schemes selection. [ABSTRACT FROM AUTHOR]

Multi-Line Transmission (MLT) was recently demonstrated as a valuable tool to increase the frame rate of ultrasound images. In this approach, the multiple beams that are simultaneously transmitted may determine cross-talk artifacts that are typically reduced, although not eliminated, by the use of Tukey apodization on both transmission and reception apertures, which unfortunately worsens the image lateral resolution. In this paper we investigate the combination, and related performance, of Filtered-Delay Multiply And Sum (F-DMAS) beamforming with MLT for high frame-rate ultrasound imaging. F-DMAS is a non-linear beamformer based on the computation of the receive aperture spatial autocorrelation, which was recently proposed for use in ultrasound B-mode imaging by some of the authors. The main advantages of such beamformer are the improved contrast resolution, obtained by lowering the beam side lobes and narrowing the main lobe, and the increased noise rejection. This study shows that in MLT images, compared to standard Delay And Sum (DAS) beamforming including Tukey apodization, F-DMAS beamforming yields better suppression of cross-talk and improved lateral resolution. The method’s effectiveness is demonstrated by simulations and phantom experiments. Preliminary in vivo cardiac images also show that the frame rate can be improved up to 8-fold by combining F-DMAS and MLT without affecting the image quality. [ABSTRACT FROM AUTHOR]

Controlling peak side-lobe level (PSL) is of great importance in high-resolution applications of multiple input multiple output (MIMO) radars. In this paper, designing sequences with good autocorrelation properties are studied. The PSL of the autocorrelation is regarded as the main merit and is optimized through newly introduced cyclic algorithms, namely, PSL minimization quadratic approach, PSL minimization algorithm where the smallest rectangular, and PSL optimization cyclic algorithm. It is revealed that minimizing PSL results in better sequences in terms of autocorrelation side lobes when compared with traditional integrated side-lobe level minimization. In order to improve the performance of these algorithms, fast-randomized singular value decomposition is utilized. To achieve waveform design for MIMO radars, this algorithm is applied to the waveform generated from a modified Bernoulli chaotic system. The numerical experiments confirm the superiority of the newly developed algorithms compared to high-performance algorithms in monostatic and MIMO radars. [ABSTRACT FROM AUTHOR]

In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) constraint, and similarity constraint, to name a few. The optimization technique we employ is the majorization–minimization (MM) method, which is iterative and enjoys guaranteed convergence to a stationary solution. We carry out the MM method in two stages: in the majorization stage, we propose three majorizing functions: two for the unified metric and one for the ISL metric; in the minimization stage, we give closed-form solutions for algorithmic updates under different constraints. The update step can be implemented with a few Fast Fourier Transformations (FFTs) and/or Inverse FFTs (IFFTs). We also show the connections between the MM and gradient projection method under our algorithmic scheme. Numerical simulations have shown that the proposed MM-based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

MIMO radar receivers need to reliably separate waveforms originating from different transmitters while suppressing interference for effective operation. In order to achieve this goal, mismatched filters may be employed at the receivers. By using mismatched filters, it is possible to reduce the power of the interference while strictly controlling the autocorrelation sidelobe and peak cross-correlation levels of the received waveforms. In this paper, we propose a mismatched filter design method that minimizes interference and jamming power at the filter output while the peak sidelobe and cross-correlation levels for all Doppler frequencies are constrained to desired values. The proposed design method is formulated as an optimization problem employing sum-of-squares representation of non-negative polynomials and solved using semidefinite relaxation. It is demonstrated that good interference suppression performance is achieved even when using an estimated covariance matrix. [ABSTRACT FROM PUBLISHER]

The use of unmanned aerial systems (UASs), which are also known as unmanned aerial vehicles, and by the term “drones” in the popular press, is growing rapidly. To ensure safety, UAS control and nonpayload communication (CNPC) links must operate very reliably in a variety of conditions. This requires an accurate quantitative characterization of the air–ground (AG) channel, and this channel characterization is the focus of this paper. After providing motivation and background, we describe our methods and modeling approach, followed by a description of our simultaneous dual-band (L-band ∼970 MHz, C-band ∼5 GHz) measurement campaign and the over-water (OW) measurement sites. Example results for path loss and root-mean-square delay spread are provided, as well as the results for channel stationarity distance (SD), used in calculating small-scale Rician $K$- factor and correlations between the two receiver antennas that we employed in each frequency band. Two distinct SD measures—the power delay profile (PDP) correlation coefficient and the spatial autocorrelation matrix collinearity—were used and found to be of the same order. Path-loss exponents are near that of free space, but significant two-ray cancelation effects for these OW settings warrant more accurate models, which we provide. Delay spreads in the OW channels are also dominated by the two-ray components and are hence typically very small (∼10 ns) but can exceed 350 ns. A third intermittent multipath component (MPC) is also present a nonnegligible fraction of time; hence, we provide statistical wideband AG channel models to represent this. Future papers in this series will report results for the AG channel with ground sites in other types of environments. [ABSTRACT FROM PUBLISHER]

A novel digital signal processing-based method for phase noise measurement on sinusoidal signals is proposed. The method obtains the power spectral density of the phase noise by Fourier transforming its autocorrelation function. The autocorrelation function of the phase noise is in turn derived from the cyclic complementary autocorrelation function of the analytical version of the sinusoidal signal under test. The method proves that, taking advantage of the cyclostationarity properties of the signal under test, it is possible to improve the sensitivity in phase noise measurements by diminishing the effects of the instrumentation noise, which mainly limits the performance of the majority of the digital processing-based approaches. [ABSTRACT FROM AUTHOR]