Replica Correlation Research Articles

Blind passive signal detection via dictionary learning in unknown multipath time-spreading distortion underwater channels

Blind passive signal detection is a challenging endeavor since typically there is no prior knowledge of the transmitted signal. This becomes further complicated in time-spreading distortion (TSD) underwater channels [R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou, “Theoretical and experimental multi-sensor signal detection in time spreading distortion underwater channels,” Proc. Oceans (2022)], where due to the presence of multiple propagation paths, the unknown signal is convolved with an unknown channel impulse response. In this paper, we introduce and develop a blind passive signal detection method, using dictionary learning [M. Sadeghi, M. Babaie-Zadeh, and C. Jutten, “Dictionary learning for sparse representation: A novel approach,” IEEE Signal Process. Lett. (2013)]. In our blind passive signal detection method, we use the received data to estimate the unknown signal, and also to separate it from the unknown channel impulse response. We have conducted simulations and underwater experiments, to generate receiver operating characteristic curves, to study the performance of the proposed method. The high detection probabilities of the blind method, compared to the replica correlation integration method—that needs to know the transmitted signal for matched filtering—demonstrate the usefulness of the method for passive detection of unknown signals in unknown TSD channels.

Analyticity of replica correlators and modular ETH

We study the two point correlation function of a local operator on an n-sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable w, dual to the Renyi parameter n. Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform f (w) has bounded behavior at infinity in the complex w plane, the discontinuity of the Renyi transform disc f (w) provides the unique analytic continuation in n of the original replica correlation function. We check our formula by explicitly calculating the Renyi transform of a particular replica correlator in a large N holographic CFTd in dimensions d > 2.We also discover that the discontinuity of the Renyi transform is related to the matrix element of local operators between two distinct eigenstates of the modular Hamiltonian. We calculate the Renyi transform in 2d conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH. We argue that in 2d, this is equivalent to the off-diagonal OPE coefficients of a CFT and show that our technique exactly reproduces recent results in the literature.

Extracellular cell-free RNA profile in human large follicles and small follicles.

Background: Previous studies have shown that a large number of valuable and functional cell-free RNAs (cfRNAs) were found in follicular fluid. However, the species and characteristics of follicular fluid cfRNAs have not been reported. Furthermore, their implications are still barely understood in the evaluation of follicular fluid from follicles of different sizes, which warrants further studies. Objective: This study investigated the landscape and characteristics of follicular fluid cfRNAs, the source of organization, and the potential for distinguishing between follicles of different sizes. Methods: Twenty-four follicular fluid samples were collected from 20 patients who received in vitro fertilization (n = 9) or ICSI (n = 11), including 16 large follicular fluid and 8 small follicular fluid samples. Also, the cfRNA profile of follicular fluid samples was analyzed by RNA sequencing. Results: This result indicated that the concentration of follicular fluid cfRNAs ranged from 0.78 to 8.76 ng/ml, and fragment length was 20–200 nucleotides. The concentration and fragment length of large follicular fluid and small follicular fluid samples were not significantly different (p > 0.05). The technical replica correlation of follicular fluid samples ranged from 0.3 to 0.9, and the correlation of small follicular fluid samples was remarkably (p < 0.001) lower than that of large follicular fluid samples. Moreover, this study found that cfRNAs of the follicular fluid could be divided into 37 Ensembl RNA biotypes, and a large number of mRNAs, circRNAs, and lncRNAs were observed in the follicular fluid. The number of cfRNAs in large follicular fluid was remarkably (p < 0.05) higher than that of small follicular fluid. Furthermore, the follicular fluid contained a large amount of intact mRNA and splice junctions and a large number of tissue-derived RNAs, which are at a balanced state of supply and elimination in the follicular fluid. KEGG pathway analysis showed that differentially expressed cfRNAs were enriched in several pathways, including thyroid hormone synthesis, the cGMP-PKG signaling pathway, and inflammatory mediator regulation of TRP channels. In addition, we further showed that four cfRNAs (TK2, AHDC1, PHF21A, and TTYH1) serve as a potential indicator to distinguish the follicles of different sizes. The ROC curve shows great potential to predict follicular fluid from follicles of different sizes [area under the curve (AUC) > 0.88]. Conclusion: Overall, our study revealed that a large number of cfRNAs could be detected in follicular fluid and could serve as a potential non-invasive biomarker in distinguishing between follicles of different sizes. These results may inform the study of the utility and implementation of cfRNAs in clinical practice.

Signal detection in time spreading underwater environments using vector and scalar sensors

In this paper, we aim to examine the effects of the time-spreading signal distortion caused by multipath propagation in underwater environments, using experimental data. We use the Replica Correlation Integration detector [B. Friedlander and A. Zeira, “Detection of broadband signals in frequency and time dispersive channels,” IEEE Trans. Signal Process. 44(7), 1613–1622 (1996)], which is designed to take the multiple echoes of the transmitted signal into consideration. We apply this detector to measured data collected by underwater acoustic sensors. We use two types of sensors. The first sensor is a hydrophone that measures only the scalar component of the acoustic field, i.e., the acoustic pressure. The second sensor is a vector sensor that simultaneously measures the scalar and the three vector components of the acoustic field, i.e., the three acoustic particle velocity x, y, and z components. This sensor can perform as a multi-channel detector. Analysis of the measured data provides insights into the signal detection capabilities of the vector field components in time-spreading underwater environments. [The work is supported in part by NSF, Grant IIP-1500123, and ONR.]

Distributed MIMO sonar for detection of moving targets in shallow sea environments

A joint processing framework is proposed for distributed multiple-input-multiple-output (MIMO) sonar systems to exploit spatial diversity and array gain for detection of moving targets. An extended moving target consisting of multiple scatterers is illuminated by widely-spaced transmitters from different angles to achieve spatial diversity. Target bearing is first estimated with high resolution by the deconvolved conventional beamforming technique. Then a replica correlation integration processor is utilized to estimate the target’s range and speed in a multipath propagation environment. A MIMO detector is designed with the estimated target position parameters and Doppler factor under the generalized likelihood ratio test framework. The effectiveness of the distributed MIMO sonar system has been validated by the localization of two moving targets in sea experiments.

Joint Bernoulli Filtering and MIMO Processing for Detection of Moving Targets in Shallow Ocean Environments

A joint multiple-input multiple-output (MIMO) processing framework is proposed to exploit spatial diversity and moving cues for the enhancement of target detection in a shallow ocean environment. Orthogonal signals are transmitted to illuminate different aspects of a target and beamforming operation is carried out over the received data for estimating target bearing. The target range is achieved by a replica correlation integrator where the beamformer outputs are matched with transmitted signals. After meanshift clustering algorithm is carried out over the bearing-range spectrums to generate the clutter centers, the potential trajectories of targets can be tracked by an improved Bernoulli filter with inputs of these centers. The at-sea experimental results have shown the effectiveness of the joint processing framework in MIMO detection of moving targets.

Robust Active Sonar Detection in Frequency and Time Dispersive Channels Using Matching Envelope Spectrum of Multi-Pulse LFM Signals

For detecting the target echoes undergoing distortion in frequency and time dispersive channels, a novel robust active sonar detector is proposed. The proposed active detector firstly extracts the matching envelope (ME) of the multi-pulse linear frequency modulation (LFM) signals, and then the peaks of the matching envelope spectrum (MES) contained in the designed grid searching windows are detected. The grid searching windows are designed based on the theoretical analysis of the features of the MES. Lastly, the detector utilizes the detected peaks to make a judgement for determining whether there are target echoes existing in the received signal. In addition, the proposed detector can be applied to detect the multi-pulse single frequency target echoes. The proposed active detector shows a more stable performance in the frequency and time dispersive channels, compared to several classical methods, including the replica correlation (RC), the segmented RC (SRC), and the RC integration (RCI) detectors. Simulation results validate the improved performance of the active detector, showing a gain of 0.5-4 dB compared with more standard state-of-the-art detectors. Experimental results based on sea trial data have also verified the validity and feasibility of the proposed active detector.

Bit error analysis of binary phase shift keying modulation over additive white gaussian noise channel using replica correlation detection

Iletisim sistemlerinde daha iyi veri aktarim sonuclarina ulasmak icin yenileme korelasyonu uygulanmistir. Iletilen darbe paketinde cogaltma korelasyon tespitine sahip bir darbe kodlu sinyal oruntusu kullanilmasi, gurultulu iletisim kanallarinda yuksek performans saglanmasini saglayan onemli bir gerekliliktir. Bu yazida, bir sistem yazilimi ile bir BPSK modulasyon tasarimi, kanallardaki cesitli gurultulu ortamlar altinda performansi incelemek icin onerilmistir. Bu tasarimi kullanarak, iletisimde kayipsiz veri elde etmek icin 7 hucreli ve 9 hucreli cogaltma korelasyon modeli uygulanmaktadir. Darbe tipi iletisim sistemlerinde sistemin gelismis performansini gosteren sonuclar uretilmistir.

Statistical Mechanics of MAP Estimation: General Replica Ansatz

The large-system performance of maximum-a-poste-rior estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix to be chosen from the large class of rotationally invariant random matrices. We take a statistical mechanical approach by introducing a spin glass corresponding to the estimator, and employing the replica method for the large-system analysis. In contrast to earlier replica based studies, our analysis evaluates the general replica ansatz of the corresponding spin glass and determines the asymptotic distortion of the estimator for any structure of the replica correlation matrix. Consequently, the replica symmetric as well as the replica symmetry breaking ansatz with $b$ steps of breaking is deduced from the given general replica ansatz. The generality of our distortion function lets us derive a more general form of the maximum-a-posterior decoupling principle. Based on the general replica ansatz, we show that for any structure of the replica correlation matrix, the vector-valued system decouples into a bank of equivalent decoupled scalar systems followed by maximum-a-posterior estimators. The structure of the decoupled system is further studied under both the replica symmetry and the replica symmetry breaking assumptions. For $b$ steps of symmetry breaking, the decoupled system is found to be an additive system with a non-Gaussian noise term given as the sum of an independent Gaussian random variable with $b$ non-Gaussian impairment terms which depend on the input symbol. The general decoupling property of the maximum-a-posterior estimator leads to the idea of a replica simulator which represents the replica ansatz through the state evolution of a transition system described by its corresponding decoupled system. As an application of our study, we investigate large compressive sensing systems by considering the $\ell _{p}$ norm minimization recovery schemes. Our numerical investigations show that the replica symmetric ansatz for $\ell _{0}$ norm recovery fails to give an accurate approximation of the mean square error as the compression rate grows, and therefore, the replica symmetry breaking ansatze are needed in order to assess the performance precisely.

Spurious long-range entanglement and replica correlation length

Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy. Here, we show that a class of short-range entangled 2D states, when put on an infinite cylinder of circumference $L$, exhibits the entanglement R\'enyi entropy of any integer index $\alpha \ge 2$ that obeys $S_\alpha = a L - \gamma$ where $a, \gamma > 0 $. Under the extrapolation method, the subleading term $\gamma$ would be identified as the topological entanglement entropy, which is spurious. A nonzero $\gamma$ is always present if the 2D state reduces to a certain symmetry-protected topological 1D state, upon disentangling spins that are far from the entanglement cut. The internal symmetry that stabilizes $\gamma > 0$ is not necessarily a symmetry of the 2D state, but should be present after the disentangling reduction. If the symmetry is absent, $\gamma$ decays exponentially in $L$ with a characteristic length, termed as a replica correlation length, which can be arbitrarily large compared to the two-point correlation length of the 2D state. We propose a simple numerical procedure to measure the replica correlation length through replica correlation functions. We also calculate the replica correlation functions for representative wave functions of abelian discrete gauge theories and the double semion theory in 2D, to show that they decay abruptly to zero. This supports a conjecture that the replica correlation length being small implies that the subleading term from the extrapolation method determines the total quantum dimension.

Information Embedding in Sonar by Modifications of Time-Frequency Properties

In the crowded underwater acoustic channels, the ability to recognize sonar transmissions based on an identifying signature is quite valuable. In this work, we propose an algorithm to embed a watermark in the time-frequency coefficients of a sonar waveform and produce a watermarked sonar. The watermark, which is a digital signature, is used to authenticate the sonar by verifying the source that is broadcasting the waveform. The embedding rule is modeled after spread spectrum modulation and driven by two secure keys. The first key consists of the spreading code that is unique to each source. The second key is an embedding mask used to select and additively modify the selected time-frequency cells of the sonar. The mask is chosen based on the frequency response of the acoustic channel (primarily, its time and frequency coherence) and the signal energy distribution in the time-frequency plane. The detector is modeled after a matched filter receiver performing a replica correlation with the spread watermark passed through the channel model. A successful detection needs access to both the spreading code and the embedding mask. Watermark detection performance is extensively evaluated based on range; watermark energy; watermark placement; ambient noise; number of multipaths; and other ocean parameters, such as depth, surface, and bottom models.

Interference Mitigation for Multistatic Active Sonar

Two methods for detecting and classifying mutual interference between sources in multistatic active sonar systems are developed and compared for frequency-modulated transmissions. Both methods compare the output of matched-filtered time-series data using two different waveform replicas: the intended transmit replica and a hypothesized interferer replica. The first method compares the absolute magnitudes of the two outputs, whereas the second method compares the local shape of the magnitude of the outputs to idealized replica correlations using an ${L}_{5}$ -norm. Simulated examples indicate that the two methods are both effective, but with different tradeoffs. The magnitude-based method often performs better when the interference is relatively strong, and the shape-based method often performs better when the interference is weaker, and thereby harder to detect. It is also shown that excising the detected interfering direct blast at the beamformer output level effectively reduces clutter on displays and removes false contacts due to the interferer. The approach also shows potential for improving multistatic detection across platforms.

A Fast GLONASS FDMA Acquisition Algorithm Using Multi-Satellite Search Strategy

Integration of US global positioning system with other existing global navigation satellite system such as recently-augmented Russian Global Navigation Satellite System (GLONASS) suffers calculation time cost in software platforms. Acquisition stage as the first part of a software receiver is a challenging part for increasing the speed. In this paper, a rapid GLONASS acquisition algorithm is proposed using multi-satellite search strategy. The proposed algorithm divides satellites in multi-groups and generates a local replica for them. Analyzing of the received signal and this replica correlation will show whether this group has in-view satellites or not. Simulations on real data base created using an AAA GLONASS receiver prove the positive effect of this algorithm in speeding up the receiver acquisition to about 2.32 with least misdetection probability.

Signal Detection in Generalized Gaussian Noise by Nonlinear Wavelet Denoising

In this paper, a nonlinear suboptimal detector whose performance in heavy-tailed noise is significantly better than that of the matched filter is proposed. The detector consists of a nonlinear wavelet denoising filter to enhance the signal-to-noise ratio, followed by a replica correlator. Performance of the detector is investigated through an asymptotic theoretical analysis as well as Monte Carlo simulations. The proposed detector offers the following advantages over the optimal (in the Neyman-Pearson sense) detector: it is easier to implement, and it is more robust with respect to error in modeling the probability distribution of noise.

Replica inference approach to unsupervised multiscale image segmentation

We apply a replica-inference-based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters ("communities" or "solutes") against a background or "solvent." Within our multiresolution approach, we compute information-theory-based correlations among multiple solutions ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations manifest by information theory overlaps. We further employ such information theory measures (such as normalized mutual information and variation of information), thermodynamic quantities such as the system entropy and energy, and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases. Within the solvable phase, transitions between contending solutions (such as those corresponding to segmentations on different scales) may also appear. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed at both zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentations appear within the "easy phase" of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images.

Acoustic pulses in the atmosphere: An outdoor teaching laboratory.

For the past two years, the Penn State Acoustic Data Measurements and Analysis course has incorporated several outdoor-sound exercises. One of these exercises is particularly amenable to illustrating concepts in acoustic propagation, signal design, and signal detection. Using relatively inexpensive hardware, student-designed pulse sequences are transmitted, received, and recorded in various outdoor environments. The advantages and disadvantages of large-bandwidth pulses are readily apparent. The students can perform replica correlation or matched filter processing and compare the achieved results to theoretical performance. The effects of the transmitting transducer on pulse shape are seen easily. Variability in the atmospheric propagation path, multipath, and upwind/downwind effects can be demonstrated as well as the impact of ambient noise on pulse detection. In addition, pulses can be reflected from moving objects (buses, for example) either for analyzing Doppler shift or for experimenting with Doppler-tolerant detection. Waveform types range from simple sinusoidal pulses to frequency-modulated pulses and frequency- or phase-shift coded maximum-length sequences to reproductions of animal vocalizations. In the fall of 2010, 40 students participated in this exercise: 20 resident students and 20 distance-education students.

Target/clutter discrimination using Bayesian active/passive data fusion.

Discriminating targets of interest from background clutter is a key challenge in undersea active sonar. This is particularly true in littoral areas, where scattering from the bottom, motion in the water column, and activity on the surface all contribute to produce echoes which are difficult to distinguish from targets of interest. Statistically, these effects manifest themselves in non-Rayleigh, heavy-tailed amplitude distributions. An approach to target/clutter discrimination is described which uses the complementary information from both active and passive acoustic sensors to facilitate this task. The method uses an efficient, grid-based Bayesian track-before-detect scheme to combine data from the two types of sensors by carefully modeling the effects of array processing, replica correlation, normalization, and clutter statistics. Representing measurements and uncertainty in terms of likelihood functions then provides a common framework for fusion. In this manner, active returns with coincident and appropriate passive signals are given more credence, while the presence of only one or the other, while perhaps suggestive, is not as compelling. The presentation will give a general overview of the approach, and an example will be used to illustrate the potential power of using passive data to mitigate active clutter. [Work supported by the Office of Naval Research.]

Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation in information, and other measures, in principle, give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can, in principle, be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 x10;{6} nodes and more than 1 x10;{9} edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200 000 nodes and 10 x 10;{6} edges on a single processor with exceptionally high accuracy. For typical cases, we find a superlinear scaling O(L1.3) for community detection and O(L1.3 log N) for the multiresolution algorithm, where L is the number of edges and N is the number of nodes in the system.

Analysis of single molecule folding studies with replica correlation functions

Single molecule experiments that can track individual trajectories of biomolecular processes provide a challenge for understanding how these stochastic trajectories relate to the global energy landscape. Using trajectories from a native structure based simulation, we use order parameters that accurately distinguish between protein folding mechanisms that involve a simple, single set of pathways versus a complex one with multiple sets of competing pathways. We show how the folding dynamics can be analyzed with replica correlation functions in a way that is compatible with single molecule experiments.

Robust replica correlation-based symbol synchronisation in OFDM systems

A simple symbol timing synchronisation (STS) scheme is proposed, based on replica correlation robust to frequency offset in orthogonal frequency division multiplexing systems. The proposed scheme applies a sequence and its modified sequence to total feasible frequency resources used in STS. A comparison is made with the current long-term evolution scheme.