Number Of Available Snapshots Research Articles

Characterizing ultra-high-redshift dark matter halo demographics and assembly histories with the gureft simulations

ABSTRACT Dark matter halo demographics and assembly histories are a manifestation of cosmological structure formation and have profound implications for the formation and evolution of galaxies. In particular, merger trees provide fundamental input for several modelling techniques, such as semi-analytic models (SAMs), sub-halo abundance matching (SHAM), and decorated halo occupation distribution models. Motivated by the new ultra-high-redshift (z ≳ 10) frontier enabled by JWST, we present a new suite of Gadget at Ultrahigh Redshift with Extra-Fine Timesteps (gureft) dark matter-only cosmological simulations that are carefully designed to capture halo merger histories and structural properties in the ultra-z universe. The simulation suite consists of four 10243-particle simulations with box sizes of 5, 15, 35, and 90 Mpc h−1, each with 170 snapshots stored between 40 ≥ z ≥ 6. With the unprecedented number of available snapshots and strategically chosen dynamic range covered by these boxes, gureft uncovers the emerging dark matter halo populations and their assembly histories in the earliest epochs of cosmic history. In this work, we present the halo mass functions (HMF) between z ∼ 20 and 6 down to log (Mvir/M⊙) ∼ 5, and show that at high redshift, these robust HMFs can differ substantially from commonly used analytic approximations or older fitting functions in the literature. We also present key physical properties of the ultra-high z halo population, such as concentration and spin, as well as their mass growth and merger rates, and again provide updated fitting functions.

Angle-incremental range estimation for FDA-MIMO radar via hybrid sparse learning

In this paper, a target parameter estimation problem is addressed for the recently emerging frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system, utilizing sparse learning. The scene is modeled as a two dimensional (2D) angle-incremental range grid. To solve the resulting sparse problem, the recently proposed user-parameter free algorithms including block sparse learning via iterative minimization (BSLIM), iterative adaptive approach (IAA), sparse iterative covariance-based estimation (SPICE), likelihood-based estimation of sparse parameters (LIKES), and orthogonal matching pursuit (OMP) are applied which achieve excellent parameter estimation performance. However, these algorithms do not exhibit a uniform performance under different scenarios such as the number of available snapshots and the number of present targets. In this paper, we propose a hybrid estimation approach which utilizes the model order selection (MOS), and automatically selects the best algorithm for the scenario under test. The performance analyses show that the proposed hybrid algorithm presents higher accuracy in terms of root mean square error (RMSE), as compared with the discussed sparse algorithms, and converges to the Cramér-Rao lower bound (CRLB).

Monostatic MIMO radar direction finding in impulse noise

This work considers direction-finding using a monostatic multiple-input multiple-output (MIMO) radar in the presence of impulsive noise. Employing a novel low-order covariance-based exponential kernel function, the proposed maximum likelihood (ML) formulation exploits an introduced quantum whale optimization algorithm (QWOA) to form the direction estimates. The resulting estimates are shown to be robust to the presence of impulsive noise, offering preferable performance as compared to recent related approaches, even in cases when the number of available snapshots is small.

Two-Stage Beamforming for Rejecting Interferences Using Deep Neural Networks

Established beamforming techniques for finding the optimal weight vectors of an antenna array, such as minimum mean squared error (MMSE) and minimum variance distortion-less response (MVDR), often require the direction of arrival (DoA) of the desired signal. In this article, we introduce a neural beamformer to estimate the desired signal in the presence of noise and interferences, without requiring the DoA. The proposed neural beamformer consists of a convolutional neural network (CNN) to estimate the interference vector from signals received at a subarray of the antennas and a bidirectional long short-term memory (bi-LSTM) to estimate the samples of the desired signal. The output signal- to- interference- and noise ratio (SINR) with the proposed neural beamformer is 10dB higher than the conventional beamformers when the number of available snapshots of the received signal is as low as 100. The beamformer can estimate the desired signal when input interference-to-signal ratio (ISR) is as high as 35dB and input signal-to noise ratio (SNR) is as low as -10 dB.

DNN‐based interference mitigation beamformer

In classical beamforming techniques such as minimum mean squared error and minimum variance distortion-less response, for computing optimum weight vector of an antenna array, direction of arrival (DoA) of desired signal should be known as prior knowledge. In this study, a deep neural-network-based beamformer is proposed for estimating the desired signal in presence of noise and interference without requiring prior knowledge on the DoA of the desired signal. In the proposed beamformer, a bidirectional long short-term memory (bi-LSTM) is employed for estimating samples of interferences. On the other hand, samples of the desired signal are estimated by either another bi-LSTM or a convolutional neural network. The signal to interference and noise ratio (SINR) at the output of the proposed beamformer is 10 dB higher than the SINR at the output of the classical beamformers when the number of available snapshots is as low as 100. The proposed beamformer has promising performance when the input interference to signal ratio is as high as 34 dB and the input signal-to-noise ratio is as low as −10 dB.

Deep‐learning‐based beamforming for rejecting interferences

Antenna arrays have been widely used for space and space–time processing to estimate the desired signals in the presence of narrowband and wideband interferences. Estimating the optimal weight vector is a challenging problem in space and space–time processing due to its high computational complexity. The problem escalates when the number of antennas and taps of filters for time-domain processing increases. In this study, a convolutional neural network is employed to estimate nearly-optimal weight vectors even when the number of available snapshots of the received signal is as low as 400 and a signal-to-noise ratio as low as −5 dB. Unlike the conventional processors, the authors proposed method requires no prior knowledge about the direction of arrival of the desired signal. In addition, due to its parallel architecture, the computational complexity of the neural processors is reasonable using a single graphical processing unit on a PC to run the algorithms. Through simulations of the uniform linear array in the presence of narrowband and wideband interferences, they demonstrate that the output signal-to-interference plus noise ratio (SINR) is very close (by <0.5 dB) to the max SINR obtained by the optimal weight vector of antenna arrays.

Reduced Dimension STAP Based on Sparse Recovery in Heterogeneous Clutter Environments

For airborne-phased array radar systems, space-time adaptive processing (STAP) is supposed to be a crucial technique for improving target detection performance in the strong clutter background. However, practical application environments are always heterogeneous and have offered a severe challenge to the implementation of STAP. To address this reality, a data-dependent reduced dimension STAP approach based on sparse recovery (SR) is proposed in this paper. To take a full account of the heterogeneous environments, we consider the extremely heterogeneous case in which only one single snapshot is available. There is no doubt that, compared with the clutter covariance matrix (CCM) calculated directly by a single snapshot, the SR technique can provide a more accurate estimate. However, we should come to realize that this estimation is not accurate enough to adaptive processing according to the presented simulation results in lots of literature, and it has been demonstrated that the performance of traditional SR-based STAP degrades dramatically when only a snapshot is available. In the proposed approach, the CCM estimated by SR technique is utilized to design the reduced dimension transformation matrix rather than to calculate adaptive weights as the traditional SR-based STAP. The relatively accurate CCM can provide better support for the design of reduced dimension transformation matrix. From the simulation results, the proposed approach can achieve great performance of clutter suppression and target detection with only a single snapshot compared with several typical STAP algorithms. It is worthwhile pointing out that the proposed approach can also be applied when multiple snapshots are available and the performance improves with increasing number of available snapshots.

Enhanced PUMA for Direction-of-Arrival Estimation and Its Performance Analysis

Direction-of-arrival (DOA) estimation is a problem of significance in many applications. In practice, due to the occurrence of coherent signals and/or when the number of available snapshots is small, it is a challenge to find DOAs accurately. This problem is revisited here through a new enhanced principal-singular-vector utilization for modal analysis (EPUMA) DOA estimation approach, which improves the threshold performance by first generating $(P+K)$ DOA candidates for $K$ sources where $P\geq K$ , and then judiciously selecting $K$ of them. The asymptotic variance of EPUMA is theoretically derived, and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of EPUMA.

Preface for Special Issue on Biology with X-ray Lasers 2.

In 1970, Breedlove and Tramel and later Solem and Baldwin (1982) suggested that the problem of radiation damage in structural biology might be solved by destroying the sample with a short pulse of intense radiation, because a few photons should be scattered before the onset of radiation damage. Following pioneering work by many, this outlandish idea is now a reality (see, e.g., Neutze et al., 2000; Gaffney and Chapman, 2007; Spence, 2008; Chapman et al., 2011; and Boutet et al., 2012)). This Special Issue, the proceedings of a meeting organized by the NSF Science & Technology Center for Biology with X-ray Lasers, constitutes a timely report on the latest developments, and a tantalizing view of what is yet to come. There has been progress on all fronts: instrumental, technical, and scientific. These developments have transformed heroic “campaigns” to focused experiments with acceptable requirements in beamtime and materials. Structure determinations, which in 2011 took 18 months from experiment to submitted paper, can now be completed in a few weeks, with a factor of 10 less beamtime, a factor of 4 less time for data analysis, and a factor of 100 less protein. Critical steps, such as de novo structure determination, have been demonstrated (Barends et al., 2014), and a wide variety of alternative approaches are under development (see this issue). The sheer range of systems shown to be amenable to Serial Femtosecond Crystallography has left little doubt about the validity of this approach, and its ability to deliver hitherto inaccessible insights into difficult systems and processes. The experimental and algorithmic methods developed for X-ray laser applications are increasingly migrating to synchrotrons. Recent experiments reported here also demonstrate the power of X-ray laser methods for time-resolved work, where the use of protein nanocrystals smaller than the optical absorption length of the pump light has produced the largest differences in a density map ever seen (Tenboer et al., 2014). Indeed, the “diffract-before-destroy” approach is now poised to extend serial femtosecond methods to non-cyclic processes, including enzymology, and sub-picosecond timescales inaccessible at synchrotrons. For longer times, mixing jets using nanocrystals smaller than diffusion lengths promise to allow diffusive mixing for the first time. More generally, the elucidation of femtosecond processes linking chemistry to biology is an enticing prospect under active investigation. The promise of determining structure without crystals has proved difficult to realize, but initial results are now emerging (Ekeberg et al., 2015), with more anticipated from an international collaboration involving many leading groups (Aquila et al., 2015). Recently, electron-based single-particle methods have begun to produce conformational movies and energy landscapes (Dashti et al., 2014) but remain constrained by the number of available snapshots. The X-ray laser has the capability to produce extremely large datasets under physiological conditions. As reported in this issue, it is imperative to develop means for compiling large datasets of useful snapshots obtained under tightly controlled and reproducible imaging conditions, and to correct any remaining imaging artifacts algorithmically. In a short time, the application of X-ray lasers to biology has moved from a debate on validity to a rapidly growing demonstration of unprecedented access to a treasure trove of new information. The reports in this Special Issue make it clear that the best is yet to come.

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrades when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators.

A Nonlinear Adaptive Beamforming Algorithm Based on Least Squares Support Vector Regression

To overcome the performance degradation in the presence of steering vector mismatches, strict restrictions on the number of available snapshots, and numerous interferences, a novel beamforming approach based on nonlinear least-square support vector regression machine (LS-SVR) is derived in this paper. In this approach, the conventional linearly constrained minimum variance cost function used by minimum variance distortionless response (MVDR) beamformer is replaced by a squared-loss function to increase robustness in complex scenarios and provide additional control over the sidelobe level. Gaussian kernels are also used to obtain better generalization capacity. This novel approach has two highlights, one is a recursive regression procedure to estimate the weight vectors on real-time, the other is a sparse model with novelty criterion to reduce the final size of the beamformer. The analysis and simulation tests show that the proposed approach offers better noise suppression capability and achieve near optimal signal-to-interference-and-noise ratio (SINR) with a low computational burden, as compared to other recently proposed robust beamforming techniques.

Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signals Case

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimension $M$ and the number of snapshots $N$ converge to $+\infty$ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values of $M$ and $N$. The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.

SMI-MVDR Beamformer Implementations for Large Antenna Array and Small Sample Size

Two online implementations of the sample matrix inversion minimum variance distortionless response (SMI-MVDR) antenna array beamformer, based on recursive updating of the diagonal loading triangular matrix decomposition, are presented. The first proposed beamformer uses the Cholesky factorization recursive updating of the matrix whose dimension is increasing. The second beamformer uses the Householder transform (HT) recursive updating of the modified input data matrix. The proposed implementations consist primarily of vector operations, that is, they are suitable for parallel implementations with FPGAs or DSPs. The computational cost of the proposed beamforming algorithms is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nk</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of antenna array elements, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is the number of processing snapshots. The proposed implementations are especially useful for large antenna array applications, where the number of available snapshots does not exceed the number of the array antenna elements. The simulation result shows that the numerical performance of the proposed beamformers is superior, relative to the conventional recursive MVDR beamformer implementation.

Analytical prediction of sample eigenvector quality deterioration in large arrays due to SNR or sample size constraints

It is well-known that subspace-based estimation methods in adaptive array processing suffer a rapid degradation in performance as either the signal-to-noise ratio (SNR) or the number of available snapshots drops below a certain threshold value. In the large system, relative large sample size limit, one can use random matrix theory to analytically predict this threshold and the degradation in the ''quality'' of the corresponding subspace estimates. In certain settings, one observes a "phase transition" phenonemon so that if the signals are too weak or there are insufficient number of snapshots or both, the subspace estimates are, statistically speaking, noise-like. We discuss the implication of these results for the subspace based detection of signals in white and colored noise using large arrays and illustrate the accuracy of the predictions with numerical simulations.

Robust Array Beamforming With Sidelobe Control Using Support Vector Machines

Robust beamforming is a challenging task in a number of applications (radar, sonar, wireless communications, etc.) due to strict restrictions on the number of available snapshots, signal mismatches, or calibration errors. We present a new approach to adaptive beamforming that provides increased robustness against the mismatch problem as well as additional control over the sidelobe level. We generalize the conventional linearly constrained minimum variance cost function by including a regularization term that penalizes differences between the actual and the target (ideal) array responses. By using the so-called epsi-insensitive loss function for the penalty term, the final cost function adopts the form of a support vector machine (SVM) for regression. In particular, the resulting cost function is convex with a unique global minimum that has traditionally been found using quadratic programming (QP) techniques. To alleviate the computational cost of conventional QP techniques, we use an iterative reweighted least-squares (IRWLS) procedure, which also converges to the SVM solution. Computer simulations demonstrate an improved performance of the proposed SVM-based beamformer, in comparison with other recently proposed robust beamforming techniques

Direction of arrival estimation based on temporal and spatial processing using a direct data domain (D/sup 3/) approach

The purpose of this paper is to estimate the direction of arrival (DOA) of the signal of interest (SOI) in the presence of both coherent and noncoherent interferences and multipath components utilizing a combined temporal and spatial processing technique based on a direct data domain approach. The concept of cyclostationarity, which deals with the temporal information of the SOI, is used to extract signals having the same cycle frequency and null out the co-channel interferences and additive noise. Hence, the signal detection capability can be significantly increased over conventional filtering when the length of the data record is limited. The main contribution of the paper is that by combining temporal and spatial processing based on a direct data domain approach one can handle number of signals along with their various coherent and noncoherent multipaths and interferences which can exceed the number of antenna elements. Hence, this methodology may be advantageous over conventional spatial processing when the number of degrees of freedom can never exceed the number of antenna elements in the array. However, the number of multipaths and interferers at the same cycle frequency has to be less than approximately 66 % of the antenna elements. Since we do not form a covariance matrix of the data, this method is quite suitable for short data lengths or when the environment is quite dynamic. Hence, in the proposed algorithm, while the estimation of the cyclic array covariance matrix is avoided, we develop a new matrix form using extremely short data samples. As a result, the computational load in the proposed approach is relatively reduced and the robustness of the estimation of SOI is significantly improved when the number of available snapshots is extremely limited. Numerical results are presented to illustrate the efficiency and accuracy of this method.