This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy and conditio
n number of the CM estimate for low-sample-support cases. We focus on data-driven techniques that automatically choose the linear shrinkage factors for shrinkage sample covariance matrix ($text{S}^2$CM) and shrinkage Tylers estimator (STE) by exploiting cross validation (CV). We propose leave-one-out cross-validation (LOOCV) choices for the shrinkage factors to optimize the beamforming performance, referred to as $text{S}^2$CM-CV and STE-CV. The (weighted) out-of-sample output power of the beamfomer is chosen as a proxy of the beamformer performance and concise expressions of the LOOCV cost function are derived to allow fast optimization. For the large system regime, asymptotic approximations of the LOOCV cost functions are derived, yielding the $text{S}^2$CM-AE and STE-AE. In general, the proposed algorithms are able to achieve near-oracle performance in choosing the linear shrinkage factors for MVDR beamforming. Simulation results are provided for validating the proposed methods.
COVID-19 pandemic and social distancing urge a reliable human face recognition system in different abnormal situations. However, there is no research which studies the influence of glass factor in facial recognition system. This paper provides a comp
rehensive review of glass factor. The study contains two steps: data collection and accuracy test. Data collection includes collecting human face images through different situations, such as clear glasses, glass with water and glass with mist. Based on the collected data, an existing state-of-the-art face detection and recognition system built upon MTCNN and Inception V1 deep nets is tested for further analysis. Experimental data supports that 1) the system is robust for classification when comparing real-time images and 2) it fails at determining if two images are of same person by comparing real-time disturbed image with the frontal ones.
This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for complex elliptically symmetric (CES) data. To obtain a well-conditioned estimate of the CM, we add penalty terms of Kullback-Leibler divergence to the
negative log-likelihood function of the associated complex angular Gaussian (CAG) distribution. This is shown to be equivalent to regularizing Tylers fixed-point equations by shrinkage. A sufficient condition that the solution exists is discussed. An iterative algorithm is applied to solve the resulting fixed-point iterations and its convergence is proved. In order to solve the critical problem of tuning the shrinkage factors, we then introduce three methods by exploiting oracle approximating shrinkage (OAS) and cross-validation (CV). When the training samples are limited, the proposed estimator, referred to as the robust shrinkage Kronecker estimator (RSKE), has better performance compared with several existing methods. Simulations are conducted for validating the proposed estimator and demonstrating its high performance.
We study the spin-boson model (SBM) with two spins in staggered biases by a numerically exact method based on variational matrix product states. Several observables such as the magnetization, the entanglement entropy between the two spins and the bos
onic environment, the ground-state energy, as well as the correlation function for two spins are calculated exactly. The characteristics of these observables suggest that the staggered biases can drive the 2nd-order quantum phase transition (QPT) to the 1st-order QPT in the sub-Ohmic SBM, while the Kosterlitz-Thouless QPT in the Ohmic SBM goes directly to the 1st-order one. A quantum tricritical point, where the continuous QPT meets the 1st-order one, can then be detected. It is found that the staggered biases would not change the universality of { the phase transition in this model} below the quantum tricritical point.
We study the anisotropic spin-boson model (SBM) with the subohmic bath by a numerically exact method based on variational matrix product states. A rich phase diagram is found in the anisotropy-coupling strength plane by calculating several observable
s. There are three distinct quantum phases: a delocalized phase with even parity (phase I), a delocalized phase with odd parity (phase II), and a localized phase with broken $Z_2$ symmetry (phase III), which intersect at a quantum tricritical point. The competition between those phases would give overall picture of the phase diagram. For small power of the spectral function of the bosonic bath, the quantum phase transition (QPT) from phase I to III with mean-field critical behavior is present, similar to the isotropic SBM. The novel phase diagram full with three different phases can be found at large power of the spectral function: For highly anisotropic case, the system experiences the QPTs from phase I to II via 1st-order, and then to the phase III via 2nd-order with the increase of the coupling strength. For low anisotropic case, the system only experiences the continuous QPT from phase I to phase III with the non-mean-field critical exponents. Very interestingly, at the moderate anisotropy, the system would display the continuous QPTs for several times but with the same critical exponents. This unusual reentrance to the same localized phase is discovered in the light-matter interacting systems. The present study on the anisotropic SBM could open an avenue to the rich quantum criticality.
Light nuclei production is sensitive to the baryon density fluctuations and can be used to probe the QCD phase transition in relativistic heavy-ion collisions. In this work, we studied the production of proton, deuteron, triton in central Au+Au colli
sions at $sqrt{s_{mathrm{NN}}}$ = 5, 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV from a transport model (JAM). Based on the coalescence production of light nuclei, we calculated the energy dependence of rapidity density $dN/dy$ and particle ratios ($d/p$, $t/p$, and $t/d$). More importantly, the yield ratio $N_{{t}} times N_{{p}} / N_{{d}}^{2}$, which is sensitive to the neutron density fluctuations, shows a flat energy dependence and cannot describe the non-monotonic trend observed by the STAR experiment. Based on the nucleon coalescence, this work can provide constraint and reference to search for the QCD critical point and/or first order phase transition with light nuclei production in future heavy-ion collision experiments.
Proton number fluctuation is sensitive observable to search for the QCD critical point in heavy-ion collisions. In this paper, we studied rapidity acceptance dependence of the proton cumulants and correlation functions in most central Au+Au collision
s at $sqrt{s_mathrm{NN}} = 5$ GeV from a microscopic hadronic transport model (JAM). At mid-rapidity, we found the effects of resonance weak decays and hadronic re-scattering on the proton cumulants and correlation functions are small, but those effects get larger when further increasing the rapidity acceptance. On the other hand, we found the baryon number conservation is a dominant background effect on the rapidity acceptance dependence of proton number fluctuations. It leads to a strong suppression of cumulants and cumulant ratios, as well as the negative proton correlation functions. We also studied those two effects on the energy dependence of cumulant ratios of net-proton distributions in most central Au+Au collisions at $sqrt{s_mathrm{NN}} = 5-200$ GeV from JAM model. This work can serve as a non-critical baseline for future QCD critical point search in heavy-ion collisions at high baryon density region.
In this paper, we propose a fast method for array response adjustment with phase-only constraint. This method can precisely and rapidly adjust the array response of a given point by only varying the entry phases of a pre-assigned weight vector. We sh
ow that phase-only array response adjustment can be formulated as a polygon construction problem, which can be solved by edge rotation in complex plain. Unlike the existing approaches, the proposed algorithm provides an analytical solution and guarantees a precise phase-only adjustment without pattern distortion. Moreover, the proposed method is suitable for an arbitrarily given weight vector and has a low computational complexity. Representative examples are presented to demonstrate the effectiveness of the proposed algorithm.
In this paper, the complex-coefficient weight vector orthogonal decomposition ($ textrm{C}^2textrm{-WORD} $) algorithm proposed in Part I of this two paper series is extended to robust sidelobe control and synthesis with steering vector mismatch. Ass
uming that the steering vector uncertainty is norm-bounded, we obtain the worst-case upper and lower boundaries of array response. Then, we devise a robust $ textrm{C}^2textrm{-WORD} $ algorithm to control the response of a sidelobe point by precisely adjusting its upper-boundary response level as desired. To enhance the practicality of the proposed robust $ textrm{C}^2textrm{-WORD} $ algorithm, we also present detailed analyses on how to determine the upper norm boundary of steering vector uncertainty under various mismatch circumstances. By applying the robust $ textrm{C}^2textrm{-WORD} $ algorithm iteratively, a robust sidelobe synthesis approach is developed. In this approach, the upper-boundary response is adjusted in a point-by-point manner by successively updating the weight vector. Contrary to the existing approaches, the devised robust $ textrm{C}^2textrm{-WORD} $ algorithm has an analytical expression and can work starting from an arbitrarily-specified weight vector. Simulation results are presented to validate the effectiveness and good performance of the robust $ textrm{C}^2textrm{-WORD} $ algorithm.
This paper presents a new array response control scheme named complex-coefficient weight vector orthogonal decomposition ($ textrm{C}^2textrm{-WORD} $) and its application to pattern synthesis. The proposed $ textrm{C}^2textrm{-WORD} $ algorithm is a
modified version of the existing WORD approach. We extend WORD by allowing a complex-valued combining coefficient in $ textrm{C}^2textrm{-WORD} $, and find the optimal combining coefficient by maximizing white noise gain (WNG). Our algorithm offers a closed-from expression to precisely control the array response level of a given point starting from an arbitrarily-specified weight vector. In addition, it results less pattern variations on the uncontrolled angles. Elaborate analysis shows that the proposed $ textrm{C}^2textrm{-WORD} $ scheme performs at least as good as the state-of-the-art $textrm{A}^textrm{2}textrm{RC} $ or WORD approach. By applying $ textrm{C}^2textrm{-WORD} $ successively, we present a flexible and effective approach to pattern synthesis. Numerical examples are provided to demonstrate the flexibility and effectiveness of $ textrm{C}^2textrm{-WORD} $ in array response control as well as pattern synthesis.
