arXiv subjects

Yanjun Han

Publications and source records attributed to Yanjun Han.

82 records · Page 5Linked to original sources

arXiv2016

"WM"-Shaped Growth of GaN on Patterned Sapphire Substrates

In metal organic vapor phase epitaxy of GaN, the growth mode is sensitive to reactor temperature. In this study, V-pit-shaped GaN has been grown on normal c-plane cone-patterned sapphire substrate by decreasing the growth temperature of high-temperature-GaN to around 950 oC, which leads to the 3-dimensional growth of GaN. The so-called "WM" well describes the shape that the bottom of GaN V-pit is just right over the top of sapphire cone, and the regular arrangement of V-pits follows the patterns of sapphire substrate strictly. Two types of semipolar facets (1101) and (1122) expose on sidewalls of V-pits. Furthermore, by raising the growth temperature to 1000 oC, the growth mode of GaN can be transferred to 2-demonsional growth. Accordingly, the size of V-pits becomes smaller and the area of c-plane GaN becomes larger, while the total thickness of GaN keeps almost unchanged during this process. As long as the 2-demonsional growth lasts, the V-pits will disappear and only flat c-plane GaN remains. This means the area ratio of c-plane and semipolar plane GaN can be controlled by the duration time of 2-demonsional growth.

cond-mat.mtrl-sci↗

arXiv2016

InGaN/GaN Multi-Quantum-Well and Light-Emitting Diode Based on V-pit-Shaped GaN Grown on Patterned Sapphire Substrate

V-pit-defects in GaN-based light-emitting diodes induced by dislocations are considered beneficial to electroluminescence because they relax the strain in InGaN quantum wells and also enhance the hole lateral injection through sidewall of V-pits. In this paper, regularly arranged V-pits are formed on c-plane GaN grown by metal organic vapor phase epitaxy on conventional c-plane cone-patterned sapphire substrates. The size of V-pits and area of flat GaN can be adjusted by changing growth temperature. Five pairs of InGaN/GaN multi-quantumwell and also a light-emitting diode structure are grown on this V-pit-shaped GaN. Two peaks around 410 nm and 450 nm appearing in both photoluminescence and cathodeluminescence spectra are from the semipolar InGaN/GaN multi-quantum-well on sidewalls of V-pits and cplane InGaN/GaN multi-quantum-well, respectively. In addition, dense bright spots can be observed on the surface of light-emitting diode when it works under small injection current, which are believed owing to the enhanced hole injection around V-pits.

cond-mat.mes-hall↗

arXiv2016

Understanding different efficiency droop behaviors in InGaN-based near-UV, blue and green light-emitting diodes through differential carrier lifetime measurements

Efficiency droop effect under high injection in GaN-based light emitting diodes (LEDs) strongly depends on wavelength, which is still not well understood. In this paper, through differential carrier lifetime measurements on commercialized near-UV, blue, and green LEDs, their different efficiency droop behaviors are attributed to different carrier lifetimes, which are prolonged as wavelength increases. This relationship between carrier lifetime and indium composition of InGaN quantum well is believed owing to the polarization-induced quantum confinement Stark effect. Long carrier lifetime not only increases the probability of carrier leakage, but also results in high carrier concentration in quantum well. In other words, under the same current density, the carrier concentration in active region in near-UV LED is the lowest while that in green one is the highest. If considering the efficiency droop depending on carrier concentration, the behaviors of LEDs with different wavelengths do not show any abnormality. The reason why the efficiency droop becomes more serious under lower temperature can be also explained by this model as well. Based on this result, the possible solutions to conquer efficiency droop are discussed. It seems that decreasing the carrier lifetime is a fundamental approach to solve the problem.

cond-mat.mtrl-sci↗

arXiv2016

Continuous-wave Raman Lasing in Aluminum Nitride Microresonators

We report the first investigation on continuous-wave Raman lasing in high-quality-factor aluminum nitride (AlN) microring resonators. Although wurtzite AlN is known to exhibit six Raman-active phonons, single-mode Raman lasing with low threshold and high slope efficiency is demonstrated. Selective excitation of A$_1^\mathrm{TO}$ and E$_2^\mathrm{high}$ phonons with Raman shifts of $\sim$612 and 660 cm$^{-1}$ is observed by adjusting the polarization of the pump light. A theoretical analysis of Raman scattering efficiency within ${c}$-plane (0001) of AlN is carried out to help account for the observed lasing behavior. Bidirectional lasing is experimentally confirmed as a result of symmetric Raman gain in micro-scale waveguides. Furthermore, second-order Raman lasing with unparalleled output power of $\sim$11.3 mW is obtained, which offers the capability to yield higher order Raman lasers for mid-infrared applications.

physics.optics↗

arXiv2016

Mutual Information Bounds via Adjacency Events

The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of $(X,Y)$ is given by the marginal distributions $P_X, P_Y$ and the adjacency relation induced by the joint distribution, where $x$ and $y$ are adjacent if $P(x,y)>0$. We derive a lower bound on the mutual information in terms of these entities. The bound is obtained by viewing the channel from $X$ to $Y$ as a probability distribution on a set of possible actions, where an action determines the output for any possible input, and is independently drawn. We also provide an alternative proof based on convex optimization, that yields a generally tighter bound. Finally, we derive an upper bound on the mutual information in terms of adjacency events between the action and the pair $(X,Y)$, where in this case an action $a$ and a pair $(x,y)$ are adjacent if $y=a(x)$. As an example, we apply our bounds to the binary deletion channel and show that for the special case of an i.i.d. input distribution and a range of deletion probabilities, our lower and upper bounds both outperform the best known bounds for the mutual information.

cs.IT↗

arXiv2015

Minimax Estimation of Discrete Distributions under $\ell_1$ Loss

We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in regimes where the alphabet size $S$ may grow with the number of observations $n$. We show that among distributions with bounded entropy $H$, the asymptotic maximum risk for the empirical distribution is $2H/\ln n$, while the asymptotic minimax risk is $H/\ln n$. Moreover, Moreover, we show that a hard-thresholding estimator oblivious to the unknown upper bound $H$, is asymptotically minimax. However, if we constrain the estimates to lie in the simplex of probability distributions, then the asymptotic minimax risk is again $2H/\ln n$. We draw connections between our work and the literature on density estimation, entropy estimation, total variation distance ($\ell_1$ divergence) estimation, joint distribution estimation in stochastic processes, normal mean estimation, and adaptive estimation.

cs.IT↗

arXiv2015

Performance Limits and Geometric Properties of Array Localization

Location-aware networks are of great importance and interest in both civil and military applications. This paper determines the localization accuracy of an agent, which is equipped with an antenna array and localizes itself using wireless measurements with anchor nodes, in a far-field environment. In view of the Cramér-Rao bound, we first derive the localization information for static scenarios and demonstrate that such information is a weighed sum of Fisher information matrices from each anchor-antenna measurement pair. Each matrix can be further decomposed into two parts: a distance part with intensity proportional to the squared baseband effective bandwidth of the transmitted signal and a direction part with intensity associated with the normalized anchor-antenna visual angle. Moreover, in dynamic scenarios, we show that the Doppler shift contributes additional direction information, with intensity determined by the agent velocity and the root mean squared time duration of the transmitted signal. In addition, two measures are proposed to evaluate the localization performance of wireless networks with different anchor-agent and array-antenna geometries, and both formulae and simulations are provided for typical anchor deployments and antenna arrays.

cs.IT↗

arXiv2015

On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels

The free-space optical (FSO) communications can achieve high capacity with huge unlicensed optical spectrum and low operational costs. The corresponding performance analysis of FSO systems over turbulence channels is very limited, especially when using multiple apertures at both transmitter and receiver sides. This paper aim to provide the ergodic capacity characterization of multiple-input multiple-output (MIMO) FSO systems over atmospheric turbulence-induced fading channels. The fluctuations of the irradiance of optical channels distorted by atmospheric conditions is usually described by a gamma-gamma ($ΓΓ$) distribution, and the distribution of the sum of $ΓΓ$ random variables (RVs) is required to model the MIMO optical links. We use an $α$-$μ$ distribution to efficiently approximate the probability density function (PDF) of the sum of independent and identical distributed $ΓΓ$ RVs through moment-based estimators. Furthermore, the PDF of the sum of independent, but not necessarily identically distributed $ΓΓ$ RVs can be efficiently approximated by a finite weighted sum of PDFs of $ΓΓ$ distributions. Based on these reliable approximations, novel and precise analytical expressions for the ergodic capacity of MIMO FSO systems are derived. Additionally, we deduce the asymptotic simple expressions in high signal-to-noise ratio regimes, which provide useful insights into the impact of the system parameters on the ergodic capacity. Finally, our proposed results are validated via Monte-Carlo simulations.

cs.IT↗

arXiv2015

Minimax Estimation of Functionals of Discrete Distributions

We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is unknown and may be comparable with the number of observations $n$. We treat the respective regions where the functional is "nonsmooth" and "smooth" separately. In the "nonsmooth" regime, we apply an unbiased estimator for the best polynomial approximation of the functional whereas, in the "smooth" regime, we apply a bias-corrected Maximum Likelihood Estimator (MLE). We illustrate the merit of this approach by thoroughly analyzing two important cases: the entropy $H(P) = \sum_{i = 1}^S -p_i \ln p_i$ and $F_α(P) = \sum_{i = 1}^S p_i^α,α>0$. We obtain the minimax $L_2$ rates for estimating these functionals. In particular, we demonstrate that our estimator achieves the optimal sample complexity $n \asymp S/\ln S$ for entropy estimation. We also show that the sample complexity for estimating $F_α(P),0<α<1$ is $n\asymp S^{1/α}/ \ln S$, which can be achieved by our estimator but not the MLE. For $1<α<3/2$, we show the minimax $L_2$ rate for estimating $F_α(P)$ is $(n\ln n)^{-2(α-1)}$ regardless of the alphabet size, while the $L_2$ rate for the MLE is $n^{-2(α-1)}$. For all the above cases, the behavior of the minimax rate-optimal estimators with $n$ samples is essentially that of the MLE with $n\ln n$ samples. We highlight the practical advantages of our schemes for entropy and mutual information estimation. We demonstrate that our approach reduces running time and boosts the accuracy compared to existing various approaches. Moreover, we show that the mutual information estimator induced by our methodology leads to significant performance boosts over the Chow--Liu algorithm in learning graphical models.

cs.IT↗

arXiv2014

Beyond Maximum Likelihood: from Theory to Practice

Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements - both in theory and in practice - over the maximum likelihood estimator (MLE), particularly in high dimensional scenarios involving parameter dimension comparable to or larger than the number of samples. This approach to estimation, building on results from approximation theory, is shown to yield minimax rate-optimal estimators for a wide class of functionals, implementable with modest computational requirements. In a nutshell, a message of this recent work is that, for a wide class of functionals, the performance of these essentially optimal estimators with $n$ samples is comparable to that of the MLE with $n \ln n$ samples. In the present paper, we highlight the applicability of the aforementioned methodology to statistical problems beyond functional estimation, and show that it can yield substantial gains. For example, we demonstrate that for learning tree-structured graphical models, our approach achieves a significant reduction of the required data size compared with the classical Chow--Liu algorithm, which is an implementation of the MLE, to achieve the same accuracy. The key step in improving the Chow--Liu algorithm is to replace the empirical mutual information with the estimator for mutual information proposed by the authors. Further, applying the same replacement approach to classical Bayesian network classification, the resulting classifiers uniformly outperform the previous classifiers on 26 widely used datasets.

stat.ME↗