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Linlin Sun

Publications and source records attributed to Linlin Sun.

At least 37 records · Page 2Linked to original sources
arXiv2020

Global existence and convergence of a flow to Kazdan-Warner equation with non-negative prescribed function

We consider an evolution problem associated to the Kazdan-Warner equation on a closed Riemann surface $(Σ,g)$ \begin{align*} -Δ_{g}u=8π\left(\frac{he^{u}}{\int_Σhe^{u}{\rm d}μ_{g}}-\frac{1}{\int_Σ{\rm d}μ_{g}}\right) \end{align*} where the prescribed function $h\geq0$ and $\max_Σh>0$. We prove the global existence and convergence under additional assumptions such as \begin{align*} Δ_{g}\ln h(p_0)+8π-2K(p_0)>0 \end{align*} for any maximum point $p_0$ of the sum of $2\ln h$ and the regular part of the Green function, where $K$ is the Gaussian curvature of $Σ$. In particular, this gives a new proof of the existence result by Yang and Zhu [Proc. Amer. Math. Soc. 145 (2017), no. 9, 3953-3959] which generalizes existence result of Ding, Jost, Li and Wang [Asian J. Math. 1 (1997), no. 2, 230-248] to the non-negative prescribed function case.

math.AP↗
arXiv2020

UAV-enabled Secure Communication with Finite Blocklength

In the finite blocklength scenario, which is suitable for practical applications, a method of maximizing the average effective secrecy rate (AESR) is proposed for a UAV-enabled secure communication by optimizing the UAV's trajectory and transmit power subject to the UAV's mobility constraints and transmit power constraints. To address the formulated non-convex optimization problem, it is first decomposed into two non-convex subproblems. Then the two subproblems are converted respectively into two convex subproblems via the first-order approximation. Finally, an alternating iteration algorithm is developed by solving the two subproblems iteratively using successive convex approximation (SCA) technique. Numerical results show that our proposed scheme achieves a better AESR performance than both the benchmark schemes.

eess.SP↗
arXiv2019

A new characterization of the Calabi torus in the unit sphere

In this paper, we study the rigidity theorem of closed minimally immersed Legendrian submanifolds in the unit sphere. Utilizing the maximum principle, we obtain a new characterization of the Calabi torus in the unit sphere which is the minimal Calabi product Legendrian immersion of a point and the totally geodesic Legendrian sphere. We also establish an optimal Simons' type integral inequality in terms of the second fundamental form of three dimensional closed minimal Legendrian submanifolds in the unit sphere.

math.DG↗
arXiv2019

A remark on a Bernstein type result for $λ$-hypersurfaces

We proved that any complete hypersurface in the Euclidean space $\mathbb{R}^{n+1}$ whose Gauss image is contained in an open hemisphere has to be proper. As applications, we derive a counterpart of Hoffman-Osserman-Schoen's result for $λ$-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \cite{CW14b}.

math.DG↗
arXiv2019

Pilot-Based Channel Estimation Design in Covert Wireless Communication

In this work, for the first time, we tackle channel estimation design with pilots in the context of covert wireless communication. Specifically, we consider Rayleigh fading for the communication channel from a transmitter to a receiver and additive white Gaussian noise (AWGN) for the detection channel from the transmitter to a warden. Before transmitting information signals, the transmitter has to send pilots to enable channel estimation at the receiver. Using a lower bound on the detection error probability, we first prove that transmitting pilot and information signals with equal power can minimize the detection performance at the warden, which is confirmed by the minimum detection error probability achieved by the optimal detector based on likelihood ratio test. This motivates us to consider the equal transmit power in the channel estimation and then optimize channel use allocation between pilot and information signals in covert wireless communication. Our analysis shows that the optimal number of the channel uses allocated to pilots increases as the covertness constraint becomes tighter. In addition, our examination shows that the optimal percentage of all the available channel uses allocated to channel estimation decreases as the total number of channel uses increases.

cs.IT↗
arXiv2019

Energy-efficient Alternating Iterative Secure Structure of Maximizing Secrecy Rate for Directional Modulation Networks

In a directional modulation (DM) network, the issues of security and privacy have taken on an increasingly important role. Since the power allocation of confidential message and artificial noise will make a constructive effect on the system performance, it is important to jointly consider the relationship between the beamforming vectors and the power allocation (PA) factors. To maximize the secrecy rate (SR), an alternating iterative structure (AIS) between the beamforming and PA is proposed. With only two or three iterations, it can rapidly converge to its rate ceil. Simulation results indicate that the SR performance of proposed AIS is much better than the null-space projection (NSP) based PA strategy in the medium and large signal-to-noise ratio (SNR) regions, especially when the number of antennas at the DM transmitter is small.

cs.IT↗
arXiv2019

Optimal Power Allocation for Secure Directional Modulation Networks with a Full-duplex UAV User

This paper make an investigation of a secure unmanned aerial vehicle (UAV)-aided communication network based on directional modulation(DM), in which one ground base station (Alice), one legitimate full-duplex (FD) user (Bob) and one illegal receiver (Eve) are involved. In this network, Alice acts as a control center to transmit confidential message and artificial noise (AN). The UAV user, moving along a linear flight trajectory, is intended to receive the useful information from Alice. At the same time, it also sends AN signals to further interference Eve's channel. Aiming at maximizing secrecy rate during the UAV flight process, a joint optimization problem is formulated corresponding to power allocation (PA) factors, beamforming vector, AN projection matrices. For simplicity, maximum ratio transmission, null-space projection and the leakage-based method are applied to form the transmit beamforming vector, AN projection matrix at Alice, and AN projection vector at Bob, respectively. Following this, the optimization problem reduces into a bivariate optimization programme with two PA factors. We put forward an alternating iterative algorithm to optimize the two PA factors. Simulation results demonstrate that the proposed strategy for FD mode achieves a higher SR than the half-duplex (HD) mode, and outperforms the FD mode with fixed PA strategy.

cs.IT↗
arXiv2018

Rigidity of closed CSL submanifolds in the unit sphere

A contact stationary Legendrian submanifold (briefly, CSL submanifold) is a stationary point of the volume functional of Legendrian submanifolds in a Sasakian manifold. Much effort has been paid in the last two decades to construct examples of such manifolds, mainly by geometers using various geometric methods. But we have rare knowledge about their geometric properties till now. Recently, Y. Luo (\cite{ Luo2, Luo1}) proved that a closed CSL surface in $\mathbb{S}^5$ with the square length of its second fundamental form belonging to $[0,2]$ must be totally geodesic or be a flat minimal Legendrian torus, which generalizes a related gap theorem of minimal Legendrian surface due to Yamaguchi et al. (\cite{YKM}). In this paper, we will study the general dimensional case of this result.

math.DG↗
arXiv2018

Some sharp differential sphere theorems for nonnegative scalar curvature manifolds

In this paper, we obtain several new intrinsic and extrinsic differential sphere theorems via Ricci flow. For intrinsic case, we show that a closed simply connected $n(\ge 4)$-dimensional Riemannian manifold $M$ is diffeomorphic to $S^n$ if one of the following conditions holds pointwisely: $$ (i)\ R_0>\left(1-\frac{24(\sqrt{10}-3)}{n(n-1)}\right)K_{max};\quad \ (ii)\ \frac{Ric^{[4]}}{4(n-1)}>\left(1-\frac{6(\sqrt{10}-3)}{n-1}\right)K_{max}.$$ Here $K_{max}$, $Ric^{[k]}$ and $R_0$ stand for the maximal sectional curvature, the $k$-th weak Ricci curvature and the normalized scalar curvature. For extrinsic case, i.e., when $M$ is a closed simply connected $n(\ge 4)$-dimensional submanifold immersed in $\bar{M}$. We prove that $M$ is diffeomorphic to $S^n$ if it satisfies some pinching curvature conditions. The only involved extrinsic quantities in our pinching conditions are the maximal sectional curvature $\bar K_{max}$ and the squared norm of mean curvature vector $\vert H\vert^2$. More precisely, we show that $M$ is diffeomorphic to $S^n$ if one of the following conditions holds: \begin{itemize} \item[(1)] $R_0\ge \left(1-\frac{2}{n(n-1)}\right)\bar{K}_{max} +\frac{n(n-2)}{(n-1)^2}\vert H\vert^2$, and strict inequality is achieved at some point; \item[(2)] $\dfrac{Ric^{[2]}}{2}\ge (n-2)\bar K_{max}+\frac{n^2}{8}\vert H\vert^2,$ and strict inequality is achieved at some point; \item[(3)] $\dfrac{Ric^{[2]}}{2} \ge\frac{n(n-3)}{n-2}\left(\bar K_{max}+\vert H\vert^2\right),$ and strict inequality is achieved at some point. \end{itemize} It is worth pointing out that, in the proof of extrinsic case, we apply suitable complex orthonormal frame and simplify the calculations considerably. We also emphasize that both of the pinching constants in (2) and (3) are optimal for $n=4$.

math.DG↗
arXiv2018

Alternating Iterative Secure Structure between Beamforming and Power Allocation for UAV-aided Directional Modulation Networks

In unmanned aerial vehicle (UAV) networks, directional modulation (DM) is adopted to improve the secrecy rate (SR) performance. Alice, a ground base station, behaves as a control center, and Bob is a UAV of flying along a linear flight trajectory who optimizes its SR performance by dynamically adjusting its beamforming vectors and power allocation (PA) strategy. Per fixed time interval during the Bob's flight process, the transmit beamforming vectors for useful messages and AN projection are given by the rule of maximizing signal-to-leakage-and-noise ratio (Max-SLNR) and maximizing AN-and-leakage-to-noise ratio (ANLNR), and the optimal PA strategy is based on maximizing SR (Max-SR). More importantly, an alternating iterative structure (AIS) between beamforming and PA is proposed to further improve the SR performance. Simulation results show that the proposed AIS converges rapidly, and can achieve substantial SR gains over Max-SLNR plus Max-ANLNR with fixed PA such as PA factor $β=$ 0.5, and 0.9. In particular, in the case of small-scale antenna array, the SR performance gain achieved by the proposed AIS is more attractive. Additionally, as the number of antennas tends to be large-scale, the average SR performance of the proposed AIS approaches an SR ceil.

cs.IT↗
arXiv2018

A Robust Secure Hybrid Analog and Digital Receive Beamforming Scheme for Efficient Interference Reduction

Medium-scale or large-scale receive antenna array with digital beamforming can be employed at receiver to make a significant interference reduction, but leads to expensive cost and high complexity of the RF-chain circuit. To deal with this issue, a classic analog-and-digital beamforming (ADB) structure was proposed in the literature for greatly reducing the number of RF-chains. Based on the ADB structure, we in this paper propose a robust hybrid ADB scheme to resist directions of arrival (DOAs) estimation errors. The key idea of our scheme is to employ null space projection (NSP) in analog beamforming domain and diagonal loading (DL) method in digital beamforming domain. Simulation results show that the proposed scheme performs more robustly, and moreover, has a significant improvement on the receive signal to interference plus noise ratio (SINR) compared to NSP ADB scheme and DL method.

cs.IT↗
arXiv2017

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

In this paper, we consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold $M$ isometrically immersed into another Riemannian manifold $\bar M$ for arbitrary codimension. We first assume the pull back Weitzenböck operator (defined in Section 2) of $\bar M$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results and a homology sphere theorem. Second, when the pull back Weitzenböck operator of $\bar M$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of $M$ and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then $M$ is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates and homology sphere theorems are optimal when $\bar M$ has constant curvature.

math.DG↗
arXiv2017

Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem

We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we derive a general existence, uniqueness and regularity theorem for solutions of Dirac equations with such boundary conditions. We also apply these estimates to a new nonlinear elliptic-parabolic problem, the Dirac-harmonic heat flow on Riemannian spin manifolds. This problem is motivated by the supersymmetric nonlinear $σ$-model and combines a harmonic heat flow type equation with a Dirac equation that depends nonlinearly on the flow.

math.DG↗