arXiv subjects

Yuanyuan Yao

Publications and source records attributed to Yuanyuan Yao.

23 records · Page 2Linked to original sources

arXiv2020

Pointwise densities of homogeneous Cantor measure and critical values

Let $N\ge 2$ and $ρ\in(0,1/N^2]$. The homogenous Cantor set $E$ is the self-similar set generated by the iterated function system \[ \left\{f_i(x)=ρx+\frac{i(1-ρ)}{N-1}: i=0,1,\ldots, N-1\right\}. \] Let $s=\dim_H E$ be the Hausdorff dimension of $E$, and let $μ=\mathcal H^s|_E$ be the $s$-dimensional Hausdorff measure restricted to $E$. In this paper we describe, for each $x\in E$, the pointwise lower $s$-density $Θ_*^s(μ,x)$ and upper $s$-density $Θ^{*s}(μ, x)$ of $μ$ at $x$. This extends some early results of Feng et al. (2000). Furthermore, we determine two critical values $a_c$ and $b_c$ for the sets \[ E_*(a)=\left\{x\in E: Θ_*^s(μ, x)\ge a\right\}\quad\textrm{and}\quad E^*(b)=\left\{x\in E: Θ^{*s}(μ, x)\le b\right\} \] respectively, such that $\dim_H E_*(a)>0$ if and only if $a 0$ if and only if $b>b_c$. We emphasize that both values $a_c$ and $b_c$ are related to the Thue-Morse type sequences, and our strategy to find them relies on ideas from open dynamics and techniques from combinatorics on words.

math.DS↗

arXiv2020

Outage Behaviors of NOMA-based Satellite Network over Shadowed-Rician Fading Channels

This paper investigates the application of non-orthogonal multiple access (NOMA) to satellite communication network over Shadowed-Rician fading channels. The impact of imperfect successive interference cancellation (ipSIC) on NOMA-based satellite network is taken into consideration from the perspective of practical scenarios. We first derive new exact expressions of outage probability for the p-th terrestrial user and provide the corresponding asymptotic analysis results. The diversity order of zero and p are achieved by the p-th terrestrial user with ipSIC and perfect successive interference cancellation (pSIC), respectively. Finally, the presented simulation results show that: 1) On the condition of pSIC, the outage behaviors of NOMA-based satellite network are superior to that of orthogonal multiple access; 2) With the value of residual interference increasing, the outage performance of terrestrial users with ipSIC is becoming worse seriously; and 3) Infrequent light shadowing of Shadowed-Rician fading brings the better outage probability compared to frequent heavy and average shadowing.

cs.IT↗

arXiv2019

Secure Communications in a Unified Non-Orthogonal Multiple Access Framework

This paper investigates the impact of physical layer secrecy on the performance of a unified non-orthogonal multiple access (NOMA) framework, where both external and internal eavesdropping scenarios are examined. The spatial locations of legitimate users (LUs) and eavesdroppers are modeled by invoking stochastic geometry. To characterize the security performance, new exact and asymptotic expressions of secrecy outage probability (SOP) are derived for both code-domain NOMA (CD-NOMA) and power-domain NOMA (PD-NOMA), in which imperfect successive interference cancellation (ipSIC) and perfect SIC (pSIC) are taken into account. For the external eavesdropping scenario, the secrecy diversity orders by a pair of LUs (the n-th user and m-th user) for CD/PD-NOMA are obtained. Analytical results make known that the diversity orders of the $n$-th user with ipSIC/pSIC for CD-NOMA and PD-NOMA are equal to zero/K and zero/one, respectively. The diversity orders of the m-th user are equal to K/one for CD/PD-NOMA. For the internal eavesdropping scenario, we examine the analysis of secrecy diversity order and observe that the m-th user to wiretap the n-th user with ipSIC/pSIC for CD-NOMA and PD-NOMA provide the diversity orders of zero/K and zero/one, respectively, which is consistent with external eavesdropping scenario. Numerical results are present to confirm the accuracy of the analytical results developed and show that: i) The secrecy outage behavior of the $n$-th user is superior to that of the m-th user; ii) By increasing the number of subcarriers, CD-NOMA is capable of achieving a larger secrecy diversity gain compared to PD-NOMA.

cs.IT↗

arXiv2018

On the structure of $λ$-Cantor set with overlaps

Given $λ\in(0, 1)$, let $E_λ$ be the self-similar set generated by the iterated function system $\{x/3,(x+λ)/3,(x+2)/3\}$. Then $E_λ$ is a self-similar set with overlaps. We obtain the necessary and sufficient condition for $E_λ$ to be totally self-similar, which is a concept first introduced by Broomhead, Montaldi, and Sidorov in 2004. When $E_λ$ is totally self-similar, all its generating IFSs are investigated, and the size of the set of points having finite triadic codings is determined. Besides, we give some properties of the spectrum of $E_λ$ and show that the spectrum of $E_λ$ vanishes if and only if $λ$ is irrational.

math.DS↗

arXiv2017

Tests of Cold Atom Clock in Orbit

Since the atomic clock was invented, its performance has been improved for one digit every decade until 90s of last century when the traditional atomic clock almost reached its limit. With laser cooled atoms, the performance can be further improved, and nowadays the cold atom based clocks are widely used as primary frequency standards. Such a kind of cold atom clocks has great applications in space. This paper presents the design and tests of a cold atom clock (CAC) operating in space. In microgravity, the atoms are cooled, trapped, launched and finally detected after being interrogated by microwave field with Ramsey method. The results of laser cooling of atoms in microgravity in orbit are presented and compared with that on ground for the first time. That the full width at half maximum (FWHM) of obtained central Ramsey fringes varies linearly with launching velocity of cold atoms shows the effects of microgravity. With appropriate parameters, a closed-loop locking of the CAC is realized in orbit and the estimated short term frequency stability of $3.0\times 10 ^{-13}/\sqrt{τ}$ has been reached.

physics.atom-ph↗