arXiv subjects

Zhirong Su

Publications and source records attributed to Zhirong Su.

3 recordsLinked to original sources

arXiv2026

Secure Beamforming for ISAC Systems Under Communication Eavesdropper and Sensing Eavesdropper

Due to great efficiency improvement in resource and hardware space, integrated sensing and communication (ISAC) has gained much attention. In the paper, the physical layer security (PLS) of ISAC system under communication eavesdropper together with sensing eavesdropper is investigated. The system secrecy rate is maximized by transmit beamforming design of communication and sensing signals when taking sensing security, sensing performance and transmit power constraint into consideration. To deal with the formulated non-convex optimization problem, the successive convex approximation (SCA) together with the first-order Taylor expansion and semidefinite relaxation (SDR) is utilized. Additionally, it is theoretically validated that the SDR does not yield sub-optimality in the paper. Thereafter, an iterated joint secure beamforming algorithm against communication and sensing eavesdroppers is proposed. Simulation results validate the effectiveness and advance of the proposed scheme.

cs.IT↗

arXiv2022

Generalize Hilbert operator acting on Dirichlet spaces

Let $μ$ be a positive Borel measure on the interval $[0,1)$. For $γ>0$, the Hankel matrix $\mathcal{H}_{μ,γ}=(μ_{n,k})_{n,k\geq0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_{n+k}=\int_{0}^{\infty}t^{n+k}dμ(t)$. formally induces the operator $$\mathcal{H}_{μ,γ}=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty}μ_{n,k}a_k\right)\frac{Γ(n+γ)}{n!Γ(γ)}z^n,$$ on the space of all analytic functions $f(z)=\sum_{k=0}^{\infty}{a_k}{z^k}$ in the unit disc $\mathbb{D}$. Following ideas from \cite{author3} and \cite{author4}, in this paper, for $0\leqα<2$, $2\leqβ<4$, $γ\geq1$. we characterize the measure $μ$ for which $\mathcal{H}_{μ,γ}$ is bounded(resp.,compact)from $\mathcal{D}_α$ into $\mathcal{D}_β$.

math.CV↗

arXiv2022

The range of Hilbert operator and Derivative-Hilbert operator acting on $H^1$

Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n,k})_{n,k\geq0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_n=\int_{[0,1)}t^{n}dμ(t)$. For $f(z)=\sum_{n=0}^{\infty}a_nz^n$ is an analytic function in $\mathbb{D}$, the Hilbert operator is defined by $$\mathcal{H}_μ(f)(z)=\sum_{n=0}^{\infty}\Bigg(\sum_{k=0}^{\infty}μ_{n,k}a_k\Bigg)z^n, \quad z\in \mathbb{D}.$$ The Derivative-Hilbert operator is defined as $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^{\infty}\Bigg(\sum_{k=0}^{\infty}μ_{n,k}a_k\Bigg)(n+1)z^n, \quad z\in \mathbb{D}.$$ In this paper, we determine the range of the Hilbert operator and Derivative-Hilbert operator acting on $H^{\infty}$.

math.CV↗