Determination of matrix potential from scattering matrix

(i) For the matrix Schr\"{o}dinger operator on the half line, it is shown that if the potential exponentially decreases fast enough then only the scattering matrix uniquely determines the self-adjoint potential and the boundary condition. (ii) For the matrix Schr\"{o}dinger operator on the full line, it is shown that if the potential exponentially decreases fast enough then the scattering matrix (or equivalently, the transmission coefficient and reflection coefficient) uniquely determine the potential. If the potential vanishes on $(-\infty,0)$ then only the left reflection coefficient uniquely determine the potential.Comment: 9 page

Inverse spectral problems for the Sturm-Liouville operator with discontinuity

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra can uniquely determine the potential and all parameters in discontinuous conditions and boundary conditions. For the case $b<1/2$, parts of either one or two spectra can uniquely determine the potential and a part of parameters.Comment: 13 page

Solvability of the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line

In this work we study the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line. We provide the necessary and sufficient conditions for the solvability of the inverse scattering problem.Comment: 29 page

Inverse resonance problems for the Schroedinger operator on the real line with mixed given data

In this work, we study inverse resonance problems for the Schr\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown that if the potential is known a priori on $[0,1/2]$, then the unique recovery of the potential on the whole interval from all eigenvalues and resonances is valid. (ii) If the potential is known a priori on $[0,a]$, then for the case $a>1/2$, infinitely many eigenvalues and resonances can be missing for the unique determination of the potential, and for the case $a<1/2$, all eigenvalues and resonances plus a part of so-called sign-set can uniquely determine the potential. (iii) It is also shown that all eigenvalues and resonances, together with a set of logarithmic derivative values of eigenfunctions and wave-functions at $1/2$, can uniquely determine the potential.Comment: 12 page

Improved Performance of RF Energy Powered Wireless Sensor Node with Cooperative Beam Selection

RF energy harvesting is a promising potential solution to provide convenient and perpetual energy supplies to low-power wireless sensor networks. In this paper, we investigate the energy harvesting performance of a wireless sensor node powered by harvesting RF energy from existing multiuser MIMO system. Specifically, we propose a random unitary beamforming (RUB) based cooperative beam selection scheme to enhance the energy harvesting performance at the sensor. Under a constant total transmission power constraint, the multiuser MIMO system tries to select a maximal number of active beams for data transmission, while satisfying the energy harvesting requirement at the sensor. We derive the exact closed-form expression for the distribution function of harvested energy in a coherence time over Rayleigh fading channels. We further investigate the performance tradeoff of the average harvested energy at the sensor versus the sum-rate of the multiuser MIMO system.Comment: 17pages, 5 figure

Reconstruction and Solvability for Discontinuous Hochstadt-Lieberman Problems

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in the right boundary condition are given. Half-inverse problems are studied, that consist in recovering the potential on the left half-interval and the left boundary condition from the eigenvalues. If the discontinuity belongs to the left half-interval, the position and the parameters of the discontinuity also can be reconstructed. In this paper, we provide reconstructing algorithms and prove existence of solutions for the considered inverse problems. Our approach is based on interpolation of entire functions

Recovering Nonlocal Differential Pencils

Inverse problems for differential pencils with nonlocal conditions are investigated. Several uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl function and Borg's inverse problem for the classical Sturm-Liouville operator.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1410.2017. substantial text overlap with arXiv:1503.0174

Recovering Dirac Operator with Nonlocal Boundary Conditions

In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl function and Borg's inverse problem for the classical Dirac operator.Comment: 11 page

Wireless Transmission of Big Data: Data-oriented Performance Limits and Their Applications

The growing popularity of big data and Internet of Things (IoT) applications bring new challenges to the wireless communication community. Wireless transmission systems should more efficiently support the large amount of data traffics from diverse types of information sources. In this article, we introduce a novel data-oriented approach for the design and optimization of wireless transmission strategies. Specifically, we define new performance metrics for individual data transmission session and apply them to compare two popular channel-adaptive transmission strategies. We develop several interesting and somewhat counterintuitive observations on these transmission strategies, which would not be possible with conventional approach. We also present several interesting future research directions that are worth pursuing with the data-oriented approach.Comment: 14 pages, 4 figure

Characterizing Energy Efficiency of Wireless Transmission for Green Internet of Things: A Data-Oriented Approach

The growing popularity of Internet of Things (IoT) applications brings new challenges to the wireless communication community. Numerous smart devices and sensors within IoT will generate a massive amount of short data packets. Future wireless transmission systems need to support the reliable transmission of such small data with extremely high energy efficiency. In this article, we introduce a novel data-oriented approach for characterizing the energy efficiency of wireless transmission strategies for IoT applications. Specifically, we present new energy efficiency performance limits targeting at individual data transmission sessions. Through preliminary analysis on two channel-adaptive transmission strategies, we develop several important design guidelines on green transmission of small data. We also present several promising future applications of the proposed data-oriented energy efficiency characterization.Comment: 14 pages, 4 figure