Optimal Power Allocation for Artificial Noise under Imperfect CSI against Spatially Random Eavesdroppers

In this correspondence, we study the secure multiantenna transmission with artificial noise (AN) under imperfect channel state information in the presence of spatially randomly distributed eavesdroppers. We derive the optimal solutions of the power allocation between the information signal and the AN for minimizing the secrecy outage probability (SOP) under a target secrecy rate and for maximizing the secrecy rate under a SOP constraint, respectively. Moreover, we provide an interesting insight that channel estimation error affects the optimal power allocation strategy in opposite ways for the above two objectives. When the estimation error increases, more power should be allocated to the information signal if we aim to decrease the rate-constrained SOP, whereas more power should be allocated to the AN if we aim to increase the SOP-constrained secrecy rate.Comment: 7 pages, 6 figure

Improving Anti-Eavesdropping Ability without Eavesdropper's CSI: A Practical Secure Transmission Design Perspective

This letter studies the practical design of secure transmissions without knowing eavesdropper's channel state information (ECSI). An ECSI-irrelevant metric is introduced to quantize the intrinsic anti-eavesdropping ability (AEA) that the transmitter has on confronting the eavesdropper via secrecy encoding together with artificial-noise-aided signaling. Non-adaptive and adaptive transmission schemes are proposed to maximize the AEA with the optimal encoding rates and power allocation presented in closed-form expressions. Analyses and numerical results show that maximizing the AEA is equivalent to minimizing the secrecy outage probability (SOP) for the worst case by ignoring eavesdropper's receiver noise. Therefore, the AEA is a useful alternative to the SOP for assessing and designing secure transmissions when the ECSI cannot be prior known.Comment: 4 pages, 2 figures, to be published on IEEE Wireless Communications Letters (WCL

Delivery-Secrecy Tradeoff for Cache-Enabled Stochastic Networks: Content Placement Optimization

Wireless caching has been widely recognized as a promising technique for efficient content delivery. In this paper, by taking different file secrecy levels into consideration, physical-layer security oriented content placement is optimized in a stochastic cache-enabled cellular network. We propose an analytical framework to investigate the nontrivial file delivery-secrecy tradeoff. Specifically, we first derive the closed-form expressions for the file hit and secrecy probabilities. The global optimal probabilistic content placement policy is then analytically derived in terms of hit probability maximization under file secrecy constraints. Numerical results are demonstrated to verify our analytical findings and show that the targeted file secrecy levels are crucial in balancing the file delivery-secrecy tradeoff.Comment: 5 pages, 4 figures, accepted to be published in IEEE Transactions on Vehicular Technolog

LpL^p estimates for fractional schrodinger operators with kato class potentials

Let $\alpha>0$, $H=(-\triangle)^{\alpha}+V(x)$, $V(x)$ belongs to the higher order Kato class K_{2\alpha}(\mathbbm{R}^n). For $1\leq p\leq \infty$, we prove a polynomial upper bound of $\|e^{-itH}(H+M)^{-\beta}\|_{L^p, L^p}$ in terms of time $t$. Both the smoothing exponent $\beta$ and the growth order in $t$ are almost optimal compared to the free case. The main ingredients in our proof are pointwise heat kernel estimates for the semigroup $e^{-tH}$. We obtain a Gaussian upper bound with sharp coefficient for integral $\alpha$ and a polynomial decay for fractal $\alpha$.Comment: 37 pages. Final version, to appear in J. Differential Equation

Secure and Energy-Efficient Transmissions in Cache-Enabled Heterogeneous Cellular Networks: Performance Analysis and Optimization

This paper studies physical-layer security for a cache-enabled heterogeneous cellular network comprised of a macro base station and multiple small base stations (SBSs). We investigate a joint design on caching placement and file delivery for realizing secure and energy-efficient transmissions against randomly distributed eavesdroppers. We propose a novel hybrid "most popular content" and "largest content diversity" caching placement policy to distribute files of different popularities. Depending on the availability and placement of the requested file, we employ three cooperative transmission schemes, namely, distributed beamforming, frequency-domain orthogonal transmission, and best SBS relaying, respectively. We derive analytical expressions for the connection outage probability and secrecy outage probability for each transmission scheme. Afterwards, we design the optimal transmission rates and caching allocation successively to achieve a maximal overall secrecy throughput and secrecy energy efficiency, respectively. Numerical results verify the theoretical analyses and demonstrate the superiority of the proposed hybrid caching policy.Comment: 13 pages in double-column, 9 figures, accepted for publication on IEEE Transactions on Communication

Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals

Cooper instability associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead Cooper instability can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the Cooper instability at zero chemical potential, which in principle are harmful to Cooper instability although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the Cooper instability is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.Comment: 18 pages; 14 figure

On the Relations of Correlation Filter Based Trackers and Struck

In recent years, two types of trackers, namely correlation filter based tracker (CF tracker) and structured output tracker (Struck), have exhibited the state-of-the-art performance. However, there seems to be lack of analytic work on their relations in the computer vision community. In this paper, we investigate two state-of-the-art CF trackers, i.e., spatial regularization discriminative correlation filter (SRDCF) and correlation filter with limited boundaries (CFLB), and Struck, and reveal their relations. Specifically, after extending the CFLB to its multiple channel version we prove the relation between SRDCF and CFLB on the condition that the spatial regularization factor of SRDCF is replaced by the masking matrix of CFLB. We also prove the asymptotical approximate relation between SRDCF and Struck on the conditions that the spatial regularization factor of SRDCF is replaced by an indicator function of object bounding box, the weights of SRDCF in its loss item are replaced by those of Struck, the linear kernel is employed by Struck, and the search region tends to infinity. Extensive experiments on public benchmarks OTB50 and OTB100 are conducted to verify our theoretical results. Moreover, we explain how detailed differences among SRDCF, CFLB, and Struck would give rise to slightly different performances on visual sequence

Salient Object Detection: A Discriminative Regional Feature Integration Approach

Salient object detection has been attracting a lot of interest, and recently various heuristic computational models have been designed. In this paper, we formulate saliency map computation as a regression problem. Our method, which is based on multi-level image segmentation, utilizes the supervised learning approach to map the regional feature vector to a saliency score. Saliency scores across multiple levels are finally fused to produce the saliency map. The contributions lie in two-fold. One is that we propose a discriminate regional feature integration approach for salient object detection. Compared with existing heuristic models, our proposed method is able to automatically integrate high-dimensional regional saliency features and choose discriminative ones. The other is that by investigating standard generic region properties as well as two widely studied concepts for salient object detection, i.e., regional contrast and backgroundness, our approach significantly outperforms state-of-the-art methods on six benchmark datasets. Meanwhile, we demonstrate that our method runs as fast as most existing algorithms

Adaptive Full-Duplex Jamming Receiver for Secure D2D Links in Random Networks

Device-to-device (D2D) communication raises new transmission secrecy protection challenges, since conventional physical layer security approaches, such as multiple antennas and cooperation techniques, are invalid due to its resource/size constraints. The full-duplex (FD) jamming receiver, which radiates jamming signals to confuse eavesdroppers when receiving the desired signal simultaneously, is a promising candidate. Unlike existing endeavors that assume the FD jamming receiver always improves the secrecy performance compared with the half-duplex (HD) receiver, we show that this assumption highly depends on the instantaneous residual self-interference cancellation level and may be invalid. We propose an adaptive jamming receiver operating in a switched FD/HD mode for a D2D link in random networks. Subject to the secrecy outage probability constraint, we optimize the transceiver parameters, such as signal/jamming powers, secrecy rates and mode switch criteria, to maximize the secrecy throughput. Most of the optimization operations are taken off-line and only very limited on-line calculations are required to make the scheme with low complexity. Furthermore, some interesting insights are provided, such as the secrecy throughput is a quasi-concave function. Numerical results are demonstrated to verify our theoretical findings, and to show its superiority compared with the receiver operating in the FD or HD mode only

On small set of one-way LOCC indistinguishability of maximally entangled states

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.Comment: 10 pages.Very recently, we became aware of related work \cite{Zhang2} in which the same $\lceil\frac{d}{2}\rceil+2$ states in $\mathbb{C}^d\otimes\mathbb{C}^d$ is proved to be one-way LOCC indistinguishable. arXiv admin note: text overlap with arXiv:1310.4220 by other autho