Convex Form Research Articles

Secrecy-Optimized Resource Allocation for Device-to-Device Communication Underlaying Heterogeneous Networks

Device-to-device (D2D) communications have recently attracted much attention for the potential capability to improve spectral efficiency (SE) underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D-worked user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource-allocation problem to maximize the secure capacity of DUEs for D2D communication underlaying HetNets, which consist of high-power nodes (HPNs) and low-power nodes (LPNs). The optimization objective function with transmit bit rate and power constraints, which is nonconvex and hard to directly derive, is first transformed into a matrix form. Then, the equivalent convex form of the optimization problem is derived according to Perron–Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of the Lagrange function. Numerical results show that the proposed radio resource-allocation solution significantly improves the secure capacity with a fast convergence speed.

A new non-iterative reconstruction method for the electrical impedance tomography problem

The electrical impedance tomography (EIT) problem consists in determining the distribution of the electrical conductivity of a medium subject to a set of current fluxes, from measurements of the corresponding electrical potentials on its boundary. EIT is probably the most studied inverse problem since the fundamental works by Calderón from the 1980s. It has many relevant applications in medicine (detection of tumors), geophysics (localization of mineral deposits) and engineering (detection of corrosion in structures). In this work, we are interested in reconstructing a number of anomalies with different electrical conductivity from the background. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives. It means that the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Thus, a trivial optimization step leads to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented, taking into account total and partial boundary measurements.

Optimal operation of stationary and mobile batteries in distribution grids

The trending integrations of Battery Energy Storage System (BESS, stationary battery) and Electric Vehicles (EV, mobile battery) to distribution grids call for advanced Demand Side Management (DSM) technique that addresses the scalability concerns of the system and stochastic availabilities of EVs. Towards this goal, a stochastic DSM is proposed to capture the uncertainties in EVs. Numerical approximation is then used to make the problem tractable. To accelerate the computational speed, the proposed DSM is tightly relaxed to a convex form using second-order cone programming. Furthermore, in light of the continuous increasing problem size, a distributed method with a guaranteed convergence is applied to shift the centralized computational burden to distributed controllers. To verify the proposed DSM, real-life EV data collected on UCLA campus is used to test the proposed DSM in an IEEE benchmark test system. Numerical results demonstrate the correctness and merits of the proposed approach.

Comparing performance sensitivity of retail and institutional mutual funds’ investment flows

In this paper, we examine and compare the form of the flow-performance relationship for U.S. retail and institutional mutual funds. We provide evidence that the convex form of the flow-performance function documented by previous research characterizes mostly the relationship in the upper region of the performance scale. In contrast, the flow-performance relationship for the low-performance region appears to be concave. Furthermore, we document that the observed convexity is more pronounced for retail funds, while the concavity can be mainly attributed to institutional funds.

Power Quality Constrained Optimal Management of Unbalanced Smart Microgrids During Scheduled Multiple Transitions Between Grid-Connected and Islanded Modes

In this paper, a novel power quality (PQ) constrained optimization framework for smart microgrids with nonlinear loads is proposed for scheduled multiple transitions between grid-connected and islanded modes. Loads, generation, and energy storage are optimally scheduled to maximize the overall microgrid profit, from selling energy to grid, while satisfying network and PQ constraints. Cost of power interruption to loads, steady-state frequency deviation during islanding, and power sharing among generators are considered. PQ and network constraints of three-phase unbalanced distribution microgrid are given in convex forms. Comprehensive simulation results are given for validating the proposed algorithm and effect of limiting total harmonic distortion on microgrid economics is investigated.

Resource Allocation and Interference Management for D2D-Enabled DL/UL Decoupled Het-Nets

In this paper, resource allocation and interference mitigation are investigated for heterogeneous networks where the lowest tier consists of device-to-device (D2D) cells. In order to alleviate dead-zone problem, we first consider downlink/uplink (DL/UL) decoupling user association and quantify its capability on interference management and network-wide D2D performance enhancement. Second, we propose an UL fractional frequency reuse scheme where subband (SB) bandwidths are adaptively determined based on: 1) user equipment (UE) density; 2) e-node-B (eNB) density; and 3) on/off switching frequency of small cells. Obtained results show that the adaptive method significantly reduces the number of outage users. Thereafter, a novel concatenated bi-partite matching (CBM) method is proposed for joint SB assignment (SA) and resource block allocation (RA) of cellular UEs. Numerical results show that the CBM provides a close performance to exhaustive solution with greatly reduced running time. The CBM is then extended to a centralized mode selection, SA, and RA for D2D cells. Alternatively, we develop offline and online semi-distributed approaches where a D2D-cell can reuse white-list RBs (WRBs), which are not occupied by the adjacent small cells. In the former, D2D-cell members are not aware of intra-cell and inter-cell interference and uniformly distribute their maximum permissible power to WRBs. In the latter, we put D2D sum rate maximization into a convex form by exploiting the proximity gain of D2D UEs. Online distributed solution is then developed by message passing of dual variables and consistency prices. Finally, virtues and drawbacks of the developed approaches are compared and explained.

Energy-Efficient Joint Power Allocation in Uplink Massive MIMO Cognitive Radio Networks With Imperfect CSI

In this paper, a joint pilot and data power allocation problem with max-min fair energy efficiency (EE) guarantee in the uplink massive multiple-input multiple-output cognitive radio networks is investigated. Given the fractional objective function, channel estimation errors, and inter-user interference, the joint allocation problem is formulated as a nonconvex and NP-hard problem. To tackle this, we transform the original problem into its convex form by introducing auxiliary variables and variable substitution, and then address it with the help of the Lagrangian dual method. Since the optimization variables are interrelated and interact on each other, it is difficult to directly obtain the closed-form solution to this problem. To settle this issue, we propose an alternative iterative algorithm to achieve the optimal power policy by a gradient-based adaption method, with its corresponding optimal Lagrangian multipliers obtained by the subgradient method. Numerical results show that the proposed approach has the best minimum EE performance and decent spectral efficiency performance. Besides, compared with the other schemes, significant saving in total transmit power and good cognitive user fairness are achieved by the proposed algorithm.

Synoptic climatology of fog in selected locations of southern Poland (1966–2015)

Abstract This paper investigates fog frequency in southern Poland in relation to various topography (concave and convex forms) and atmospheric circulation types. It also discusses long-term variability in the annual and seasonal number of days with fog. Daily information on fog occurrence was taken from three high quality synoptic stations representing various landforms: Kraków-Balice (bottom of the hollow), Katowice-Muchowiec (Silesian Upland) and Bielsko-Aleksandrowice (summit of Carpathian Foothill). In the central part of southern Poland during the last 50 years (1966-2015) fog occurred on average during 53-67 days a year. The annual number of foggy days in Kraków (67 days) located in a structural basin was by 14-15 days higher than in Bielsko (53 days) situated in the Silesian Foothills. In the annual course, high fog occurrence (above 6 days per month) was observed from September to January, with the maximum in Kraków (10 days in October). At every station the monthly minimum of fog occurrence fell in July (2 days). In summer and spring the highest probability of fog occurrence was found on days with anticyclonic types and air advection from the northeastern (Na, NEa) and eastern (Ea, SEa) sectors. In autumn, a high probability was also found for the anticyclonic types with advection of air mass from the eastern and southern sectors. In the Carpathian Foothills (Bielsko) the probability of fog occurrence in winter was significantly enhanced only for the cyclonic types with air advection from the eastern sector (NEc, Ec, SEc) and nonadvective types Cc (cyclone centre) and Bc (cyclonic trough). Trends in the fog frequency were mostly insignificant. The only significant decreasing trend was found in Kraków on the annual scale and in summer when fog frequency was low.

The technology of preparing green coating by conducting micro-arc oxidation on AZ91D magnesium alloy

Abstract Micro-arc oxidation was applied to AZ91D magnesium alloy by taking K2Cr2O7 as the colouring salt in the silicate system. It was shown that the green coating obtained through performing micro-arc oxidation on magnesium alloy consisted of Mg, Mg2SiO4, MgO, and MgCr2O4 based on analysis of X-ray diffraction (XRD), and scanning electron microscopy (SEM). Among which, MgCr2O4 was the colouring salt; there were something in the lamellar, pit, and convex forms found on the surface of the coating. The coating consisted of a porous, and a compact, layer from the outside to the inside. As demonstrated, the colour of the coating depended on the K2Cr2O7 concentration: it became gradually deeper with the addition of K2Cr2O7 and the increasing micro-arc oxidation time. The corrosion resistance and hardness of the green coating were greater than that of the matrix.

Heat conduction with fractional Cattaneo–Christov upper-convective derivative flux model

Fractional order derivatives are global operators for which the time fractional order derivative possesses memory character while the space ones reflects non-local behavior. In this paper, a new time and space fractional Cattaneo–Christov upper-convective derivative flux heat conduction model is suggested where the space fractional derivative is characterized by the weight coefficient of forward versus backward transition probability. Governing equation is formulated and solved by L1-approximation and shifted Grünwald formula. Results show that the fractional parameters, time and location parameters, relaxation parameter, weight coefficient and convection velocity have remarkable impacts on heat transfer characteristics. Temperature distribution profiles are monotonically decreasing in a concave form versus time fractional parameter with existing of relaxation parameter, while in a convex form with space fractional parameter evolution under three special conditions, i.e., the right region, the larger weight coefficient (γ ≥ 0.5) and smaller convection parameter u.

Multiplicity of periodic orbits for dynamically convex contact forms

We give a sharp lower bound for the number of geometrically distinct contractible periodic orbits of dynamically convex Reeb flows on prequantizations of symplectic manifolds that are not aspherical. Several consequences of this result are obtained, like a new proof that every bumpy Finsler metric on $$S^n$$ carries at least two prime closed geodesics, multiplicity of elliptic and non-hyperbolic periodic orbits for dynamically convex contact forms with finitely many geometrically distinct contractible closed orbits and precise estimates of the number of even periodic orbits of perfect contact forms. We also slightly relax the hypothesis of dynamical convexity. A fundamental ingredient in our proofs is the common index jump theorem due to Y. Long and C. Zhu.

Analytical investigation on thermal-induced warpage behavior of ultrathin chip-on-flex (UTCOF) assembly

The serious warpage issues of ultrathin chip-on-flex (UTCOF) assembly induced by mismatched thermal stresses have greatly affected the mechanical stability and reliability of emerging ultrathin chip packaging technology. Currently, a theoretical prediction as a convenient and straightforward approach is still lacked for describing effectively the thermal-mechanical behavior of UTCOF during the adhesive curing and cooling process. In consideration of the adhesive thickness approximating to ultrathin chip and flexible substrate thickness, we develop a layerwise-model of ultrathin chip-adhesive-flex structure under plain strain condition, where the behavior of thick adhesive bonding can be described precisely through increasing the subdivided mathematical plies. Further, the analytical results show that the concave and convex forms of ultrathin chip warpage yield at the end of the curing and cooling process respectively. Meanwhile, the effects of its structure dimensions and material properties are also revealed for discussing a way to relieve the extent of ultrathin chip warpage. Additionally, in order to verify the validity of the theoretical prediction, we also introduce the corresponding numerical technique and experimental method. These results suggest that a kind of rigid and ultrathin flexible substrate such as metal foil should be adopted for small warpage of ultrathin assembly.

A joint time synchronization and localization method without known clock parameters

Time synchronization and localization should be jointly conducted for time-related localization model when the local clock of sensor node has clock drift with respect to the real clock for imperfect hardware. A joint estimation method for the source locations and clock parameters is proposed by using the time difference of arrival (TDOA) measurements. The proposed joint estimation method does not rely on the clock parameters of anchor nodes. To estimate the clock parameters and source locations, the noncooperative linear estimators including unconstrained weighting least square (UWLS) and constrained weighting least square (CWLS) are put forward. The noncooperative and cooperative semidefinite programming (SDP) algorithms are also designed by relaxing the optimization function of maximum likelihood (ML) estimator as convex form. The proposed UWLS, CWLS and SDP algorithms provide the joint estimates for the source locations and clock parameters and avoid the shortcoming of ML estimator which requires an initial solution. The simulations show that the cooperative approaches provide better accuracy performance compared with the noncooperative approaches including the linear UWLS and CWLS estimators since more measurements are involved into the model. The cooperative SDP algorithm provides more robust estimates for the clock parameters and source locations especially when the source node is outside of the convex hull of the anchor nodes.

Radio Frequency Interference Suppression Algorithm Based on SOCP in OTHR

Sky wave over-the-horizon radar is easily affected by radio frequency interference (RFI) since it shares the high-frequency band with many radio services. Among the existing methods, spatial filtering method is ineffective to suppress the mainlobe RFI, and time-frequency method usually weakens the target signal while rejecting RFI. In this paper, we notice that, before matched filtering, RFI is usually a narrowband signal but the target echo is a broadband signal. According to this feature, an efficient RFI suppression algorithm is proposed by designing a new matched waveform based on a constrained optimization problem. Further, we show that this problem can be reformulated in a convex form as the second-order cone program and solved efficiently using the well-established interior point method. Compared with the existing methods, the proposed algorithm can suppress the RFI from any direction of arrival and get a higher output signal-to-interference-plus-noise ratio. Experimental results demonstrate that the proposed algorithm outperforms the existing methods.

A parametric propagator for pairs of Sum constraints with a discrete convexity property

We introduce a propagator for pairs of Sum constraints, where the expressions in the sums respect a form of convexity. This propagator is parametric and can be instantiated for various concrete pairs, including Deviation, Spread, and the conjunction of Linear≤ and Among. We show that despite its generality, our propagator is competitive in theory and practice with state-of-the-art propagators.

Convex Incentives and Tail Risk-Taking

This paper examines how convexity in incentives affects tail risks across and within different types of investment funds. The literature has documented different forms of convexity that a fund manager faces: discounts in closed-end funds, tournaments and fund flow-performance relation in open-end funds, and high-water mark provisions in hedge funds. Sorting funds by the degree of convexity and comparing skewness between the group with the most convexity and the group with the least convexity, we conclude that convexity affects fund tail risks. This result suggests that both implicit and explicit convexities provide incentives for fund managers to take systematic and idiosyncratic bets with tail risks.

Energy‐efficiency resource allocation for cognitive heterogeneous networks with imperfect channel state information

In this study, the authors focus on the downlink resource allocation to optimise energy-efficiency (EE) of orthogonal frequency division multiplexing-based cognitive heterogeneous network (HetNet), where network service providers operate multi-radio access technologies. A more practical case is considered, in which imperfect channel state information (CSI) is available for wireless channels between secondary base stations and secondary users (SUs), primary users (PUs). Since imperfect CSI may result in outage in secondary networks and make collision occur in primary networks, a joint subcarrier and power allocation scheme for the cognitive HetNet is proposed to guarantee quality of service requirements for both SUs and PUs in probabilistic manners. Then the probabilistic EE optimisation scheme is approximated into a deterministic convex form, and the optimal solutions for the scheme are derived by double-loop iteration method. Afterwards, the authors develop a low-complexity algorithm in the presence of imperfect CSI with a small reduction of system performance. Simulation results are provided to show the impact of channel estimation error on the EE optimisation problem and to highlight the performance improvement from considering channel estimation error in the joint subcarrier and power allocation scheme for the cognitive HetNet system.

Joint Beamforming, Power, and Channel Allocation in Multiuser and Multichannel Underlay MISO Cognitive Radio Networks

In this paper, we consider joint beamforming, power, and channel allocation in a multiuser and multichannel underlay multiple-input–single-output (MISO) cognitive radio network (CRN). In this system, the primary users' spectrum can be reused by secondary-user transmitters (SU-TXs) to maximize spectrum utilization, whereas intrauser interference is minimized by implementing beamforming at each SU-TX. After formulating the joint optimization problem as a nonconvex mixed-integer nonlinear programming problem, we propose a solution that consists of two stages. In the first stage, a feasible solution for power allocation and beamforming vectors is derived under a given channel allocation by converting the original problem into a convex form with an introduced optimal auxiliary variable and a semidefinite relaxation approach. In the second stage, two explicit searching algorithms, i.e., genetic algorithm (GA) and simulated annealing (SA)-based algorithm, are proposed to determine suboptimal channel allocations. Simulation results show that the beamforming and power and channel allocation with SA algorithm can achieve a close-to-optimal sum rate while having lower computational complexity compared with the beamforming and power and channel allocation with the GA algorithm. Furthermore, our proposed allocation scheme has significant improvement in achievable sum rate compared with the existing zero-forcing beamforming.

A Unified Successive Pseudoconvex Approximation Framework

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively refined approximate problems, each of which is much easier to solve than the original problem. To achieve convergence, the approximate problem only needs to exhibit a weak form of convexity, namely, pseudo-convexity. We show that the proposed framework not only includes as special cases a number of existing methods, for example, the gradient method and the Jacobi algorithm, but also leads to new algorithms which enjoy easier implementation and faster convergence speed. We also propose a novel line search method for nondifferentiable optimization problems, which is carried out over a properly constructed differentiable function with the benefit of a simplified implementation as compared to state-of-the-art line search techniques that directly operate on the original nondifferentiable objective function. The advantages of the proposed algorithm are shown, both theoretically and numerically, by several example applications, namely, MIMO broadcast channel capacity computation, energy efficiency maximization in massive MIMO systems and LASSO in sparse signal recovery.

Robust beamforming and power splitting design in MISO SWIPT downlink system

In this study, the authors consider simultaneous wireless information and power transfer (SWIPT) in a multiple-input-single-output (MISO) downlink system, where power splitting scheme is considered for each user of this system. Since channel state information of each user cannot be available at the transmitter, robust beamforming for SWIPT in the MISO downlink system is presented by incorporating with different types of channel uncertainty models. The authors first formulate the robust power minimisation problem subject to the signal-to-inference-plus-noise ratio (SINR) and energy harvesting (EH) constraints by incorporating two Gaussian channel uncertainties. The original problem is not convex in terms of channel uncertainties, and cannot be solved efficiently. The authors employ the well-known Bernstein-type inequality and Gaussian error function to make probability based constraints tractable, respectively, in order to recast the original problem as the convex form. Moreover, the robust power minimisation problem with the probability based SINR and EH constraints is formulated by incorporating random distribution with known error mean and covariance matrix. By exploiting conditional value-at-risk functional and semi-definite relaxation, this optimisation problem is relaxed as the convex form. Finally, numerical results are provided to validate the performance of these proposed robust schemes.