This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigati...
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ISBN:
(纸本)9781728181929
This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various measures to evaluate the tightness of the solution procured by the convex relaxation approaches. Therefore, three tightness measures are leveraged to illustrate the performance of convex relaxation methods under different demand scenarios. The main issue of convex relaxation methods is recovering an optimal solution which is not necessarily feasible for the original non-convex problem in networks with cycles. Thus, a cycle measure is introduced to evaluate the performance of relaxation schemes. The presented case study investigates the merit of using various tightness measures to evaluate the performance of various relaxation methods under different circumstances.
The massive Multiple-input Multiple-output (MIMO) and Non-Orthogonal Multiple Access (NOMA) are considered as two key techniques for the coming 5G wireless communications. Through beam selection, the massive MIMO syst...
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ISBN:
(数字)9781728123455
ISBN:
(纸本)9781728123462
The massive Multiple-input Multiple-output (MIMO) and Non-Orthogonal Multiple Access (NOMA) are considered as two key techniques for the coming 5G wireless communications. Through beam selection, the massive MIMO systems can reduce the number of required radio-frequency (RF) chains while without distinct performance degradation, which can enhance energy efficiency of the systems. In order to further improve energy efficiency, in this paper, we propose an energy efficient power allocation design for beamspace based multi-user multiple-input single-output (MISO) NOMA systems. First, according to the beamspace channel state information (CSI) matrix obtained by beam selection, we get the precoding matrix through zero-forcing (ZF) method. Then we formulate the energy efficiency maximization (EEmax) optimization problem with power allocation considerations. Through sequential convex approximation (SCA) and second-order cone programming (SOCP), the original non-convex problem can be reformulated as a convex optimization problem. Finally, we choose iterative optimization algorithm to solve the reformulated problem. Numerical results show that the proposed power allocation design is effective in achieving better energy efficiency comparing with the conventional methods.
We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computati...
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We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.
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