19,029 research outputs found
Pareto efficiency for the concave order and multivariate comonotonicity
In this paper, we focus on efficient risk-sharing rules for the concave
dominance order. For a univariate risk, it follows from a comonotone dominance
principle, due to Landsberger and Meilijson [25], that efficiency is
characterized by a comonotonicity condition. The goal of this paper is to
generalize the comonotone dominance principle as well as the equivalence
between efficiency and comonotonicity to the multi-dimensional case. The
multivariate setting is more involved (in particular because there is no
immediate extension of the notion of comonotonicity) and we address it using
techniques from convex duality and optimal transportation
An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces
This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality approach. As particular cases, we investigate the use of the prominent Tammer–Weidner nonlinear scalarizing functionals, without assuming any topology, in our context. We also derive numerical methods to obtain approximate minimal elements of families of finitely many sets by means of our obtained results
Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission with Statistical CSIT
As a key technology for future wireless networks, massive multiple-input
multiple-output (MIMO) can significantly improve the energy efficiency (EE) and
spectral efficiency (SE), and the performance is highly dependant on the degree
of the available channel state information (CSI). While most existing works on
massive MIMO focused on the case where the instantaneous CSI at the transmitter
(CSIT) is available, it is usually not an easy task to obtain precise
instantaneous CSIT. In this paper, we investigate EE-SE tradeoff in single-cell
massive MIMO downlink transmission with statistical CSIT. To this end, we aim
to optimize the system resource efficiency (RE), which is capable of striking
an EE-SE balance. We first figure out a closed-form solution for the
eigenvectors of the optimal transmit covariance matrices of different user
terminals, which indicates that beam domain is in favor of performing RE
optimal transmission in massive MIMO downlink. Based on this insight, the RE
optimization precoding design is reduced to a real-valued power allocation
problem. Exploiting the techniques of sequential optimization and random matrix
theory, we further propose a low-complexity suboptimal two-layer
water-filling-structured power allocation algorithm. Numerical results
illustrate the effectiveness and near-optimal performance of the proposed
statistical CSI aided RE optimization approach.Comment: Typos corrected. 14 pages, 7 figures. Accepted for publication on
IEEE Transactions on Signal Processing. arXiv admin note: text overlap with
arXiv:2002.0488
- …