Tucker Decomposition For Rotated Codebook in 3D MIMO System Under Spatially Correlated Channel

This correspondence proposes a new rotated codebook for three-dimensional (3D) multi-input-multi-output (MIMO) system under spatially correlated channel. To avoid the problem of high dimensionality led by large antenna array, the rotation matrix in the rotated codebook is proposed to be decomposed by Tucker decomposition into three lowdimensional units, i.e., statistical channel direction information in horizontal and vertical directions respectively, and statistical channel power in the joint horizontal and vertical direction. A closed-form suboptimal solution is provided to reduce the computational complexity in Tucker decomposition. The proposed codebook has a significant dimension reduction from conventional rotated codebooks, and is applicable for 3D MIMO system with arbitrary form of antenna array. Simulation results demonstrate that the proposed codebook works very well for various 3D MIMO systems.Comment: accepted by IEEE Transactions on Vehicular Technolog

Uniformly expanding vacuum: a possible interpretation of the dark energy

Following the spirit of the equivalence principle, we take a step further to recognize the free fall of the observer as a method to eliminate causes that would lead the perceived vacuum to change its original state. Thus, it is expected that the vacuum should be in a rigid Minkowski state or be uniformly expanding. By carefully investigating the impact on measurement caused by the expansion, we clarify the exact meaning of the uniformly expanding vacuum and find that this proposal may be able to explain the current observations of an accelerating universe.Comment: 5 pages, accepted by Physics of the Dark Univers

Emergent cosmic space in Rastall theory

Padmanabhan's emergent cosmic space proposal is employed to study the Rastall theory which involves modifying the conservation law of energy-momentum tensor. As a necessary element for this approach, we firstly propose a modified Komar energy which reflects the evolution of the energy-momentum itself in the case of a perfect fluid. After that, an expansion law is invoked to reobtain the Friedmann equation in this theory.Comment: 8 pages, no figures, published version in CQ

Generalized Hodge dual for torsion in teleparallel gravity

For teleparallel gravity in four dimensions, Lucas and Pereira have shown that a generalized Hodge dual for torsion tensor can be defined with coefficients determined by mathematical consistency. In this paper, we demonstrate that a direct generalization to other dimensions fails and no new generalized Hodge dual operator could be given. Furthermore, if one enforces the definition of a generalized Hodge dual to be consistent with the action of teleparallel gravity in general dimensions, the basic identity for any sensible Hodge dual would require an \textit{ad hoc} definition for the second Hodge dual operation which is totally unexpected. Therefore, we conclude that at least for the torsion tensor, the observation of Lucas and Pereira only applies to four dimensions.Comment: 12 pages, corrected typos, rearranged reference

A modified variational principle for gravity in modified Weyl geometry

The usual interpretation of Weyl geometry is modified in two senses. First, both the additive Weyl connection and its variation are treated as (1, 2) tensors under the action of Weyl covariant derivative. Second, a modified covariant derivative operator is introduced which still preserves the tensor structure of the theory. With its help, the Riemann tensor in Weyl geometry can be written in a more compact form. We justify this modification in detail from several aspects and obtain some insights along the way. By introducing some new transformation rules for the variation of tensors under the action of Weyl covariant derivative, we find a Weyl version of Palatini identity for Riemann tensor. To derive the energy-momentum tensor and equations of motion for gravity in Weyl geometry, one naturally applies this identity at first, and then converts the variation of additive Weyl connection to those of metric tensor and Weyl gauge field. We also discuss possible connections to the current literature on Weyl-invariant extension of massive gravity and the variational principles in f(R) gravity.Comment: 16 pages. Minor correction

Hidden conformal symmetry of extremal Kaluza-Klein black hole in four dimensions

We study the hidden conformal symmetry of four-dimensional extremal Kaluza-Klein black hole. The scalar Laplacian corresponding to the radial equation in the near-region is rewritten in terms of the $SL(2,\mathbb R)$ quadratic Casimir. Using the first law of black hole thermodynamics, this symmetry enables us to obtain the conjugate charges for the CFT side. The real-time correlators are also found to agree with the CFT expectations

A sphere theorem for Bach-flat manifolds with positive constant scalar curvature

We show a closed Bach-flat Riemannian manifold with a fixed positive constant scalar curvature has to be locally spherical if its Weyl and traceless Ricci tensors are small in the sense of either $L^\infty$ or $L^{\frac{n}{2}}$-norm. Compared with the complete non-compact case done by Kim, we apply a different method to achieve these results. These results generalize a rigidity theorem of positive Einstein manifolds due to M.-A.Singer. As an application, we can partially recover the well-known Chang-Gursky-Yang's $4$-dimensional conformal sphere theorem.Comment: 11 page

DEBIT: Distributed Energy Beamforming and Information Transfer for Multiway Relay Networks

In this paper, we propose a new distributed energy beamforming and information transfer (DEBIT) scheme for realizing simultaneous wireless information and power transfer (SWIPT) in multiway relay networks (MWRNs), where multiple single-antenna users exchange information via an energy-constrained single-antenna relay node. We investigate the optimal transceiver designs to maximize the achievable sum-rate or the harvested power. The resultant sum-rate maximization problem is non-convex and the global optimal solution can be obtained through a three-dimensional search in combination with conventional convex optimization. To reduce the computation complexity, a suboptimal DEBIT scheme is also proposed, for which the optimization problem becomes linear programming. The achievable sum-rate performance is analyzed and a closed-form lower bound is derived for the MWRN with a large number of users. Furthermore, we consider the harvested-power maximization problem under a target sum-rate constraint, and derive a lower bound of the average harvested power for MWRNs with a large number of users. Numerical results show that the DEBIT scheme significantly outperforms the conventional SWIPT and the derived lower bounds are tight.Comment: 8 page

A Dynamic Programming Implemented 2x2 non-cooperative Game Theory Model for ESS Analysis

Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this paper we present a dynamic programming implemented method to compute 2x2 non-cooperative finite resource allocation game's payoff matrix. We assume in one population there exists two types of individuals, aggressive and non-aggressive and each individual has equal and finite resource. The strength of individual could be described by a function of resource consumption in discrete development stages. Each individual undergoes logistic growth hence we divide the development into three stages: initialization, quasilinear growth and termination. We first discuss the theoretical frame of how to dynamic programming to calculate payoff matrix then give three numerical examples representing three different types of aggressive individuals and calculate the payoff matrix for each of them respectively. Based on the numerical payoff matrix we further investigate the evolutionary stable strategies (ESS) of the games.Comment: 9 pages 3 sub models to illustrate how dynamic programming is implemented to construct payoff matrix of 2x2 symmetric gam

Equivalence of SLNR Precoder and RZF Precoder in Downlink MU-MIMO Systems

The signal-to-leakage-and-noise ratio (SLNR) precoder is widely used for MU-MIMO systems in many works, and observed with improved performance from zeroforcing (ZF) precoder. Our work proofs SLNR precoder is completely equivalent to conventional regulated ZF (RZF) precoder, which has significant gain over ZF precoder at low SNRs. Therefore, with our conclusion, the existing performance analysis about RZF precoder can be readily applicable to SLNR precoder