NOMA-Based Collaborative Beam Hopping Frequency Allocation Mechanism for Future LEO Satellite Systems

Low Earth orbit(LEO) satellite systems provide terrestrial users with services that are not limited by geographical location. However, the conflict between existing allocation schemes and the business variability between beams is becoming increasingly prominent. Beam hopping technology allows for a more flexible and versatile approach to satellite resource allocation. This paper proposes a beam hopping pattern optimization scheme that jointly considers the interference threshold distance and beam service priority, reducing the inter-beam co-channel interference(CCI). In the cluster area, a non-orthogonal multiple access(NOMA)-based collaborative beam hopping(NCBH) scheme is proposed to minimize the cell-edge user(CEU) interference. Since there is a difference in channel gain between the CEU and cellcenter user(CCU), this scheme forms a NOMA cluster to perform power domain multiplexing and formulates a NOMA cluster pairing strategy according to the user location to reduce the CCI of the CEU. After NOMA cluster pairing, the optimal carrier frequency of the NOMA cluster is selected by a reinforcement learning algorithm. The simulation results verify the excellent performance of the proposed NCBH scheme regarding the user’s received power, transmission rate, and outage probability.

Graph Laplacian Matrix Learning from Smooth Time-Vertex Signal

In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.

Mobile channel estimation for MU-MIMO systems using KL expansion based extrapolation

In multi-user multiple input multiple output （MU-MIMO） systems, the outdated channel state information at the transmit- ter caused by channel time variation has been shown to greatly reduce the achievable ergodic sum capacity. A simple yet effec- tive solution to this problem is presented by designing a channel extrapolator relying on Karhunen-Loeve （KL） expansion of time- varying channels. In this scheme, channel estimation is done at the base station （BS） rather than at the user terminal （UT）, which thereby dispenses the channel parameters feedback from the UT to the BS. Moreover, the inherent channel correlation and the parsimonious parameterization properties of the KL expan- sion are respectively exploited to reduce the channel mismatch error and the computational complexity. Simulations show that the presented scheme outperforms conventional schemes in terms of both channel estimation mean square error （MSE） and ergodic capacity.

f-Harmonic Maps Within Bounded Distance from Quasi-isometric Maps

In this article,we prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from an f-harmonic map.

Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group

The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equation for the Gauss map is obtained,and it is shown that this equation is the complete integrability condition of the representation.

The Extension of the H^k Mean Curvature Flow in Riemannian Manifolds

In this paper,the authors consider a family of smooth immersions Ft : Mn→Nn+1of closed hypersurfaces in Riemannian manifold Nn+1with bounded geometry,moving by the Hkmean curvature flow.The authors show that if the second fundamental form stays bounded from below,then the Hkmean curvature flow solution with finite total mean curvature on a finite time interval [0,Tmax)can be extended over Tmax.This result generalizes the extension theorems in the paper of Li(see "On an extension of the Hkmean curvature flow,Sci.China Math.,55,2012,99–118").

Proper Submanifolds in Product Manifolds

The authors obtain various versions of the Omori-Yau's maximum principle on complete properly immersed submanifolds with controlled mean curvature in certain product manifolds,in complete Riemannian manifolds whose k-Ricci curvature has strong quadratic decay,and also obtain a maximum principle for mean curvature flow of complete manifolds with bounded mean curvature.Using the generalized maximum principle,an estimate on the mean curvature of properly immersed submanifolds with bounded projection in N1 in the product manifold N1 ×N2 is given.Other applications of the generalized maximum principle are also given.

A Rigidity Result of Spacelike Self-Shrinkers in Pseudo-Euclidean Spaces

In this paper, the author proves that the spacelike self-shrinker which is closed with respect to the Euclidean topology must be flat under a growth condition on the mean curvature by using the Omori-Yau maximum principle.

Ricci-Bourguignon Flow on Manifolds with Boundary

The authors consider the short time existence for Ricci-Bourguignon flow on manifolds with boundary.If the initial metric has constant mean curvature and satisfies some compatibility conditions,they show the short time existence of the Ricci-Bourguignon flow with constant mean curvature on the boundary.