Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by-product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory.Comment: 28 page

Optimal Beamforming for Physical Layer Security in MISO Wireless Networks

A wireless network of multiple transmitter-user pairs overheard by an eavesdropper, where the transmitters are equipped with multiple antennas while the users and eavesdropper are equipped with a single antenna, is considered. At different levels of wireless channel knowledge, the problem of interest is beamforming to optimize the users' quality-of-service (QoS) in terms of their secrecy throughputs or maximize the network's energy efficiency under users' QoS. All these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors. The paper develops path-following computational procedures of low-complexity and rapid convergence for the optimal beamforming solution. Their practicability is demonstrated through numerical examples

Real-time Optimal Resource Allocation for Embedded UAV Communication Systems

We consider device-to-device (D2D) wireless information and power transfer systems using an unmanned aerial vehicle (UAV) as a relay-assisted node. As the energy capacity and flight time of UAVs is limited, a significant issue in deploying UAV is to manage energy consumption in real-time application, which is proportional to the UAV transmit power. To tackle this important issue, we develop a real-time resource allocation algorithm for maximizing the energy efficiency by jointly optimizing the energy-harvesting time and power control for the considered (D2D) communication embedded with UAV. We demonstrate the effectiveness of the proposed algorithms as running time for solving them can be conducted in milliseconds.Comment: 11 pages, 5 figures, 1 table. This paper is accepted for publication on IEEE Wireless Communications Letter