Optimal waveform design via control theoretic concepts

This paper presents the formulation of a class of optimal signal design problems; in particular, the design of optimal “modulation≓ waveforms (under amplitude and energy constraints) to be used for the optimal estimation or prediction of the state of a linear dynamical system in the presence of Markov and white noise. The Kalman-Bucy theory is used to formulate an optimization problem in which the “state of the plant≓ is given by the elements of covariance matrices (which satisfy matrix Riccati differential equations), the “control≓ is related to the modulation signal, and the “cost≓ is a linear functional of the covariance matrix. The problem statement is in such a form so that the Maximum Principle of Pontryagin can be applied to obtain the necessary conditions and it is used to derive the so-called “on-off≓ principle. The results prove that under total energy and peak amplitude constraints, the optimal signal, as a function of time, must alternate between its peak-power and its zero-power levels. A set of matrix differential equations—with split boundary conditions—is also derived; the numerical solution of this set of equations can yield the explicit time-dependence of the optimal waveform

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201