Source Pulse Optimizations for UWB Radio Systems

Abstract

This paper presents optimization solutions for the source pulses in ultra-wide band (UWB) radio systems, which simultaneously consider the radiated pulse spectrum, the received pulse duration and the received pulse energy. An optimization model, or a functional, of the source pulse is established by defining the "usable energy" in the received pulse. By using the calculus of variations to extremize the functional, the optimization solutions are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation to obtain the optimized source pulses. As a numerical example, optimization is demonstrated for a simplified UWB radio system consisting of a voltage source with internal impedance, a termination load and two identical planar elliptical dipole antennas. Specially, the optimized results are also compared with several common pulse waveforms including the Gaussian pulse, the modulated Gaussian pulse and the Rayleigh pulse.