Solutions for Optimal Waveforms for an Ultra-Wideband (UWB) link have been presented using transmit and receive antennas that are realistic and specific. Yet antenna expert David M. Pozar, who hails from the Department of Electrical and Computer Engineering at the University of Massachusetts (Amherst, MA), asserts that a better approach might be to determine the best performance that can be obtained for any antenna with certain constraints, such as antenna size and quality factor (Q). Specifically, Pozar presents solutions for the fundamental limitations on UWB antenna performance that can be achieved in terms of either the maximum radiated electric-field amplitude at a given time and far-field position or the maximization of the radiated energy density in a particular direction during a specified time interval. In both cases, the total radiated energy, Q of the antenna, and size of the antenna are constrained.
The solution is developed using a sphericalmode expansion of the fields radiated by an arbitrary antenna, which is enclosed by a spherical mathematical surface. It is optimized using variational methods. In the case of amplitude maximization, a closed-form result is obtained. For energy maximization in a time interval, an integral equation must be solved numerically.
With both solutions, the shapes of the optimal radiated-field waveforms were found to be largely independent of the antenna's size. The solutions indicate that the antenna characteristics that provide optimum field amplitudeor energy in the transient caseare identical to those associated with maximum gain in the continuous-wave (CW) case. Results also are provided for energy density in a specified time interval for low-pass signals.
Examples highlight the findings that resulted from this research. An arbitrary UWB antenna, for instance, is enclosed by a sphere of radius of 5 cm for a bandpass signal over the band of fm = 100 MHz to fM = 2 GHz. The total radiated energy is normalized to 1 Joule. Increasing the size of the enclosing sphere has little effect on the waveform's shape. But the peak amplitude will scale proportionally with the antenna's size. This result is assumed to be derived from the effect that makes antenna gain proportional to antenna aperture area. See "Optimal Radiated Waveforms from an Arbitrary UWB Antenna," IEEE Transactions on Antennas and Propagation, December 2007, p. 3384.