Issues pertaining to the rate of beam divergence, the beam intensity, and the measured energy efficiency of beams generated by arrays of radiating elements are central to the practical applications of those beams. It will be shown that a localized-wave pulse-driven array can be designed to outperform similar continuous-wave pulse-driven arrays with respect to each of these beam characteristics. This improved performance is quantified by deriving bounds on those beam quantities for the field generated by an arbitrary pulse-driven array. These bounds extend the meaning of near-field distances or diffraction lengths to the situation where the array driving functions can be broad-bandwidth signals. Particular attention is given to transmitting- and receiving-array systems consisting of elements that are not large in comparison to the shortest wavelength of significance contained in the signals driving them. The output signals of such systems are related to the input driving functions by several time derivatives. It is demonstrated that the properties of the resulting beams depend on the higher-order moments of the spectra of the input driving functions and that diffraction degrades the coherence of these higher-order moments more slowly than its lower orders.