Optimization of pulse radiation from dipole arrays for maximum energy in a specified time interval

The optimum solution for maximized radiated energy in a specified time interval from an
N
-element dipole array at a specified farfield position is presented. The solution is obtained in terms of time-domain dipole terminal voltages which are constrained in bandwidth and total input energy, with the currents on the dipoles satisfying Pocklington's integral equation. The orthogonality of characteristic terminal modes is used in the derivation of the optimum solution, and the far-zone field is expanded as a finite sum of characteristic modal fields with unknown mode coefficients. The optimum mode coefficients are found in terms of prolate spheroidal wave functions. An additional constraint can be used to find the optimum solution with a reduced sidelobe level. The effects of signal bandwidth and time interval specification on the peak field intensity and energy density in the direction of optimization are shown and limiting cases are found to agree with previous results.