Circular-sectoral arrays of log-periodic (LP) antennas are presented for frequency-independent operation and beam-steering capability. Specifically, nonplanar trapezoidal tooth LP antennas are considered in a circular array configuration, where closely spaced antennas occupy a sector of the circle. Electromagnetic interactions of the array elements, each of which is a complicated LP antenna structure, are rigorously computed with the multilevel fast multipole algorithm (MLFMA). Genetic algorithms (GAs) are also employed in combination with MLFMA for synthesis and design purposes. By optimizing the excitations of the array elements via GAs, beam-steering ability is achieved in addition to the broadband (nearly frequency-independent) characteristics of the designed arrays. Computational results are presented to demonstrate the important properties of LP arrays.