Antenna arrays benefit from spatial diversity, which enables the control of the pattern specifications in space. Adding frequency diversity to arrays provides an opportunity to control the beams in the Space-Time domain. Contrary to the conventional arrays, the added frequency diversity in the Frequency Diverse Arrays (FDA) leads to time-variant and range-dependent patterns. The time variation of the pattern affects both steering and auto-scanning applications. The array factor depends coherently on the frequency and spatial distributions of elements, in the same way, the spatial and time behavior of the FDA’s pattern is correlated. Due to this space-frequency coherency, an adjoint spatial-frequency design algorithm is the best approach for controlling the array's spatial and time behaviors. Although Due to the complexity of the array factor formulations in the FDA, the frequency and spatial distribution of the elements has been separately designed. This study proposes an algorithm to concurrently, allocate the location and frequency of the elements for a desired pattern. First, using some symmetry, a straightforward formulation for the array factor is obtained and used to design a symmetrical FDA for a stable and periodic scanning beam. Second, by analyzing the formulations, two important design parameters and some crucial design criteria of the FDA pattern for scanning applications are suggested, and using these parameters a designing algorithm is extracted. The novelty of the proposed approach is the simultaneous design of the location and frequency of the elements in the space-frequency plane, which results in meeting the time and spatial requirement of the pattern. Using this approach, two different planar arrays are designed, and their results are compared with those of other planar configurations. This study paves the way for a new approach to designing FDAs.