Wireless communication security has become a hot topic in recent years. The directional modulation (DM) is a promising secure communication technique that has attracted attentions of many researchers. Several different frequency diverse arrays (FDAs) are used to obtain the direction-range-dependent DM signals in previous literatures. However, most of them are not ideal enough to obtain a nonperiodic dot-shaped secure area. In this paper, the symmetrical multi-carrier frequency diverse array with logarithmical frequency increment, named the symmetrical-multilog-FDA, is used to obtain the direction-range-dependent DM signals that are normal at the desired locations while disordered at other locations. Based on the symmetrical-multilog-FDA, we derive the closed-form expression of baseband-weighted vector using the artificial-noise-aided zero-forcing approach. Compared with previous schemes, the proposed scheme can obtain a more fine-focusing nonperiodic dot-shaped secure area at the desired location. In addition, it can achieve a point-to-multipoint secure communication for multiple cooperative receivers at different locations.