Low Probability of Intercept (LPI) radars are used to detect targets at low distances by means of coded signals without being intercepted by hostile elements. Frequency Shift Keying (FSK) is one of the signal types used by LPI radars. In LPI radars, the frequency sets of FSK signals, which are constructed with continuous wave, are obtained by using Costas arrays. In this paper, basic construction methods of Costas arrays and their variations are examined. The ambiguity functions of FSK signals, which are constructed by means of Costas arrays, are analyzed and compared with the ambiguity function of frequency modulated continuous wave (FMCW) signals. Basic construction methods of Costas arrays are compared with the data obtained by the implementation.