Aimed at the problems that the optimization based on ambiguity function is an important means of Frequency Diverse Array (FDA) radar waveform design, the ambiguity function of subarraybased Frequency Diverse Array is lack of research in the existing literature, a data model for FDA transmitting simple pulses under narrowband conditions is established and the beampattern characteristics of FDA arrays is compared to the phased arrays. On this basis, based on the time domain convolution of the signal through the matched filter output, the ambiguity function of the FDA array under three received signal processing architectures is derived. Then, the transmit beampattern characteristics and the ambiguity function characteristics of the cross subarraybased FDAs with different frequency offset are analyzed separately. The result shows that the FDA with sinusoidal frequency offset has a good interference suppression performance. The correctness of the analysis is verified and an important foundation is laid by this method for a series of studies in designing radar waveforms based on the ambiguity function of the subarraybased FDA to achieve interference suppression.