This paper is focused on the problem of resolving the range ambiguity in a fixed phase coding-phased array (FPC-PA) radar. At the modeling stage, the FPC-PA radar is configured by a fixed phase coding in both transmit elements and pulses, where the transmit beam is modulated with a coding phase in each pulse. Then, after some appropriate signal processing procedures, the degrees-of-freedom (DoFs) in the transmit domain is obtained, and the range region numbers, namely the index of the range ambiguity region, are discriminated in the transmit spatial frequency domain. Particularly, echoes from different range ambiguity regions correspond to different pointing directions of the equivalent transmit beampattern. Moreover, in order to obtain the range ambiguity index and angle of the target, a three-stage algorithm is developed to enhance the performance against the effect of amplitude and phase errors. At the analysis stage, the parameter estimation performance is assessed in comparison with the Cramér-Rao lower bound (CRLB). Experimental and numerical results are provided to demonstrate the effectiveness of resolving range ambiguity and parameter estimation with the proposed method.