In this paper, we consider a radar system with a subarray-based frequency diverse array (FDA) as the transmitting array, which consists of two FDA subarrays with different frequency increments to achieve single maximum beam response for any target. In order to distinguish the desired signal and multiple interferences with close spatial directions in most scenarios, a novel polarization sensitive FDA (PSFDA) is proposed as the receiving array to suppress interference and further improve the signal to interference-plus-noise ratio (SINR) for accurate target detection. Joint transmit-receive beampattern optimization is particularly investigated here. Specifically, in our work, we aim at maximizing the output SINR of the proposed polarization-subarray-based FDA radar by jointly optimizing the FDA transmit beamforming, the PSFDA spatial pointings and the PSFDA receive beamforming. To tackle the nonconvexity of the formulated SINR maximization problem, an alternating optimization algorithm is proposed to decompose the original problem into three convex subproblems, which can all be efficiently solved by the interior point method. Numerical experiments verify the superior output SINR performance of the proposed iterative algorithm.