The problem of adaptive radar detection with a polarimetric frequency diverse array multiple-input multiple-output radar is addressed in this article. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to suboptimal design strategies based on the generalized likelihood ratio criterion. The resulting detectors demand, under the H1 hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the linearized array manifold, the gradient projection method, and the coordinate descent algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded constant false alarm rate property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.