Abstract: This paper deals with the problem of adaptive detection for range-spread targets with unknown complex amplitude and known Doppler in the presence of compound-Gaussian clutter modeled as an autoregressive (AR) process with unknown parameters. Since no uniformly most powerful test exists for this problem, we devise and assess the AR-model-based detection strategy based on the Wald test. The unknown parameters are estimated by maximum likelihood criterion only under hypothesis H1 for the use in Wald test. Different to the traditional covariance-matrix-based detectors, we consider no secondary data; the AR-model-based detector adjusts itself to the environment utilizing only the primary data in the cells under test. Moreover, the AR-model-based Wald test ensure the constant false alarm rate (CFAR) property with respect to the clutter power level, and are asymptotically CFAR with respect to the clutter covariance matrix. Finally, the performance assessments, conducted by Monte Carlo simulations, also in comparison to previously proposed detectors, have shown the newly proposed detector possesses better detection performance than its counterpart resorting to the generalized likelihood ratio test (GLRT) approach. In addition, the newly proposed AR-model-based Wald test possesses the same asymptotical performance as the two-step GLRT-based detector with perfect knowledge about the clutter covariance matrix.