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High Frequency Surface Wave Radar (HFSWR) is a technology used for over-the-horizon detection of ocean vessels. This radar exploits the diffraction of electromagnetic waves around the curved surface of the Earth. To minimize the attenuation of the diffracted waves, the radar must operate at frequencies in the lower part of the high frequency (HF) band. However, radar signals at these frequencies also reflect from the Earth's ionosphere, which leads to radar clutter at ranges beyond 200 km. The linear broadside receive arrays used by conventional HFSWR systems cannot filter out this clutter as the arrays do not have any resolving power in elevation angle. Reported here are experimental investigations of the clutter suppression capability of one- and two-dimensional HFSWR adaptive processors. Three configurations are compared: one-dimensional spatial adaptive processing, two-dimensional spatial adaptive processing, and space-time adaptive processing. In all cases the number of adaptive degrees of freedom is 16. It is found that the best results are achieved by two-dimensional spatial adaptive processing, where a processing gain of up to about 20 dB can be achieved.