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The performance of subsurface deep sounding is investigated with reference to the radar sounder, MARSIS (Mars advanced radar for subsurface and ionosphere sounding), aboard the Mars Express mission, designed to investigate the presence of water-related interfaces in the subsurface of Mars. The analysis aims at providing the necessary tools for (i) performance prediction and (ii) data processor design. Using well known models for the backscattered signal, we compare the expected signal-to-clutter ratio values under most of the instrument's operating conditions. The generalized likelihood ratio (GLR) approach is followed for subsurface interface detection, and along-track integration is introduced in order to achieve the desired performance. In particular, we address the design of the integration window, and the requirements of data homogeneity. A thorough performance analysis is presented to cope with the expected MARSIS scenarios. In particular, we investigate several sources of mismatch between the assumed model and collected data, and derive the performance degradation due to each source.