This work analyses the structure of the different contributions to the image spectrum derived by the three-dimensional Fourier decomposition of sea clutter time series measured by ordinary X-band marine radars. The goal of this investigation is to derive a method to estimate the significant wave height of the ocean wave fields imaged by the radar. The proposed method is an extension of a technique developed for the analysis of ocean wave fields by using synthetic aperture radar systems. The basic idea behind this method is that the significant wave height is linearly dependent on the square root of the signal-to-noise ratio, where the signal is assumed as the radar analysis estimation of the wave spectral energy and the noise is computed as the energy due to the sea surface roughness, which is closely related to the speckle of the radar image. The proposed method to estimate wave heights is validated using data sets of sea clutter images measured by a marine radar and significant wave heights derived from measurements taken by a buoy used as reference sensor.

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The application of adaptive systems to approximate the Neyman-Pearson detector is considered. The training error function is proved to be the key parameter that determines the possibility of approximating this detector. Based on the calculus of the approximated function for the selected error criterion, a sufficient condition is derived. Decision rules based on expressions of the optimum Bayes discriminant function, such as those approximated for the LMSE or the cross-entropy error criteria, have been analyzed. Previous works were based on the assumption that the system was trained to minimize the probability of error over the training set, so its performance was only optimal for the minimum probability of error threshold (system "operating point"). In this work, we prove that the decision rule based on the function approximated for an error function that fulfil the derived sufficient condition is optimum for all possible P F A values. So, the concept of "operating point" will have no sense.

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