Model Order Selection for Complex Sinusoids in the Presence of Unknown Correlated Gaussian Noise


We tend to contemplate the problem of detecting and estimating the amplitudes and frequencies of an unknown variety of complicated sinusoids based on noisy observations from an unstructured array. In parametric detection problems like this, data theoretic criteria like minimum description length (MDL) and Akaike info criterion (AIC) have previously been used for joint detection and estimation. In our paper, model choice primarily based on extreme value theory (EVT), that has previously been used for enumerating real sinusoidal parts from one-dimensional observations, is generalized to the case of multidimensional complicated observations in the presence of noise with an unknown spatial correlation matrix. In contrast to the previous work, the chance ratios thought-about in the mutlidimensional case cannot be addressed using Gaussian random fields. Instead, chi-sq. random fields related to the generalized likelihood ratio check are encountered and EVT is used to analyze the model order overestimation probability for a general class of likelihood penalty terms including MDL and AIC, and a novel chance penalty term derived based on EVT. Since the exact EVT penalty term involves a Lambert-W function, an approximate penalty term is also derived that's a lot of tractable. We have a tendency to provide threshold signal-to-noise ratios (SNRs) and show that the model order underestimation likelihood is asymptotically vanishing for EVT and MDL. We have a tendency to additionally show that MDL and EVT are asymptotically consistent while AIC is not, and that with finite samples, the detection performance of EVT outperforms MDL and AIC. Finally, the accuracy of the derived threshold SNRs is additionally demonstrated.

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