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The nested likelihood ratios are shown to be asymptotically independent and sufficient for estimating the number of signals and to implement resolutions of superimposed signals into individual signals. As a result, estimating the number of signals can be reduced to a sequence of independent and simple tests. The procedure suggests an engineering sense that estimating the number of signals is based on complete resolutions of multiple signals. Simulations for estimating the number of overlapping echoes are given for illustration.
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Huaijin Gu (1998) studied this question.
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