On the CRB for frequency estimation of superimposed multidimensional sinusoids
Nick Letzepis · 2014
The Cramér-Rao bound (CRB) is derived for frequency estimation of the superposition of multidimensional complex sinusoids assuming the complex gains are known. The Fisher information matrix is derived in terms of the Dirichlet kernel, a kernel well-known for its use in Fourier series. In general, it is shown that the frequency estimation error variance for a particular sinusoid can be lower bounded by its isolated (single) multidimensional sinusoid CRB times a scaling factor that is dependent on its frequency separation from each sinusoid.