Three-way arrays for harmonic retrieval: The colored noise case

In this work, we deal with multilinear representations of an harmonic process composed by a mixture of complex sinusoids contaminated by a colored Gaussian noise of unknown probability density function. High-Order Statistics, and in particular Fourth-Order Cumulants (FOC), are popular tools to mitigate the effect of the colored noise and can be viewed as a natural enhancement of the noisy mixture. As the FOC of an harmonic process is a multilinear function, it seems natural to map this quantity onto a structured multi-way array (aka. tensor). However, an harmonic process can be understood as a pure stationary random process or as a deterministic process corrupted by a stationary noise. In this paper, we explore the relation existing between these two models in the context of the multilinear decomposition theory.