We consider reception of non-persistently excitated radio signals that overlap in time and frequency from a group of transmitters to a single receiver. The signals can be categorized as using a linear modulation or a non-linear modulation that can be approximated as a finite sum of linearly modulated signals. An analysis of a particular slice of the fourth-order cumulant spectra (trispectra) of this signal mixture reveals that the structure of their combined trispectrum can be modeled as a 3-dimensional tensor formed by a sum of rank 1 tensors corresponding to the trispectra of the component signals which fits the Canonical Decomposition/Parallel Factors (CP) tensor model. We develop an algorithm to decompose the trispectrum tensor which allows us to blindly estimate the power spectra, activity (in time) sequences, and number of signals contributing to an approximation of nonlinear signals. We then simulate the algorithm to verify results and quantify performance.