Identifiability conditions for deterministic blind beamforming in the presence of incoherent multipath with small delay spread

In a recent paper, van der Veen has developed a baseband-equivalent data model for antenna array reception of multiple sources subject to incoherent multipath with small delay spread. Capitalizing on the structure of this model, van der Veen proposed a SVD/EVD-based blind beamforming algorithm. The starting point of our work is the realization that the above model can be viewed as a low-rank (trilinear) decomposition of a three-way received data array. Using a basic uniqueness result for low-rank decomposition of three-way arrays, data smoothing, and two new Lemmas pertaining to the so-called k-rank of certain structured matrices, we derive herein several interesting identifiability results for deterministic blind beamforming in the presence of incoherent multipath with small delay spread. The utility of the core results also extends beyond the application scope of this paper.