Abstract
The use of antenna arrays is indispensable in radar and multiple-input multiple-output (MIMO) wireless communications areas, as it permits the treatment of wavefronts in the spatial domain, enabling important applications such as beamforming and target detection. Spatial information is commonly given in terms of spatial correlation functions (SCFs), but its representation in terms of angular domain, such as the power azimuth spectrums (PASs), is sometimes more convenient. Therefore, transforming from SCF to PAS, and vice versa, is often required. This is commonly done by employing so-called beamformers, where the Bartlett beamformer (BB) is the most commonly utilized. However, the use of beamformers alone is not enough for retrieving PAS information from a given SCF. Particularly, this paper shows that a non-linear operation is missing in relating SCFs to PASs as provided by current beamformers. The paper also shows the mathematical expressions that correctly relate SCFs to PASs and wavenumber spectrums (WNSs) for the general case of systems with antenna arrays. The developed theory results in two new beamformers, which, corroborated by simulation results, solve any previous inconsistency in estimating PASs from SCFs.
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