On the grating lobe of phased array antennas: A tutorial

This Tutorial provides a comprehensive and in-depth pedagogical insight into the phased-array antennas (PAAs), considering their widespread applications in the state-of-the-art 5G-Advanced/6G and high-capacity satellite communications. In addition to reviewing the PAA concept and its working mechanism, the Tutorial focuses on the grating lobe (GL) phenomena associated with the PAAs. The occurrence conditions and locations of these GLs are analyzed with the help of the directional cosine method. In particular, the Tutorial contributes a new rule to analytically regulate the critical element spacings for a general grating-lobe-free planar PAA that scans to an arbitrary direction (θ0, φ0) in the visible space. This new rule depends on both θ0 and φ0, which is found to be more relaxed than the classical rule inferred from linear PAA. A number of specific PAAs are considered such that their radiation patterns are graphically presented to show the interesting characteristics of the GLs. The Tutorial also discusses a random-element-position technique and illustratively shows its ability to suppress the GLs.