Multiple Beams From Planar Arrays

The paper describes a general theory of Multiple Beams from Planar Arrays establishing necessary and sufficient conditions for admitting a realizable lossless beamforming network. The developed theory applies concepts deriving from the Whittaker-Kotelnikov-Shannon (WKS) sampling theory, and from its multidimensional extension due to Miyakawa- Petersen- Middleton (MPM), to the problem of generating simultaneous multiple beams from planar phased arrays with generic periodicity and layout. It is proven that the multiple beams positions must satisfy certain reciprocal lattice conditions and that the phase steering vectors of the lossless beamforming network must correspond to the multi-dimensional discrete Fourier transform (MD-DFT). The nontrivial Hermitian orthogonality of the steering vectors, as well as of the multiple beams, is also proven.