Super-Beamforming in Holographic MIMO
The conventional linear scaling of beamforming gain with the number of antennas $N$ is not a fundamental physical limitation, but rather a consequence of the half-wavelength spacing that minimizes mutual coupling. Relaxing this constraint enables gains that, in the vicinity of the array axis, exceed those of uncoupled arrays. This paper shows that mutual coupling facilitates the synthesis of super-beams whose widths scale as $1/N$, in contrast to the conventional $1/\sqrt{N}$. These narrower beams achieve a quadratic gain scaling with $N$ provided antenna losses remain sufficiently small, decaying at least exponentially with growing $N$ and polynomially with decreasing spacing. Notably, this gain enhancement does not necessarily require vanishing spacings; it may also emerge for spacings slightly below half wavelength as the array aperture increases.