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Beam-forming networks combine signals from small antennae into a pattern that is more directional than each antenna by itself because of array factor. Beam-formers are used in radar and communications. An radar example is a linear array capable of four beams in azimuth for an automotive radar; an communications example is a two-dimensional beam-former used in a satellite to cover a broad ground area in multiple spots.
Beam-forming networks can provide simultaneous beam coverage, like ESA's Artemis satellite, or single-point coverage, like a classic phase array radar. It seems funny to use the term "classic" and phased array in the same sentence, but this technology is moving ahead rapidly and new capabilities are being explored.
Beams can be fixed in a design, or adaptive using beam-steering computer control.
Possible beam-forming networks include:
Phased array
Passive electronically steerable antenna (PESA)
Active electronically steerable antenna (AESA)
5G beamforming (new for November 2016)
Butler matrix
Rotman lens
Monopulse network
What is the advantage of an electronically steerable antenna? No moving parts! The servo that controls a dish antenna, and the rotary joint that is needed to interface to the antenna to the transmit/receive system all have short lifetimes compared to solid-state electronics.
What is the down side of a BFN, compared to a steerable antenna? When you steer off from broadside, the gain drops because the equivalent aperture shrinks as cosine theta.