A Primer on Digital Beamforming

(1)
Beamforming is the combination of radio signals from a set of small non-directional antennas to simulate a large directional antenna. In communications, beamforming is used to point an antenna at the signal source to reduce interference and improve communication quality. In direction finding applications, beamforming can be used to steer an antenna to determine the direction of the signal source.
(2)
A transmitting antenna generates stronger electromagnetic waves in some directions than others. A plot of field strength vs. direction is called the antenna’s “radiation pattern.” It’s always the same for receiving as for transmitting.
An electromagnetic wave measured at a point far from the antenna is the sum of the radiation from all parts of the antenna. Each small part of the antenna is radiating waves of a different amplitude and phase, and each of these waves travels a different distance to the point where a receiver is located. In some directions,
these waves add constructively to give a gain. In some directions they add destructively to give a loss.
(3)Directional Antenna
A directional antenna is one designed to have a gain in one direction and a loss in others. An antenna is made directional by increasing its size. This spreads the radiating conductors of the antenna over a larger distance, so that the constructive and destructive interference can be better controlled to give a directional
radiation pattern.
A satellite dish antenna can, simplistically, be considered a circular surface that radiates electromagnetic waves equally from all parts. It has a narrow central “beam” of high gain, as shown in the following figure, that is aimed at the satellite. As the dish diameter, in wavelengths, is increased the central beam gets
narrower. Notice the smaller beams, called “side lobes”, on either side of the central beam. Directions in which the signal strength is zero are called “nulls.”
(4)Linear Arrays
A simple directional antenna consists of a linear array of small radiating antenna elements, each fed with identical signals (the same amplitude and phase) from one transmitter. As the total width of the array increases, the central beam becomes narrower. As the number of elements increases, the side lobes become smaller.
(5)Electronically Steered Arrays
By varying the signal phases of the elements in a linear array, its main beam can be steered. The simplest
way of controlling signal phase is to systematically vary the cable lengths to the elements. Cables delay the signal and so shift the phase. However, this does not allow the antenna to be dynamically steered.
(6)Beamforming
In beamforming, both the amplitude and phase of each antenna element are controlled. Combined amplitude and phase control can be used to adjust side lobe levels and steer nulls better than can be achieved by phase control alone.
The combined relative amplitude ak and phase shift qk for each antenna is called a “complex weight” and is represented by a complex constant wk (for the kth antenna).
A beamformer for a radio transmitter applies the complex weight to the transmit signal (shifts the phase and sets the amplitude) for each element of the antenna array.
A beamformer for radio reception applies the complex weight to the signal from each antenna element, then sums all of the signals into one that has the desired directional pattern.
(7)Digital Beamforming