Antenna array

An antenna array (or array antenna) is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called "elements") are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together (interfering constructively) to enhance the power radiated in desired directions, and cancelling (interfering destructively) to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions. More sophisticated array antennas may have multiple transmitter or receiver modules, each connected to a separate antenna element or group of elements. 
An antenna array can achieve higher gain (directivity), that is a narrower beam of radio waves, than could be achieved by a single element. In general, the larger the number of individual antenna elements used, the higher the gain and the narrower the beam. Some antenna arrays (such as military phased array radars) are composed of thousands of individual antennas. Arrays can be used to achieve higher gain, to give path diversity (also called MIMO) which increases communication reliability, to cancel interference from specific directions, to steer the radio beam electronically to point in different directions, and for radio direction finding (RDF).
The term antenna array most commonly means a "driven array" consisting of multiple identical driven elements all connected to the receiver or transmitter. A "parasitic array" consists of a single driven element connected to the feedline, and other elements which are not, called parasitic elements. It is usually another name for a Yagi-Uda antenna.
A "phased array" usually means an "electronically scanned array"; a driven array antenna in which each individual element is connected to the transmitter or receiver through a phase shifter controlled by a computer. The beam of radio waves can be steered electronically to point instantly in any direction over a wide angle, without moving the antennas. However the term "phased array" is sometimes used to mean an ordinary array antenna.
How arrays work.
Small antennas around one wavelength in size, such as quarter-wave monopoles and half-wave dipoles, don't have much directivity (gain); they are omnidirectional antennas which radiate radio waves over a wide angle. To create a directional antenna (high gain antenna), which radiates radio waves in a narrow beam, two general techniques can be used. One technique is to use reflection by large metal surfaces such as parabolic reflectors or horns, or refraction by dielectric lenses to change the direction of the radio waves, to focus the radio waves from a single low gain antenna into a beam. This type is called an "aperture antenna". A parabolic dish is an example of this type of antenna.
A second technique is to use multiple antennas which are fed from the same transmitter or receiver; this is called an array antenna, or antenna array. If the currents are fed to the antennas with the proper phase, due to the phenomenon of interference the spherical waves from the individual antennas combine (superpose) in front of the array to create plane waves, a beam of radio waves traveling in a specific direction. In directions in which the waves from the individual antennas arrive in phase, the waves add together (constructive interference) to enhance the power radiated. In directions in which the individual waves arrive out of phase, with the peak of one wave coinciding with the valley of another, the waves cancel (destructive interference) reducing the power radiated in that direction. Similarly, when receiving, the oscillating currents received by the separate antennas from radio waves received from desired directions are in phase and when combined in the receiver reinforce each other, while currents from radio waves received from other directions are out of phase and when combined in the receiver cancel each other.
The radiation pattern of such an antenna consists of a strong beam in one direction, the main lobe, plus a series of weaker beams at different angles called sidelobes, usually representing residual radiation in unwanted directions. The larger the width of the antenna and the greater the number of component antenna elements, the narrower the main lobe, and the higher the gain which can be achieved, and the smaller the sidelobes will be.
Arrays in which the antenna elements are fed in phase are broadside arrays; the main lobe is emitted perpendicular to the plane of the elements.
The largest array antennas are radio interferometers used in the field of radio astronomy, in which multiple radio telescopes consisting of large parabolic antennas are linked together into an antenna array, to achieve higher resolution. Using the technique called aperture synthesis such an array can have the resolution of an antenna with a diameter equal to the distance between the antennas. In the technique called Very Long Baseline Interferometry (VLBI) dishes on separate continents have been linked, creating "array antennas" thousands of miles in size.
Types.
Most array antennas can be divided into two classes based on how the component antennas' axis is related to the direction of radiation. 
There are also arrays (such as phased arrays) which don't belong to either of these categories, in which the direction of radiation is at some other angle to the antenna axis.
"Driven array" - This is an array in which the individual component antennas are all "driven" - connected to the transmitter or receiver. The individual antennas, which are usually identical, often consist of single "driven element"s, such as half-wave dipoles, but may also be composite antennas such as Yagi antennas or turnstile antennas.
"Parasitic array" - This is an endfire array which consist of multiple antenna elements in a line of which only one, the driven element, is connected to the transmitter or receiver, while the other elements, called parasitic elements, are not. The parasitic elements function as resonators, absorbing radio waves from the driven element and reradiating them with a different phase, to modify the radiation pattern of the antenna, increasing the power radiated in the desired direction. Since these have only one driven element they are often called "antennas" instead of "arrays".
Matching to a multiport antenna array.
A single-port antenna array may be regarded as a single-port antenna. It follows that the power reflection coefficient defined by Kurokawa is a matching metric that correctly characterizes the power transfer between a single-port generator and a single-port antenna array used for emission, or between a single-port antenna array used for reception and a single-port load. The ideal value of the power reflection coefficient is zero, which corresponds to a power received by the antenna that is equal to the power available from the generator. According to the maximum power transfer theorem, this occurs when the source and load impedances are complex conjugates of each other.
In the special case where the internal impedance of the single-port generator is real and equal to a reference resistance formula_1, the power reflection coefficient is the square of the absolute value of the voltage reflection coefficient for the reference resistance formula_1, so that this reflection coefficient and the corresponding standing wave ratio (VSWR) are matching metrics that correctly characterize the power transfer.
If there is no interaction between the port of a multiport antenna array, and between the ports of the multiport device coupled to the port of the multiport antenna array, each port of the multiport antenna array may be considered independently of the others as regards matching, and characterized with a power reflection coefficient. In the opposite case, matching to the multiport antenna array is more involved, because : the power transfer ratio formula_3 between a multiport generator and the multiport antenna array used for emission depends on the excitation produced by the multiport generator; and the power transfer ratio formula_4 between the multiport antenna array used for reception and a multiport load depends on the excitation produced by the multiport antenna array. Here, a suitable matching metric is the power match figure formula_5 given by
where formula_7 is the least element of the set of the values of the power transfer ratio formula_3 for all nonzero open circuit voltages lying in formula_9, where formula_10 is the number of ports of the multiport antenna array. The ideal value of the power match figure is zero, which corresponds to a power received by the antenna that is equal to the power available from the generator. According to the maximum power transfer theorem for multiports, this occurs when the source and load impedance matrices are each the hermitian adjoint of the other.