Antenna array

[1]: p.149 [2] 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.

In general, the larger the number of individual antenna elements used, the higher the gain and the narrower the beam.

Arrays can be used to achieve higher gain, to give path diversity (also called MIMO)[3] 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).

[4] The term antenna array most commonly means a driven array consisting of multiple identical driven elements all connected to the receiver or transmitter.

The beam of radio waves can be steered electronically to point instantly in any direction over a wide angle, without moving the antennas.

[4] From the Rayleigh criterion, the directivity of an antenna, the angular width of the beam of radio waves it emits, is proportional to the wavelength of the radio waves divided by the width of the antenna.

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.

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.

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.

In the technique called Very Long Baseline Interferometry (VLBI) dishes on separate continents have been linked, creating "array antennas" thousands of miles in size.

Array antennas can also be categorized by how the element antennas are arranged (disposed): Let us consider a linear array whose elements are arranged along the x-axis of an orthogonal Cartesian reference system.

It is assumed that radiators have the same orientation and the same polarization of the electric field.

(in meters) are the complex excitation coefficient and the position of the n-th radiator, respectively,

being the wavelength, then the magnitude of the array factor has a period, in the domain of

Now, suppose that the excitation coefficients are positive real variables.

, the array factor magnitude has a main lobe with maximum value at

Grating lobes are a source of disadvantages in both transmission and reception.

In fact, in transmission, they can lead to radiation in unwanted directions, while, in reception, they can be a source of ambiguity since the desired signal entering the mainlobe region could be strongly disturbed by other signals (unwanted interfering signals) entering the regions of the various grating lobes.

As seen above, when the spacing is constant between adjacent radiators, the array factor is characterized by the presence of grating lobes.

Several methods have been developed to synthesize arrays in which also the positions represent further degrees of freedom (unknowns).

, are independent and identically distributed random variables whose support coincides with the whole array aperture.

Narrow beams can be formed, provided the phasing of each element of the array is appropriate.

If, in addition, the amplitude of the excitation received by each element (during emission) is also well chosen, it is possible to synthesize a single-port array having a radiation pattern that closely approximates a specified pattern.

Additional issues to be considered are matching, radiation efficiency and bandwidth.

Here, the antenna array has multiple ports, so that the subject matters of matching and efficiency are more involved than in the single-port case.

Moreover, matching and efficiency depend on the excitation, except when the interactions between the antennas can be ignored.

Here also, the subject matters of matching and efficiency are involved, especially in the case of an antenna array of a mobile device (see chapter 10 of [11]), since, in this case, the surroundings of the antenna array influence its behavior, and vary over time.