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# Design documentation¶

## Overview¶

The Antenna module provides:

1. a new base class (AntennaModel) that provides an interface for the modeling of the radiation pattern of an antenna;
2. a set of classes derived from this base class that each models the radiation pattern of different types of antennas.

## AntennaModel¶

The AntennaModel uses the coordinate system adopted in [Balanis] and depicted in Figure Coordinate system of the AntennaModel. This system is obtained by traslating the cartesian coordinate system used by the ns-3 MobilityModel into the new origin which is the location of the antenna, and then transforming the coordinates of every generic point of the space from cartesian coordinates into spherical coordinates . The antenna model neglects the radial component , and only considers the angle components . An antenna radiation pattern is then expressed as a mathematical function that returns the gain (in dB) for each possible direction of transmission/reception. All angles are expressed in radians.

Coordinate system of the AntennaModel

## Provided models¶

In this section we describe the antenna radiation pattern models that are included within the antenna module.

### IsotropicAntennaModel¶

This antenna radiation pattern model provides a unitary gain (0 dB) for all direction.

### CosineAntennaModel¶

This is the cosine model described in [Chunjian]: the antenna gain is determined as:

where is the azimuthal orientation of the antenna (i.e., its direction of maximum gain) and the exponential

determines the desired 3dB beamwidth . Note that this radiation pattern is independent of the inclination angle .

A major difference between the model of [Chunjian] and the one implemented in the class CosineAntennaModel is that only the element factor (i.e., what described by the above formulas) is considered. In fact, [Chunjian] also considered an additional antenna array factor. The reason why the latter is excluded is that we expect that the average user would desire to specify a given beamwidth exactly, without adding an array factor at a latter stage which would in practice alter the effective beamwidth of the resulting radiation pattern.

### ParabolicAntennaModel¶

This model is based on the parabolic approximation of the main lobe radiation pattern. It is often used in the context of cellular system to model the radiation pattern of a cell sector, see for instance [R4-092042a] and [Calcev]. The antenna gain in dB is determined as:

where is the azimuthal orientation of the antenna (i.e., its direction of maximum gain), is its 3 dB beamwidth, and is the maximum attenuation in dB of the antenna. Note that this radiation pattern is independent of the inclination angle .

 [Balanis] C.A. Balanis, “Antenna Theory - Analysis and Design”, Wiley, 2nd Ed.
 [Chunjian] (1, 2, 3) Li Chunjian, “Efficient Antenna Patterns for Three-Sector WCDMA Systems”, Master of Science Thesis, Chalmers University of Technology, Göteborg, Sweden, 2003
 [Calcev] George Calcev and Matt Dillon, “Antenna Tilt Control in CDMA Networks”, in Proc. of the 2nd Annual International Wireless Internet Conference (WICON), 2006
 [R4-092042a] 3GPP TSG RAN WG4 (Radio) Meeting #51, R4-092042, Simulation assumptions and parameters for FDD HeNB RF requirements.