1.. include:: replace.txt
2
3
4++++++++++++++++++++
5Design documentation
6++++++++++++++++++++
7
8--------
9Overview
10--------
11
12The Antenna module provides:
13
14 #. a class (Angles) and utility functions to deal with angles
15 #. a base class (AntennaModel) that provides an interface for the modeling of the radiation pattern of an antenna;
16 #. a set of classes derived from this base class that each models the radiation pattern of different types of antennas;
17 #. a base class (PhasedArrayModel) that provides a flexible interface for modeling a number of Phase Antenna Array (PAA) models
18 #. a class (UniformPlanarArray) derived from this base class, implementing a Uniform Planar Array (UPA) supporting both rectangular and linear lattices
19
20
21------
22Angles
23------
24
25The Angles class holds information about an angle in 3D space using spherical coordinates in radian units.
26Specifically, it uses the azimuth-inclination convention, where
27
28* Inclination is the angle between the zenith direction (positive z-axis) and the desired direction. It is included in the range [0, pi] radians.
29* Azimuth is the signed angle measured from the positive x-axis, where a positive direction goes towards the positive y-axis. It is included in the range [-pi, pi) radians.
30
31Multiple constructors are present, supporting the most common ways to encode information on a direction.
32A static boolean variable allows the user to decide whether angles should be printed in radian or degree units.
33
34A number of angle-related utilities are offered, such as radians/degree conversions, for both scalars and vectors, and angle wrapping.
35
36
37------------
38AntennaModel
39------------
40
41The AntennaModel uses the coordinate system adopted in [Balanis]_ and
42depicted in Figure :ref:`fig-antenna-coordinate-system`. This system
43is obtained by translating the Cartesian coordinate system used by the
44ns-3 MobilityModel into the new origin :math:`o` which is the location
45of the antenna, and then transforming the coordinates of every generic
46point :math:`p` of the space from Cartesian coordinates
47:math:`(x,y,z)` into spherical coordinates
48:math:`(r, \theta,\phi)`.
49The antenna model neglects the radial component :math:`r`, and
50only considers the angle components :math:`(\theta, \phi)`. An antenna
51radiation pattern is then expressed as a mathematical function
52:math:`g(\theta, \phi) \longrightarrow \mathcal{R}` that returns the
53gain (in dB) for each possible direction of
54transmission/reception. All angles are expressed in radians.
55
56
57.. _fig-antenna-coordinate-system:
58
59.. figure:: figures/antenna-coordinate-system.*
60   :align: center
61
62   Coordinate system of the AntennaModel
63
64---------------------
65Single antenna models
66---------------------
67
68In this section we describe the antenna radiation pattern models that
69are included within the antenna module.
70
71
72IsotropicAntennaModel
73+++++++++++++++++++++
74
75This antenna radiation pattern model provides a unitary gain (0 dB)
76for all direction.
77
78
79
80CosineAntennaModel
81++++++++++++++++++
82
83This is the cosine model described in [Chunjian]_: the antenna gain is
84determined as:
85
86.. math::
87
88  g(\phi, \theta) = \cos^{n} \left(\frac{\phi - \phi_{0}}{2}  \right)
89
90where :math:`\phi_{0}` is the azimuthal orientation of the antenna
91(i.e., its direction of maximum gain) and the exponential
92
93.. math::
94
95  n = -\frac{3}{20 \log_{10} \left( \cos \frac{\phi_{3dB}}{4} \right)}
96
97determines the desired 3dB beamwidth :math:`\phi_{3dB}`. Note that
98this radiation pattern is independent of the inclination angle
99:math:`\theta`.
100
101A major difference between the model of [Chunjian]_ and the one
102implemented in the class CosineAntennaModel is that only the element
103factor (i.e., what described by the above formulas) is considered. In
104fact, [Chunjian]_ also considered an additional antenna array
105factor. The reason why the latter is excluded is that we expect that
106the average user would desire to specify a given beamwidth exactly,
107without adding an array factor at a latter stage which would in
108practice alter the effective beamwidth of the resulting radiation
109pattern.
110
111
112
113ParabolicAntennaModel
114+++++++++++++++++++++
115
116This 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:
117
118.. math::
119
120  g_{dB}(\phi, \theta) = -\min \left( 12 \left(\frac{\phi  - \phi_{0}}{\phi_{3dB}} \right)^2, A_{max} \right)
121
122where :math:`\phi_{0}` is the azimuthal orientation of the antenna
123(i.e., its direction of maximum gain), :math:`\phi_{3dB}` is its 3 dB
124beamwidth, and :math:`A_{max}` is the maximum attenuation in dB of the
125antenna. Note that this radiation pattern is independent of the inclination angle
126:math:`\theta`.
127
128
129
130ThreeGppAntennaModel
131++++++++++++++++++++
132
133This model implements the antenna element described in [38901]_.
134Parameters are fixed from the technical report, thus no attributes nor setters are provided.
135The model is largely based on the `ParabolicAntennaModel`_.
136
137------------------
138Phased Array Model
139------------------
140
141The class PhasedArrayModel has been created with flexibility in mind.
142It abstracts the basic idea of a Phased Antenna Array (PAA) by removing any constraint on the
143position of each element, and instead generalizes the concept of steering and beamforming vectors,
144solely based on the generalized location of the antenna elements.
145For details on Phased Array Antennas see for instance [Mailloux]_.
146
147Derived classes must implement the following functions:
148
149* GetNumberOfElements: returns the number of antenna elements
150* GetElementLocation: returns the location of the antenna element with the specified index, normalized with respect to the wavelength
151* GetElementFieldPattern: returns the horizontal and vertical components of the antenna element field pattern at the specified direction. Same polarization (configurable) for all antenna elements of the array is considered.
152
153The class PhasedArrayModel also assumes that all antenna elements are equal, a typical key assumption which allows to model the PAA field pattern as the sum of the array factor, given by the geometry of the location of the antenna elements, and the element field pattern.
154Any class derived from AntennaModel is a valid antenna element for the PhasedArrayModel, allowing for a great flexibility of the framework.
155
156
157UniformPlanarArray
158++++++++++++++++++
159
160The class UniformPlanarArray is a generic implementation of Uniform Planar Arrays (UPAs),
161supporting rectangular and linear regular lattices.
162It loosely follows the implementation described in the 3GPP TR 38.901 [38901]_,
163considering only a single a single panel, i.e., :math:`N_{g} = M_{g} = 1`.
164
165By default, the array is orthogonal to the x-axis, pointing towards the positive
166direction, but the orientation can be changed through the attributes "BearingAngle",
167which adjusts the azimuth angle, and "DowntiltAngle", which adjusts the elevation angle.
168The slant angle is instead fixed and assumed to be 0.
169
170The number of antenna elements in the vertical and horizontal directions can be configured
171through the attributes "NumRows" and "NumColumns", while the spacing between the horizontal
172and vertical elements can be configured through the attributes "AntennaHorizontalSpacing"
173and "AntennaVerticalSpacing".
174
175The polarization of each antenna element in the array is determined by the polarization
176slant angle through the attribute "PolSlantAngle", as described in [38901]_ (i.e., :math:`{\zeta}`).
177
178
179.. [Balanis] C.A. Balanis, "Antenna Theory - Analysis and Design",  Wiley, 2nd Ed.
180
181.. [Chunjian] Li Chunjian, "Efficient Antenna Patterns for
182   Three-Sector WCDMA Systems", Master of Science Thesis, Chalmers
183   University of Technology, Göteborg, Sweden, 2003
184
185.. [Calcev] George Calcev and Matt Dillon, "Antenna Tilt Control in
186   CDMA Networks", in Proc. of the 2nd Annual International Wireless
187   Internet Conference (WICON), 2006
188
189.. [R4-092042a]  3GPP TSG RAN WG4 (Radio) Meeting #51, R4-092042, Simulation
190   assumptions and parameters for FDD HeNB RF requirements.
191
192.. [38901] 3GPP. 2018. TR 38.901, Study on channel model for frequencies from 0.5 to 100 GHz, V15.0.0. (2018-06).
193
194.. [Mailloux] Robert J. Mailloux, "Phased Array Antenna Handbook", Artech House, 2nd Ed.
195