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.. include:: replace.txt 
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.. include:: replace.txt 


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.. highlight:: cpp 
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.. _Propagation: 
4 
Propagation 


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########### 
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The ns3 propagation module defines two generic interfaces, namely :cpp:class:`PropagationLossModel` 
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Propagation 
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and :cpp:class:`PropagationDelayModel`, for the modeling of respectively propagation loss and propagation delay. 
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########### 


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9 
The ns3 propagation module defines two generic interfaces, namely ``PropagationLossModel`` and ``PropagationDelayModel``, for the modeling of respectively propagation loss and propagation delay. 
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PropagationLossModel 


11 
******************** 
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12 



13 
Propagation loss models calculate the Rx signal power considering the Tx signal power and the 
14 
mutual Rx and Tx antennas positions. 
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15 

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++++++++++++++++++++ 
16 
A propagation loss model can be "chained" to another one, making a list. The final Rx power 
13 
PropagationLossModel 
17 
takes into account all the chained models. In this way one can use a slow fading and a fast 
14 
++++++++++++++++++++ 
18 
fading model (for example), or model separately different fading effects. 
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The following propagation delay models are implemented: 
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* Cost231PropagationLossModel 
23 
* FixedRssLossModel 
24 
* FriisPropagationLossModel 
25 
* ItuR1411LosPropagationLossModel 
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* ItuR1411NlosOverRooftopPropagationLossModel 
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* JakesPropagationLossModel 
28 
* Kun2600MhzPropagationLossModel 
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* LogDistancePropagationLossModel 
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* MatrixPropagationLossModel 
31 
* NakagamiPropagationLossModel 
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* OkumuraHataPropagationLossModel 
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* RandomPropagationLossModel 
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* RangePropagationLossModel 
35 
* ThreeLogDistancePropagationLossModel 
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* TwoRayGroundPropagationLossModel 
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Other models could be available thanks to other modules, e.g., the ``building`` module. 
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Each of the available propagation loss models of ns3 is explained in 
40 
Each of the available propagation loss models of ns3 is explained in 
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one of the following subsections. 
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one of the following subsections. 
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FriisPropagationLossModel 
44 
========================= 
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45 



46 
This model implements the Friis propagation loss model. This model was first described in [friis]_. 
47 
The original equation was described as: 
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48 

22 
FriisPropagationLossModel 
49 
.. math:: 
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++++++++++++++++++++++++++++++++++++ 
50 



51 
\frac{P_r}{P_t} = \frac{A_r A_t}{d^2\lambda^2} 
52 

53 
with the following equation for the case of an isotropic antenna with no heat loss: 
54 

55 
.. math:: 
56 

57 
A_{isotr.} = \frac{\lambda^2}{4\pi} 
58 

59 
The final equation becomes: 
60 

61 
.. math:: 
62 

63 
\frac{P_r}{P_t} = \frac{\lambda^2}{(4 \pi d)^2} 
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65 
Modern extensions to this original equation are: 
66 

67 
.. math:: 
68 

69 
P_r = \frac{P_t G_t G_r \lambda^2}{(4 \pi d)^2 L} 
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71 
With: 
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73 
:math:`P_t` : transmission power (W) 
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75 
:math:`P_r` : reception power (W) 
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:math:`G_t` : transmission gain (unitless) 
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:math:`G_r` : reception gain (unitless) 
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:math:`\lambda` : wavelength (m) 
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:math:`d` : distance (m) 
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:math:`L` : system loss (unitless) 
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In the implementation, :math:`\lambda` is calculated as 
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:math:`\frac{C}{f}`, where :math:`C = 299792458` m/s is the speed of light in 
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vacuum, and :math:`f` is the frequency in Hz which can be configured by 
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the user via the Frequency attribute. 
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The Friis model is valid only for propagation in free space within 
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the socalled far field region, which can be considered 
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approximately as the region for :math:`d > 3 \lambda`. 
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The model will still return a value for :math:`d > 3 \lambda`, as 
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doing so (rather than triggering a fatal error) is practical for 
97 
many simulation scenarios. However, we stress that the values 
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obtained in such conditions shall not be considered realistic. 
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Related with this issue, we note that the Friis formula is 
101 
undefined for :math:`d = 0`, and results in 
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:math:`P_r > P_t` for :math:`d < \lambda / 2 \sqrt{\pi}`. 
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Both these conditions occur outside of the far field region, so in 
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principle the Friis model shall not be used in these conditions. 
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In practice, however, Friis is often used in scenarios where accurate 
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propagation modeling is not deemed important, and values of 
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:math:`d = 0` can occur. 
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To allow practical use of the model in such 
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scenarios, we have to 1) return some value for :math:`d = 0`, and 
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2) avoid large discontinuities in propagation loss values (which 
113 
could lead to artifacts such as bogus capture effects which are 
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much worse than inaccurate propagation loss values). The two issues 
115 
are conflicting, as, according to the Friis formula, 
116 
:math:`\lim_{d \to 0} P_r = +\infty`; 
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so if, for :math:`d = 0`, we use a fixed loss value, we end up with an infinitely large 
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discontinuity, which as we discussed can cause undesirable 
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simulation artifacts. 
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To avoid these artifact, this implementation of the Friis model 
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provides an attribute called MinLoss which allows to specify the 
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minimum total loss (in dB) returned by the model. This is used in 
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such a way that 
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:math:`P_r` continuously increases for :math:`d \to 0`, until 
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MinLoss is reached, and then stay constant; this allow to 
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return a value for :math:`d = 0` and at the same time avoid 
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discontinuities. The model won't be much realistic, but at least 
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the simulation artifacts discussed before are avoided. The default value of 
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MinLoss is 0 dB, which means that by default the model will return 
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:math:`P_r = P_t` for :math:`d <= \lambda / 2 \sqrt{\pi}`. 
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We note that this value of :math:`d` is outside of the far field 
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region, hence the validity of the model in the far field region is 
134 
not affected. 
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26 
TwoRayGroundPropagationLossModel 
137 
TwoRayGroundPropagationLossModel 
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++++++++++++++++++++++++++++++++ 
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================================ 


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This model implements a TwoRay Ground propagation loss model ported from NS2 
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The Tworay ground reflection model uses the formula 
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.. math:: 
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P_r = \frac{P_t * G_t * G_r * (H_t^2 * H_r^2)}{d^4 * L} 
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148 
The original equation in Rappaport's book assumes :math:`L = 1`. 
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To be consistent with the free space equation, :math:`L` is added here. 
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:math:`H_t` and :math:`H_r` are set at the respective nodes :math:`z` coordinate plus a model parameter 
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set via SetHeightAboveZ. 
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The tworay model does not give a good result for short distances, due to the 
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oscillation caused by constructive and destructive combination of the two 
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rays. Instead the Friis freespace model is used for small distances. 
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The crossover distance, below which Friis is used, is calculated as follows: 
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.. math:: 
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dCross = \frac{(4 * \pi * H_t * H_r)}{\lambda} 
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In the implementation, :math:`\lambda` is calculated as 
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:math:`\frac{C}{f}`, where :math:`C = 299792458` m/s is the speed of light in 
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vacuum, and :math:`f` is the frequency in Hz which can be configured by 
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the user via the Frequency attribute. 
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LogDistancePropagationLossModel 
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LogDistancePropagationLossModel 
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+++++++++++++++++++++++++++++++ 
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=============================== 


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This model implements a log distance propagation model. 
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The reception power is calculated with a socalled 
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logdistance propagation model: 
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.. math:: 
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L = L_0 + 10 n \log(\frac{d}{d_0}) 
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where: 
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:math:`n` : the path loss distance exponent 
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:math:`d_0` : reference distance (m) 
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:math:`L_0` : path loss at reference distance (dB) 
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:math:`d` :  distance (m) 
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:math:`L` : path loss (dB) 
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When the path loss is requested at a distance smaller than 
195 
the reference distance, the tx power is returned. 
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ThreeLogDistancePropagationLossModel 
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ThreeLogDistancePropagationLossModel 
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++++++++++++++++++++++++++++++++++++ 
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==================================== 


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This model implements a log distance path loss propagation model with three distance 
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fields. This model is the same as ns3::LogDistancePropagationLossModel 
202 
except that it has three distance fields: near, middle and far with 
203 
different exponents. 
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Within each field the reception power is calculated using the logdistance 
206 
propagation equation: 
207 

208 
.. math:: 
209 

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L = L_0 + 10 \cdot n_0 \log_{10}(\frac{d}{d_0}) 
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Each field begins where the previous ends and all together form a continuous function. 
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There are three valid distance fields: near, middle, far. Actually four: the 
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first from 0 to the reference distance is invalid and returns txPowerDbm. 
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.. math:: 
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\underbrace{0 \cdots\cdots}_{=0} \underbrace{d_0 \cdots\cdots}_{n_0} \underbrace{d_1 \cdots\cdots}_{n_1} \underbrace{d_2 \cdots\cdots}_{n_2} \infty 
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Complete formula for the path loss in dB: 
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.. math:: 
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\displaystyle L = 
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\begin{cases} 
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0 & d < d_0 \\ 
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L_0 + 10 \cdot n_0 \log_{10}(\frac{d}{d_0}) & d_0 \leq d < d_1 \\ 
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L_0 + 10 \cdot n_0 \log_{10}(\frac{d_1}{d_0}) + 10 \cdot n_1 \log_{10}(\frac{d}{d_1}) & d_1 \leq d < d_2 \\ 
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L_0 + 10 \cdot n_0 \log_{10}(\frac{d_1}{d_0}) + 10 \cdot n_1 \log_{10}(\frac{d_2}{d_1}) + 10 \cdot n_2 \log_{10}(\frac{d}{d_2})& d_2 \leq d 
232 
\end{cases} 
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where: 
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:math:`d_0, d_1, d_2` : three distance fields (m) 
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:math:`n_0, n_1, n_2` : path loss distance exponent for each field (unitless) 
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:math:`L_0` : path loss at reference distance (dB) 
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:math:`d` :  distance (m) 
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:math:`L` : path loss (dB) 
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When the path loss is requested at a distance smaller than the reference 
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distance :math:`d_0`, the tx power (with no path loss) is returned. The 
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reference distance defaults to 1m and reference loss defaults to 
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:cpp:class:`FriisPropagationLossModel` with 5.15 GHz and is thus :math:`L_0` = 46.67 dB. 
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JakesPropagationLossModel 
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JakesPropagationLossModel 
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+++++++++++++++++++++++++ 
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========================= 
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PropagationLossModel 
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ToDo 
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++++++++++++++++++++ 
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```` 
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RandomPropagationLossModel 
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RandomPropagationLossModel 
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++++++++++++++++++++++++++ 
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========================== 


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The propagation loss is totally random, and it changes each time the model is called. 
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As a consequence, all the packets (even those between two fixed nodes) experience a random 
263 
propagation loss. 
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NakagamiPropagationLossModel 
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NakagamiPropagationLossModel 
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++++++++++++++++++++++++++++ 
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============================ 


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This propagation loss model implements Nakagamim fast fading propagation loss model. 
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The Nakagamim distribution is applied to the power level. The probability density function is defined as 
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.. math:: 
273 

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p(x; m, \omega) = \frac{2 m^m}{\Gamma(m) \omega^m} x^{2m  1} e^{\frac{m}{\omega} x^2} = 2 x \cdot p_{\text{Gamma}}(x^2, m, \frac{m}{\omega}) 
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with :math:`m` the fading depth parameter and :math:`\omega` the average received power. 
277 

278 
It is implemented by either a :cpp:class:`GammaRandomVariable` or a :cpp:class:`ErlangRandomVariable` 
279 
random variable. 
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Like in :cpp:class:ThreeLogDistancePropagationLossModel`, the :math:`m` parameter is varied 
282 
over three distance fields: 
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.. math:: 
285 

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\underbrace{0 \cdots\cdots}_{m_0} \underbrace{d_1 \cdots\cdots}_{m_1} \underbrace{d_2 \cdots\cdots}_{m_2} \infty 
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For :math:`m = 1` the Nakagamim distribution equals the Rayleigh distribution. Thus 
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this model also implements Rayleigh distribution based fast fading. 
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FixedRssLossModel 
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FixedRssLossModel 
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+++++++++++++++++ 
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================= 


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This model sets a constant received power level independent of the transmit power. 
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The received power is constant independent of the transmit power; the user 
297 
must set received power level. Note that if this loss model is chained to other loss 
298 
models, it should be the first loss model in the chain. 
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Else it will disregard the losses computed by loss models that precede it in the chain. 
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MatrixPropagationLossModel 
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MatrixPropagationLossModel 
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++++++++++++++++++++++++++ 
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========================== 


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The propagation loss is fixed for each pair of nodes and doesn't depend on their actual positions. 
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This model shoud be useful for synthetic tests. Note that by default the propagation loss is 
306 
assumed to be symmetric. 
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RangePropagationLossModel 
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RangePropagationLossModel 
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+++++++++++++++++++++++++ 
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========================= 
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This propagation loss depends only on the distance (range) between transmitter and receiver. 
57 

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The single MaxRange attribute (units of meters) determines path loss. 


314 
Receivers at or within MaxRange meters receive the transmission at the 
315 
transmit power level. Receivers beyond MaxRange receive at power 
316 
1000 dBm (effectively zero). 
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OkumuraHataPropagationLossModel 
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OkumuraHataPropagationLossModel 
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+++++++++++++++++++++++++++++++ 
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=============================== 
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This model is used to model open area pathloss for long distance (i.e., > 1 Km). In order to include all the possible frequencies usable by LTE we need to consider several variants of the well known Okumura Hata model. In fact, the original Okumura Hata model [hata]_ is designed for frequencies ranging from 150 MHz to 1500 MHz, the COST231 [cost231]_ extends it for the frequency range from 1500 MHz to 2000 MHz. Another important aspect is the scenarios considered by the models, in fact the all models are originally designed for urban scenario and then only the standard one and the COST231 are extended to suburban, while only the standard one has been extended to open areas. Therefore, the model cannot cover all scenarios at all frequencies. In the following we detail the models adopted. 
321 
This model is used to model open area pathloss for long distance (i.e., > 1 Km). 
64 

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In order to include all the possible frequencies usable by LTE we need to consider 
65 

323 
several variants of the well known Okumura Hata model. In fact, the original Okumura 


324 
Hata model [hata]_ is designed for frequencies ranging from 150 MHz to 1500 MHz, 
325 
the COST231 [cost231]_ extends it for the frequency range from 1500 MHz to 2000 MHz. 
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Another important aspect is the scenarios considered by the models, in fact the all 
327 
models are originally designed for urban scenario and then only the standard one and 
328 
the COST231 are extended to suburban, while only the standard one has been extended 
329 
to open areas. Therefore, the model cannot cover all scenarios at all frequencies. 
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In the following we detail the models adopted. 
66 

331 

67 
The pathloss expression of the COST231 OH is: 
332 
The pathloss expression of the COST231 OH is: 
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333 


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F(h_\mathrm{M}) = \left\{\begin{array}{ll} (1.1\log(f))0.7 \times h_\mathrm{M}  (1.56\times \log(f)0.8) & \mbox{for medium and small size cities} \\ 3.2\times (\log{(11.75\times h_\mathrm{M}}))^2 & \mbox{for large cities}\end{array} \right. 
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F(h_\mathrm{M}) = \left\{\begin{array}{ll} (1.1\log(f))0.7 \times h_\mathrm{M}  (1.56\times \log(f)0.8) & \mbox{for medium and small size cities} \\ 3.2\times (\log{(11.75\times h_\mathrm{M}}))^2 & \mbox{for large cities}\end{array} \right. 
78 

343 

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80 
.. math:: 
344 
.. math:: 
81 

345 

82 
C = \left\{\begin{array}{ll} 0dB & \mbox{for mediumsize cities and suburban areas} \\ 3dB & \mbox{for large cities}\end{array} \right. 
346 
C = \left\{\begin{array}{ll} 0dB & \mbox{for mediumsize cities and suburban areas} \\ 3dB & \mbox{for large cities}\end{array} \right. 

131 
L_\mathrm{O} = L_\mathrm{U}  4.70 (\log{f})^2 + 18.33\log{f}  40.94 
395 
L_\mathrm{O} = L_\mathrm{U}  4.70 (\log{f})^2 + 18.33\log{f}  40.94 
132 

396 

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397 

134 
The literature lacks of extensions of the COST231 to open area (for suburban it seems that we can just impose C = 0); therefore we consider it a special case fo the suburban one. 
398 
The literature lacks of extensions of the COST231 to open area (for suburban it seems that 


399 
we can just impose C = 0); therefore we consider it a special case fo the suburban one. 
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402 
Cost231PropagationLossModel 
403 
=========================== 
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ToDo 
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```` 
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ItuR1411LosPropagationLossModel 
408 
ItuR1411LosPropagationLossModel 
140 
+++++++++++++++++++++++++++++++ 
409 
=============================== 
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This model is designed for LineofSight (LoS) short range outdoor communication in the frequency range 300 MHz to 100 GHz. This model provides an upper and lower bound respectively according to the following formulas 
411 
This model is designed for LineofSight (LoS) short range outdoor communication in the 


412 
frequency range 300 MHz to 100 GHz. This model provides an upper and lower bound 
413 
respectively according to the following formulas 
143 

414 

144 
.. math:: 
415 
.. math:: 
145 

416 


175 

446 

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447 

177 
ItuR1411NlosOverRooftopPropagationLossModel 
448 
ItuR1411NlosOverRooftopPropagationLossModel 
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+++++++++++++++++++++++++++++++++++++++++++ 
449 
=========================================== 
179 

450 

180 
This model is designed for NonLineofSight (LoS) short range outdoor communication over rooftops in the frequency range 300 MHz to 100 GHz. This model includes several scenariodependent parameters, such as average street width, orientation, etc. It is advised to set the values of these parameters manually (using the ns3 attribute system) according to the desired scenario. 
451 
This model is designed for NonLineofSight (LoS) short range outdoor communication over 


452 
rooftops in the frequency range 300 MHz to 100 GHz. This model includes several scenariodependent 
453 
parameters, such as average street width, orientation, etc. It is advised to set the values of 
454 
these parameters manually (using the ns3 attribute system) according to the desired scenario. 
181 

455 

182 
In detail, the model is based on [walfisch]_ and [ikegami]_, where the loss is expressed as the sum of freespace loss (:math:`L_{bf}`), the diffraction loss from rooftop to street (:math:`L_{rts}`) and the reduction due to multiple screen diffraction past rows of building (:math:`L_{msd}`). The formula is: 
456 
In detail, the model is based on [walfisch]_ and [ikegami]_, where the loss is expressed 


457 
as the sum of freespace loss (:math:`L_{bf}`), the diffraction loss from rooftop to 
458 
street (:math:`L_{rts}`) and the reduction due to multiple screen diffraction past 
459 
rows of building (:math:`L_{msd}`). The formula is: 
183 

460 

184 
.. math:: 
461 
.. math:: 
185 

462 


216 
:math:`\varphi` : is the street orientation with respect to the direct path (degrees) 
493 
:math:`\varphi` : is the street orientation with respect to the direct path (degrees) 
217 

494 

218 

495 

219 
The multiple screen diffraction loss depends on the BS antenna height relative to the building height and on the incidence angle. The former is selected as the higher antenna in the communication link. Regarding the latter, the "settled field distance" is used for select the proper model; its value is given by 
496 
The multiple screen diffraction loss depends on the BS antenna height relative to the building 


497 
height and on the incidence angle. The former is selected as the higher antenna in the communication 
498 
link. Regarding the latter, the "settled field distance" is used for select the proper model; 
499 
its value is given by 
220 

500 

221 
.. math:: 
501 
.. math:: 
222 

502 


226 

506 

227 
:math:`\Delta h_b = h_b  h_m` 
507 
:math:`\Delta h_b = h_b  h_m` 
228 

508 

229 
Therefore, in case of :math:`l > d_s` (where `l` is the distance over which the building extend), it can be evaluated according to 
509 
Therefore, in case of :math:`l > d_s` (where `l` is the distance over which the building extend), 


510 
it can be evaluated according to 
230 

511 

231 
.. math:: 
512 
.. math:: 
232 

513 


279 
\rho = \sqrt{\Delta h_b^2 + b^2} 
560 
\rho = \sqrt{\Delta h_b^2 + b^2} 
280 

561 

281 

562 



563 
Kun2600MhzPropagationLossModel 
564 
============================== 
282 

565 

283 
Kun2600MhzPropagationLossModel 
566 
This is the empirical model for the pathloss at 2600 MHz for urban areas which is described in [kun2600mhz]_. 
284 
++++++++++++++++++++++++++++++ 
567 
The model is as follows. Let :math:`d` be the distance between the transmitter and the receiver 
285 

568 
in meters; the pathloss :math:`L` in dB is calculated as: 
286 
This is the empirical model for the pathloss at 2600 MHz for urban areas which is described in [kun2600mhz]_. The model is as follows. Let :math:`d` be the distance between the transmitter and the receiver in meters; the pathloss :math:`L` in dB is calculated as: 


287 

569 

288 
.. math:: 
570 
.. math:: 
289 

571 

290 
L = 36 + 26\log{d} 
572 
L = 36 + 26\log{d} 
291 

573 

292 

574 

293 



294 

295 
+++++++++++++++++++++ 
296 
PropagationDelayModel 
575 
PropagationDelayModel 
297 
+++++++++++++++++++++ 
576 
********************* 
298 



299 

577 

300 
The following propagation delay models are implemented: 
578 
The following propagation delay models are implemented: 
301 

579 

302 
PropagationDelayModel 
580 
* ConstantSpeedPropagationDelayModel 
303 
+++++++++++++++++++++ 
581 
* RandomPropagationDelayModel 


582 

583 
ConstantSpeedPropagationDelayModel 
584 
================================== 
585 

586 
In this model, the signal travels with constant speed. 
587 
The delay is calculated according with the trasmitter and receiver positions. 
588 
The Euclidean distance between the Tx and Rx antennas is used. 
589 
Beware that, according to this model, the Earth is flat. 
304 

590 

305 
RandomPropagationDelayModel 
591 
RandomPropagationDelayModel 
306 
+++++++++++++++++++++++++++ 
592 
=========================== 
307 

593 

308 
ConstantSpeedPropagationDelayModel 
594 
The propagation delay is totally random, and it changes each time the model is called. 
309 
++++++++++++++++++++++++++++++++++ 
595 
All the packets (even those between two fixed nodes) experience a random delay. 


596 
As a consequence, the packets order is not preserved. 
310 

597 

311 

598 



599 
References 
600 
********** 
312 

601 

313 

602 
.. [friis] Friis, H.T., "A Note on a Simple Transmission Formula," Proceedings of the IRE , vol.34, no.5, pp.254,256, May 1946 
314 

603 

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.. [hata] M.Hata, "Empirical formula for propagation loss in land mobile radio 
604 
.. [hata] M.Hata, "Empirical formula for propagation loss in land mobile radio 
316 
services", IEEE Trans. on Vehicular Technology, vol. 29, pp. 317325, 1980 
605 
services", IEEE Trans. on Vehicular Technology, vol. 29, pp. 317325, 1980 