.. _Propagation:

Propagation

-----------

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The |ns3| propagation module defines two generic interfaces, namely :cpp:class:`PropagationLossModel`

Propagation

and :cpp:class:`PropagationDelayModel`, for the modeling of respectively propagation loss and propagation delay.

###########

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

PropagationLossModel

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A propagation loss model can be "chained" to another one, making a list. The final Rx power 

PropagationLossModel

takes into account all the chained models. In this way one can use a slow fading and a fast 

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fading model (for example), or model separately different fading effects.

FriisPropagationLossModel

.. math::

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

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

.. math::

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

The final equation becomes:

.. math::

  \frac{P_r}{P_t} = \frac{\lambda^2}{(4 \pi d)^2}

Modern extensions to this original equation are:

.. math::

  P_r = \frac{P_t G_t G_r \lambda^2}{(4 \pi d)^2 L}

With:

  :math:`P_t` : transmission power (W)

  :math:`P_r` : reception power (W)

  :math:`G_t` : transmission gain (unit-less)

  :math:`G_r` : reception gain (unit-less)

  :math:`\lambda` : wavelength (m)

  :math:`d` : distance (m)

  :math:`L` : system loss (unit-less)

In the implementation, :math:`\lambda` is calculated as 

:math:`\frac{C}{f}`, where :math:`C = 299792458` m/s is the speed of light in

vacuum, and :math:`f` is the frequency in Hz which can be configured by

the user via the Frequency attribute.

The Friis model is valid only for propagation in free space within

the so-called far field region, which can be considered

approximately as the region for :math:`d > 3 \lambda`.

The model will still return a value for :math:`d > 3 \lambda`, as

doing so (rather than triggering a fatal error) is practical for

many simulation scenarios. However, we stress that the values

obtained in such conditions shall not be considered realistic. 

Related with this issue, we note that the Friis formula is

undefined for :math:`d = 0`, and results in 

:math:`P_r > P_t` for :math:`d < \lambda / 2 \sqrt{\pi}`.

Both these conditions occur outside of the far field region, so in

principle the Friis model shall not be used in these conditions. 

In practice, however, Friis is often used in scenarios where accurate

propagation modeling is not deemed important, and values of 

:math:`d = 0` can occur.

To allow practical use of the model in such

scenarios, we have to 1) return some value for :math:`d = 0`, and

2) avoid large discontinuities in propagation loss values (which

could lead to artifacts such as bogus capture effects which are

much worse than inaccurate propagation loss values). The two issues

are conflicting, as, according to the Friis formula, 

:math:`\lim_{d \to 0}  P_r = +\infty`;

so if, for :math:`d = 0`, we use a fixed loss value, we end up with an infinitely large

discontinuity, which as we discussed can cause undesirable

simulation artifacts.

To avoid these artifact, this implementation of the Friis model

provides an attribute called MinLoss which allows to specify the

minimum total loss (in dB) returned by the model. This is used in

such a way that 

:math:`P_r` continuously increases for :math:`d \to 0`, until

MinLoss is reached, and then stay constant; this allow to

return a value for :math:`d = 0` and at the same time avoid

discontinuities. The model won't be much realistic, but at least

the simulation artifacts discussed before are avoided. The default value of

MinLoss is 0 dB, which means that by default the model will return 

:math:`P_r = P_t` for :math:`d <= \lambda / 2 \sqrt{\pi}`.

We note that this value of :math:`d` is outside of the far field

region, hence the validity of the model in the far field region is

not affected.

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================================

This model implements a Two-Ray Ground propagation loss model ported from NS2

The Two-ray ground reflection model uses the formula

.. math::

  P_r = \frac{P_t * G_t * G_r * (H_t^2 * H_r^2)}{d^4 * L}

The original equation in Rappaport's book assumes :math:`L = 1`.

To be consistent with the free space equation, :math:`L` is added here.

:math:`H_t` and :math:`H_r` are set at the respective nodes :math:`z` coordinate plus a model parameter

set via SetHeightAboveZ.

The two-ray model does not give a good result for short distances, due to the

oscillation caused by constructive and destructive combination of the two

rays. Instead the Friis free-space model is used for small distances. 

The crossover distance, below which Friis is used, is calculated as follows:

.. math::

  dCross = \frac{(4 * \pi * H_t * H_r)}{\lambda}

In the implementation,  :math:`\lambda` is calculated as 

:math:`\frac{C}{f}`, where :math:`C = 299792458` m/s is the speed of light in

vacuum, and :math:`f` is the frequency in Hz which can be configured by

the user via the Frequency attribute.

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===============================

This model implements a log distance propagation model.

The reception power is calculated with a so-called

log-distance propagation model:

.. math::

  L = L_0 + 10 n \log(\frac{d}{d_0})

where:

  :math:`n` : the path loss distance exponent

  :math:`d_0` : reference distance (m)

  :math:`L_0` : path loss at reference distance (dB)

  :math:`d` :  - distance (m)

  :math:`L` : path loss (dB)

When the path loss is requested at a distance smaller than

the reference distance, the tx power is returned.

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====================================

This model implements a log distance path loss propagation model with three distance

fields. This model is the same as ns3::LogDistancePropagationLossModel

except that it has three distance fields: near, middle and far with

different exponents.

Within each field the reception power is calculated using the log-distance

propagation equation:

.. math::

  L = L_0 + 10 \cdot n_0 \log_{10}(\frac{d}{d_0})

Each field begins where the previous ends and all together form a continuous function.

There are three valid distance fields: near, middle, far. Actually four: the

first from 0 to the reference distance is invalid and returns txPowerDbm.

.. math::

  \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 

Complete formula for the path loss in dB:

.. math::

  \displaystyle L =

  \begin{cases}

  0 & d < d_0 \\

  L_0 + 10 \cdot n_0 \log_{10}(\frac{d}{d_0}) & d_0 \leq d < d_1 \\

  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 \\

  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

  \end{cases}

where:

  :math:`d_0, d_1, d_2` : three distance fields (m)

  :math:`n_0, n_1, n_2` : path loss distance exponent for each field (unitless)

  :math:`L_0` : path loss at reference distance (dB)

  :math:`d` :  - distance (m)

  :math:`L` : path loss (dB)

When the path loss is requested at a distance smaller than the reference

distance :math:`d_0`, the tx power (with no path loss) is returned. The

reference distance defaults to 1m and reference loss defaults to

:cpp:class:`FriisPropagationLossModel` with 5.15 GHz and is thus :math:`L_0` = 46.67 dB.

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=========================

PropagationLossModel

ToDo

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````

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==========================

The propagation loss is totally random, and it changes each time the model is called.

As a consequence, all the packets (even those between two fixed nodes) experience a random

propagation loss.

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============================

This propagation loss model implements Nakagami-m fast fading propagation loss model.

The Nakagami-m distribution is applied to the power level. The probability density function is defined as

.. math::

  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})

with :math:`m` the fading depth parameter and :math:`\omega` the average received power.

It is implemented by either a :cpp:class:`GammaRandomVariable` or a :cpp:class:`ErlangRandomVariable`

random variable.

Like in :cpp:class:ThreeLogDistancePropagationLossModel`, the :math:`m` parameter is varied

over three distance fields:

.. math::

  \underbrace{0 \cdots\cdots}_{m_0} \underbrace{d_1 \cdots\cdots}_{m_1} \underbrace{d_2 \cdots\cdots}_{m_2} \infty

For :math:`m = 1` the Nakagami-m distribution equals the Rayleigh distribution. Thus

this model also implements Rayleigh distribution based fast fading.

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=================

This model sets a constant received power level independent of the transmit power.

The received power is constant independent of the transmit power; the user

must set received power level.  Note that if this loss model is chained to other loss

models, it should be the first loss model in the chain. 

Else it will disregard the losses computed by loss models that precede it in the chain. 

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==========================

The propagation loss is fixed for each pair of nodes and doesn't depend on their actual positions.

This model shoud be useful for synthetic tests. Note that by default the propagation loss is 

assumed to be symmetric.

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=========================

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

Receivers at or within MaxRange meters receive the transmission at the

transmit power level. Receivers beyond MaxRange receive at power

-1000 dBm (effectively zero).

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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.

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.

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.

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.

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===============================

This model is designed for Line-of-Sight (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

This model is designed for Line-of-Sight (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

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===========================================

This model is designed for Non-Line-of-Sight (LoS) short range outdoor communication over rooftops in the frequency range 300 MHz to 100 GHz. This model includes several scenario-dependent parameters, such as average street width, orientation, etc. It is advised to set the values of these parameters manually (using the ns-3 attribute system) according to the desired scenario. 

This model is designed for Non-Line-of-Sight (LoS) short range outdoor communication over 

rooftops in the frequency range 300 MHz to 100 GHz. This model includes several scenario-dependent 

parameters, such as average street width, orientation, etc. It is advised to set the values of 

these parameters manually (using the ns-3 attribute system) according to the desired scenario. 

In detail, the model is based on [walfisch]_ and [ikegami]_, where the loss is expressed as the sum of free-space 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:

In detail, the model is based on [walfisch]_ and [ikegami]_, where the loss is expressed 

as the sum of free-space 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:

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

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

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

Therefore, in case of :math:`l > d_s` (where `l` is the distance over which the building extend), 

it can be evaluated according to

Kun2600MhzPropagationLossModel

This is the empirical model for the pathloss at 2600 MHz for urban areas which is described in [kun2600mhz]_. 

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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:

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:

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PropagationDelayModel

* ConstantSpeedPropagationDelayModel

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* RandomPropagationDelayModel

ConstantSpeedPropagationDelayModel

==================================

In this model, the signal travels with constant speed.

The delay is calculated according with the trasmitter and receiver positions.

The Euclidean distance between the Tx and Rx antennas is used.

Beware that, according to this model, the Earth is flat.

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===========================

ConstantSpeedPropagationDelayModel

The propagation delay is totally random, and it changes each time the model is called.

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All the packets (even those between two fixed nodes) experience a random delay.

As a consequence, the packets order is not preserved. 

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

  NS_LOG_DEBUG ("attenuation coefficent="<<rxc<<"Db");

  NS_LOG_DEBUG ("attenuation coefficient="<<rxc<<"Db");

 * discontinuity, which as we discussed can cause undesireable

 * discontinuity, which as we discussed can cause undesirable

 * To avoid these artifact, this implmentation of the Friis model

 * To avoid these artifact, this implementation of the Friis model

 * \f$ Pr = \frac{Pt * Gt * Gr * (ht^2 * hr^2)}{d^4 * L} \f$

 * \f$ Pr = \frac{P_t * G_t * G_r * (H_t^2 * H_r^2)}{d^4 * L} \f$

 * \f$ dCross = \frac{(4 * pi * Ht * Hr)}{lambda} \f$

 * \f$ dCross = \frac{(4 * \pi * H_t * H_r)}{\lambda} \f$