Free-Space Path Loss with Log-Normal Shadowing

Superclass:  Path Loss   

On This Page

• About
• Creating a Free-Space Path Loss with Log-Normal Shadowing Object
• Key Properties
• Setting the Log-Normal Shadowing Variance
• Example Setup
• Getting the Attenuation
• List of Properties
• List of Methods
• Methods Documentation

About

The path_loss_free_space_log_normal_shadowing object represents a free-space path loss model with log-normal shadowing. It is a subclass of the path_loss_free_space object (and thus of the path_loss object), supplying the deterministic loss of a free-space path loss model with a random shadowing term.

Recall that deterministic free-space path loss can be described entirely by three parameters:

1. the carrier wavelength $\lambda$
2. the distance $d$
3. the path loss exponent $\eta$

The path loss (or attenuation) stemming from a free-space path loss with log-normal shadowing can be described as

where $G^2$ is the path gain and $1/G^2$ is the path loss; and $\gamma$ is the shadowing parameter.

Typically, $\eta \geq 2$ except in rare settings with significant clutter. Most often, $\eta \in [2,4]$.

In log-normal shadowing, realizations $\gamma$ of the random variable $\Gamma$ are distributed as

where $\sigma_{\gamma}^2$ is the variance of log-normal shadowing.

Creating a Free-Space Path Loss with Log-Normal Shadowing Object

A free-space path loss with log-normal shadowing object path_loss_free_space_log_normal_shadowing can be created via

p = path_loss.create('free-space-log-normal-shadowing')

Key Properties

The path_loss_free_space_log_normal_shadowing object inherits all properties of the path_loss_free_space object, the key ones being

p.attenuation
p.carrier_frequency
p.carrier_wavelength
p.propagation_velocity
p.distance
p.path_loss_exponent

In addition, it also has the property

p.log_normal_shadowing_variance

which captures the log-normal shadowing variance (i.e., $\sigma_{\gamma}^2$).

Setting the Log-Normal Shadowing Variance

To set the variance of log-normal shadowing of a free space path loss with log-normal shadowing object p, use

p.set_log_normal_shadowing_variance(var)

where var is the variance of log-normal shadowing (a non-negative number).

Example Setup

A typical path_loss_free_space_log_normal_shadowing object setup looks something similar to

p = path_loss.create()
p.set_carrier_frequency(fc)
p.set_propagation_velocity(vel)
p.set_distance(d)
p.set_path_loss_exponent(ple)
p.set_log_normal_shadowing_variance(var)

Invoking a Realization

To realize the path loss, use

atten = p.realization()

which, when appropriately setup, will return the attenuation atten for the given carrier wavelength, distance, path loss exponent, and log-normal shadowing variance.

Note that atten is related to the large-scale gain $G$ by simply atten $= G^{-2}$.

Getting the Attenuation

To get the realized attenuation of a path_loss_free_space_log_normal_shadowing object p, one can also use

atten = p.get_attenuation()

where atten is the attenuation of the path loss (power loss, linear scale).

List of Properties

The path_loss_free_space_log_normal_shadowing object contains the following properties:

• path_loss_free_space_log_normal_shadowing.log_normal_shadowing_variance
• path_loss_free_space_log_normal_shadowing.path_loss_exponent
• path_loss_free_space_log_normal_shadowing.name
• path_loss_free_space_log_normal_shadowing.type
• path_loss_free_space_log_normal_shadowing.distance
• path_loss_free_space_log_normal_shadowing.attenuation
• path_loss_free_space_log_normal_shadowing.carrier_frequency
• path_loss_free_space_log_normal_shadowing.carrier_wavelength
• path_loss_free_space_log_normal_shadowing.propagation_velocity

List of Methods

The path_loss_free_space_log_normal_shadowing object contains the following methods:

• path_loss_free_space_log_normal_shadowing.compute_path_loss_attenuation Computes the path attenuation (path loss) according to the free-space path loss (FSPL) formula.
• path_loss_free_space_log_normal_shadowing.create Creates a path loss object of a specific type.
• path_loss_free_space_log_normal_shadowing.get_attenuation Returns the realized attenuation of the path loss model.
• path_loss_free_space_log_normal_shadowing.initialize Initializes a path loss object.
• path_loss_free_space_log_normal_shadowing.initialize_free_space Initializes a free-space path loss object.
• path_loss_free_space_log_normal_shadowing.initialize_free_space_log_normal_shadowing Initializes a free-space path loss with log-normal shadowing object.
• path_loss_free_space_log_normal_shadowing.path_loss_free_space_log_normal_shadowing Creates a free-space path loss with log-normal shadowing object.
• path_loss_free_space_log_normal_shadowing.realization Invokes a realization of the path loss.
• path_loss_free_space_log_normal_shadowing.realization_log_normal_shadowing Realizes log-normal shadowing based on the current log-normal shadowing variance.
• path_loss_free_space_log_normal_shadowing.set_carrier_frequency Sets the carrier frequency of the channel. Also updates the carrier wavelength accordingly.
• path_loss_free_space_log_normal_shadowing.set_distance Sets the distance of the path (in meters).
• path_loss_free_space_log_normal_shadowing.set_log_normal_shadowing_variance Sets the log-normal shadowing variance.
• path_loss_free_space_log_normal_shadowing.set_name Sets the name of the path loss model.
• path_loss_free_space_log_normal_shadowing.set_path_loss_attenuation Sets the attenuation of the path loss model.
• path_loss_free_space_log_normal_shadowing.set_path_loss_exponent Sets the path loss exponent.
• path_loss_free_space_log_normal_shadowing.set_propagation_velocity Sets the propagation velocity of the channel. Also updates the carrier wavelength accordingly.
• path_loss_free_space_log_normal_shadowing.set_type Sets the type of path loss model.

Methods Documentation

compute_path_loss_attenuation()

Computes the path attenuation (path loss) according to the free-space path loss (FSPL) formula.

Usage:

atten = compute_path_loss_attenuation()

Return Values:

atten — the path attenuation (path loss) (a power loss)

Notes:

The free-space path loss (FSPL) equation used is G = (lambda / (4*pi))^2 * (1/d)^ple, where G is the inverse path loss in terms of power.

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create(type)

Creates a path loss object of a specific type.

Usage:

obj = path_loss.create()

obj = path_loss.create(type)

Input Arguments:

type — (optional) a string specifying which path loss model to create

Return Values:

obj — a path loss object

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get_attenuation()

Returns the realized attenuation of the path loss model.

Usage:

val = get_attenuation()

Return Values:

val — the attenuation (power loss) of the path

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initialize()

Initializes a path loss object.

Usage:

initialize()

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initialize_free_space()

Initializes a free-space path loss object.

Usage:

initialize_free_space()

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initialize_free_space_log_normal_shadowing()

Initializes a free-space path loss with log-normal shadowing object.

Usage:

initialize_free_space_log_normal_shadowing()

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path_loss_free_space_log_normal_shadowing(name)

Creates a free-space path loss with log-normal shadowing object.

Usage:

obj = path_loss_free_space_log_normal_shadowing()

obj = path_loss_free_space_log_normal_shadowing(name)

Input Arguments:

name — an optional name for the object

Return Values:

obj — an object representing free-space path loss

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realization()

Invokes a realization of the path loss.

Usage:

atten = realization()

Return Values:

val — the realized path loss attenuation with shadowing

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realization_log_normal_shadowing()

Realizes log-normal shadowing based on the current log-normal shadowing variance.

Usage:

val = realization_log_normal_shadowing()

Return Values:

val — the realized shadowing factor

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set_carrier_frequency(fc)

Sets the carrier frequency of the channel. Also updates the carrier wavelength accordingly.

Usage:

set_carrier_frequency(fc)

Input Arguments:

fc — carrier frequency (Hz)

Notes:

Also updates carrier wavelength.

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set_distance(d)

Sets the distance of the path (in meters).

Usage:

set_distance(d) Sets the distance of the link to a specific

value.

Input Arguments:

d — distance of the path (in meters)

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set_log_normal_shadowing_variance(var)

Sets the log-normal shadowing variance.

Usage:

set_log_normal_shadowing_variance(var)

Input Arguments:

var — log-normal shadowing variance (a quantity in dB)

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set_name(name)

Sets the name of the path loss model.

Usage:

set_name()

set_name(name)

Input Arguments:

name — (optional) a string; if not passed, ‘path-loss’ is the default name used

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set_path_loss_attenuation(atten)

Sets the attenuation of the path loss model.

Usage:

set_path_loss_attenuation(atten)

Input Arguments:

atten — the attenuation (power loss) of the path

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set_path_loss_exponent(ple)

Sets the path loss exponent.

Usage:

set_path_loss_exponent(ple)

Input Arguments:

ple — path loss exponent (a positive number)

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set_propagation_velocity(val)

Sets the propagation velocity of the channel. Also updates the carrier wavelength accordingly.

Usage:

set_propagation_velocity(val)

Input Arguments:

val — propagation velocity (meters/sec)

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set_type(type)

Sets the type of path loss model.

Usage:

set_type()

set_type(type)

Input Arguments:

type — (optional) a string; if not passed, ‘default’ is the default type used

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