Superclass:  Channel

Rayleigh-faded channels are represented by the channel_rayleigh object, which is a subclass of the generic channel object.

A Rayleigh-faded channel is described by the fact that its entries are drawn i.i.d. from a complex Normal distribution with mean 0 and variance 1.

### Video Tutorial

A Rayleigh-faded channel can be created via

c = channel.create('Rayleigh')


which will create a channel_rayleigh object c.

The channel_rayeligh object is a subclass of the channel object, meaning it will inherit the properties and methods of the channel object.

### Key Properties

The channel_rayleigh object is a subclass of the channel object and thus inherits all of its properties and methods.

It does not contain any important properties beyond those inherited from the channel object, which are summarized below.

c.array_transmit
c.num_antennas_transmit
c.carrier_frequency
c.carrier_wavelength
c.propagation_velocity
c.channel_matrix


### Example Setup

The setup of a Rayleigh-faded channel, by virtue of its simplicity, is practically identical to that of a generic channel object, which looks similar to

c = channel.create()
c.set_carrier_frequency(fc)
c.set_propagation_velocity(vel)
c.set_arrays(atx,arx)


where fc is the carrier frequency (in Hz), vel is the propagation velocity (in m/s), and atx and arx are array objects at the channel input and output, respectively.

### Invoking a Channel Realization

Generating a realization of the Rayleigh-faded channel c is as simple as executing

H = c.realization()


where H is the realized channel matrix whose entries are drawn i.i.d. from a complex Normal distribution with mean 0 and variance 1.

The channel matrix can also be retrieved via

H = c.get_channel_matrix()


though this does not invoke a new channel realization but rather merely returns the current channel matrix.

### Shorthand Methods

The channel_rayleigh object inherits the following shorthand methods from the channel object.

• c.H — Returns the channel matrix.
• c.Nt — Returns the number of transmit antennas at the channel input.
• c.Nr — Returns the number of receive antennas at the channel output.

### List of Properties

The channel_rayleigh object contains the following properties:

• channel_rayleigh.name
• channel_rayleigh.channel_matrix
• channel_rayleigh.num_antennas_transmit
• channel_rayleigh.num_antennas_receive
• channel_rayleigh.array_transmit
• channel_rayleigh.array_receive
• channel_rayleigh.carrier_frequency
• channel_rayleigh.carrier_wavelength
• channel_rayleigh.propagation_velocity
• channel_rayleigh.normalized_channel_energy
• channel_rayleigh.force_channel_energy_normalization

### List of Methods

The channel_rayleigh object contains the following methods:

### Methods Documentation

#### H()

Returns the channel matrix.

Usage:
val = H()
Return Values:
val — the channel matrix

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#### Nr()

Returns the number of receive antennas out of the channel.

Usage:
val = Nr()
Return Values:
val — the number of receive antennas out of the channel

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#### Nt()

Returns the number of transmit antennas into the channel.

Usage:
val = Nt()
Return Values:
val — the number of transmit antennas into the channel

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#### channel_rayleigh(name)

Creates a MIMO channel object.

Usage:
obj = CHANNEL()
obj = CHANNEL(name)
Input Arguments:
name — an optional name for the object
Return Values:
obj — an object representing a MIMO channel

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#### create(type)

Creates a channel object of a specific type.

Usage:
c = channel.create()
c = channel.create(type)
Input Arguments:
type — (optional) a string specifying what type of channel to create
Return Values:
c — a channel object of the type specified

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#### enforce_channel_energy_normalization(H)

Normalizes the channel matrix so that its total energy (squared Frobenius norm) is equal the current normalized channel energy property. The default normalized channel energy is the product of the number of transmit antenans and the number of receive antennas.

Usage:
G = enforce_channel_energy_normalization()
G = enforce_channel_energy_normalization(H)
Input Arguments:
H — (optional) a channel matrix; if not passed, the current channel matrix will be used and overwritten with the normalized version; if passed, the channel matrix property will not be set
Return Values:
G — the normalized channel matrix

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#### get_channel_matrix()

Returns the channel matrix.

Usage:
H = get_channel_matrix()
Return Values:
H — channel matrix

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#### initialize()

Initializes a channel.

Usage:
initialize()

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#### realization()

Realizes a Rayleigh channel matrix where each entry in the channel matrix is drawn i.i.d. from a complex normal distribution.

Usage:
H = realization()
Return Values:
H — a channel matrix whose entries are Rayleigh-faded

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#### set_array_receive(array)

Sets the receive array object. Also sets the number of receive antennas accordingly.

Usage:
set_array_receive(array)
Input Arguments:
array — an array object

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#### set_array_transmit(array)

Sets the transmit array object. Also sets the number of transmit antennas accordingly.

Usage:
set_array_transmit(array)
Input Arguments:
array — an array object

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#### set_arrays(array_transmit,array_receive)

Sets the transmit and receive arrays at the input and output of the channel.

Usage:
set_arrays(array_transmit,array_receive)
Input Arguments:
array_transmit — an array object at the channel input
array_receive — an array object at the channel output

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#### set_carrier_frequency(fc)

Sets the carrier frequency of the channel.

Usage:
set_carrier_frequency(fc)
Input Arguments:
fc — carrier frequency (Hz)
Notes:

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#### set_channel_matrix(H)

Sets the channel matrix.

Usage:
set_channel_matrix(H)
Input Arguments:
H — channel matrix

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#### set_force_channel_energy_normalization(force)

Sets the enforcement of channel energy normalization. If true, the channel matrix will always be normalized such that its energy is of the desired value.

Usage:
set_force_channel_energy_normalization(force)
Input Arguments:
force — a boolean indicating if the channel matrix should be normalized or not

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#### set_name(name)

Sets the name of the channel.

Usage:
set_name()
set_name(name)
Input Arguments:
name — (optional) a string; if not passed, ‘channel’ is the default name used

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#### set_normalized_channel_energy(E)

Sets the normalized energy of the channel.

Usage:
set_normalized_channel_energy()
set_normalized_channel_energy(E)
Input Arguments:
E — (optional) the desired normalized channel energy; if not passed, the product of the number of transmit antennas and the number of receive antennas will be used

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#### set_propagation_velocity(val)

Sets the propagation velocity of the channel.

Usage:
set_propagation_velocity(val)
Input Arguments:
val — propagation velocity (meters/sec)

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#### set_receive_array(array)

Sets the receive array object (LEGACY).

Usage:
set_receive_array(array)
Input Arguments:
array — an array object

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#### set_transmit_array(array)

Sets the transmit array object (LEGACY).

Usage:
set_transmit_array(array)
Input Arguments:
array — an array object

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