Wideband Free Space
Broadband free-space propagation channel.
Description
The Wideband Free Space block simulates the propagation of a signal in free space from one point to another. The block models propagation time, propagation loss in free space and Doppler shift. The block assumes that the propagation speed is much greater than the speed of the target or antenna array, in which case the stop-and-hop model is valid.
When propagating a signal in a line-of-sight (LOS) channel to and from an object, you have the choice of using one block to calculate the two-way propagation delay in free space or two blocks to perform one-way propagation delays in each direction. Since the free-space propagation delay is not necessarily an integer multiple of the calculation step, it may be that the total round-trip delay in the calculation when using a two-way propagation block is different from the delay in the calculation when using two one-way propagation blocks. For this reason, it is recommended that a single two-way propagation unit be used whenever possible.
Ports
Input
X - wideband signal
complex vector-column M by 1 | complex matrix M by N
A wideband signal in the form of a complex vector-column M by 1 or a complex matrix M by N. The value of M is the number of samples of the signal, and N is the number of signals to propagate. When you specify N signals, you need to specify N signal sources or N signal destinations.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64.
Pos1 - coordinates of the signal source
valid vector-column 3 by 1 | valid matrix 3 by N
The position of the signal source is given as a valid vector-column 3 by 1 or a valid matrix 3 by N. The value of N is the number of signals to be propagated and is equal to the dimension specified in the signal at port X. If Pos1 is a column vector, it takes the form . If Pos1 is a matrix, each column specifies a different signal origin and is of the form . Pos1 and Pos2 cannot both be specified as matrices - at least one must be a 3 by 1 column vector. The units of position are metres.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64.
Pos2 - coordinates of the irradiated object
valid column vector 3 by 1 | valid matrix 3 by N
The coordinates of the irradiation object are given as a valid vector-column 3 by 1 or a valid matrix 3 by N. The value of N is the number of signals to be propagated and is equal to the dimension specified in the signal at port X. If Pos2 is a column vector, it takes the form . If Pos2 is a matrix, each column specifies a different signal origin and is of the form . Pos1 and Pos2 cannot both be specified as matrices - at least one must be a 3 by 1 column vector. The units of position are metres.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64.
Vel1 - velocity of the irradiated object
valid column vector 3 by 1 | valid matrix 3 by N
The velocity of the irradiated object in the form of a valid vector-column 3 by 1 or a valid matrix 3 by N. The value of N is the number of signals to be propagated and is equal to the dimension specified in the signal at the X port. If Vel1 is a column vector, it takes the form ]. If Vel1 is a matrix, each column specifies a different origin of the signal and is of the form ]. Vel1 and Vel2 cannot both be specified as matrices - at least one must be a 3 by 1 column vector. The units of position are metres.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64.
Vel2 - rate of signal assignment
valid column vector 3 by 1 | valid matrix 3 by N
The rate of assignment of a signal as a valid vector-column 3 by 1 or a valid matrix 3 by N. The value of N is the number of signals to be propagated and is equal to the dimensionality specified in the signal to port X. If Vel2 is a column vector, it takes the form . If Vel2 is a matrix, each column specifies a different signal origin and is of the form . Vel1 and Vel2 cannot both be specified as matrices - at least one must be a 3 by 1 column vector. The units of position are metres.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64.
Output
Port_1 - propagated wideband signal
complex vector-column M by 1 | complex matrix M by N
A propagated signal returned as a complex vector-column M by 1 or a complex matrix M by N.
If X is a column vector or matrix, Y is also a column vector or matrix with the same dimensions.
The output of Y contains the signal samples arriving at the signal destination during the current time interval. The current time period is defined as the time covered by the current input. Whenever it takes longer than the current time interval to propagate the signal from the source to the destination, the output data does not contain the contribution from the current time interval input.
Parameters
*Propagation speed (m/s)` - the propagation speed of the signal
3e8 (by default) | positive scalar
Signal propagation speed as a real positive scalar.
By default, the value of the speed of light is 3e8.
Signal carrier frequency (Hz) - the carrier frequency of the signal
3e8 (By default) | positive scalar
The carrier frequency of the signal as a positive real scalar. The unit of measurement is hertz.
Number of subbands - number of sub-bands
1e6 (by default) | `positive integer'.
The number of processing subbands specified as a positive integer.
Perform two-way propagation - switch off two-way propagation
disabled (by default) | on
Select this check box to perform two-way propagation between source and destination. Otherwise, the unit performs one-way propagation from source to destination.
Inherit sample rate - inherit sample rate
On (By default) | Off.
Select the checkbox to inherit sample rate from upstream blocks. Otherwise, set the sample rate using the Sample rate (Hz) parameters.
Sample rate (Hz) - sampling rate
1e6 (By default) | Positive scalar
The sampling frequency of the signal as a positive scalar. The unit of measurement is hertz.
Dependencies
To use this parameters, clear the Inherit sample rate checkbox.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.
Maximum one-way propagation distance (m) - maximum one-way propagation distance
10e3 (By default)
The maximum distance in metres between the signal source and the object of exposure as a positive scalar quantity. The amplitudes of any signals that propagate beyond this distance will be set to zero.
Algorithms
Propagation delay, Doppler shift and path loss in free space
When the source and target are stationary relative to each other, the block output can be written as . The value represents the delay and represents the propagation loss. The delay is calculated from , where is the propagation distance and is the propagation velocity. The free-space path loss is defined by the expression
,
where: is the wavelength of the signal.
This formula assumes that the target is in the far zone of the transmitting antenna element or antenna array. In the near zone, the free-space propagation path loss formula is invalid and may result in a loss less than unity, which is equivalent to signal gain. For this reason, the loss is set equal to unity for the range values .
When there is relative motion between source and target, processing also introduces a frequency shift. This shift corresponds to the Doppler shift between the source and target points. The frequency shift is for one-way propagation and for two-way propagation. The parameters is the relative velocity of the target relative to the source.