phased.WidebandLOSChannel

Wideband LOS propagation channel

Description

The phased.WidebandLOSChannel models the propagation of narrowband electromagnetic signals through a line-of-sight (LOS) channel from a source to a destination. In an LOS channel, propagation paths are straight lines from point to point. The propagation model in the LOS channel includes free-space attenuation in addition to attenuation due to atmospheric gases, rain, fog, and clouds. You can use phased.WidebandLOSChannel to model the propagation of signals between multiple points simultaneously. The System object™ works for all frequencies.

While the attenuation models for atmospheric gases and rain are valid for electromagnetic signals in the frequency range 1–1000 GHz only, the attenuation model for fog and clouds is valid for 10–1000 GHz. Outside these frequency ranges, the System object uses the nearest valid value.

The phased.WidebandLOSChannel System object applies range-dependent time delays to the signals, as well as gains or losses. When either the source or destination is moving, the System object applies Doppler shifts.

Like the phased.WidebandFreeSpace System object, the phased.WidebandLOSChannel System object supports two-way propagation.

To compute the propagation delay for specified source and receiver points:

Define and set up your Wideband LOS channel using the Construction procedure. You can set the System object properties during construction or leave them at their default values.
Call the step method to compute the propagated signal using the properties of the phased.WidebandLOSChannel System object. You can change tunable properties before or after any call to the step method.

Note

Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

sWBLOS = phased.WidebandLOSChannel creates a Wideband LOS attenuating propagation channel System object, sWBLOS.

sWBLOS = phased.WidebandLOSChannel(Name,Value) creates a System object, sWBLOS, with each specified property Name set to the specified Value. You can specify additional name and value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

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`PropagationSpeed` — Signal propagation speed
`physconst('LightSpeed')` (default) | positive scalar

Signal propagation speed, specified as a positive scalar. Units are in meters per second. The default propagation speed is the value returned by physconst('LightSpeed'). See physconst for more information.

Example: 3e8

Data Types: double

`OperatingFrequency` — Operating frequency
`300e6` (default) | positive scalar

Operating frequency, specified as a positive scalar. Units are in Hz.

Example: 1e9

Data Types: double

`SpecifyAtmosphere` — Enable atmospheric attenuation model
`false` (default) | `true`

Option to enable the atmospheric attenuation model, specified as a false or true. Set this property to true to add signal attenuation caused by atmospheric gases, rain, fog, or clouds. Set this property to false to ignore atmospheric effects in propagation.

`TwoWayPropagation` — Enable two-way propagation
`false` (default) | `true`

Enable two-way propagation, specified as a false or true. Set this property to true to perform round-trip propagation between the signal origin and destination specified in step. Set this property to false to perform only one-way propagation from the origin to the destination.

Example: true

Data Types: logical

`SampleRate` — Sample rate of signal
`1e6` (default) | positive scalar

Sample rate of signal, specified as a positive scalar. Units are in Hz. The System object uses this quantity to calculate the propagation delay in units of samples.

Example: 1e6

Data Types: double

`NumSubbands` — Number of processing subbands
`64` (default) | positive integer

Number of processing subbands, specified as a positive integer.

Example: 128

Data Types: double

`MaximumDistanceSource` — Source of maximum one-way propagation distance
`'Auto'` (default) | `'Property'`

Source of maximum one-way propagation distance, specified as 'Auto' or 'Property'. The maximum one-way propagation distance is used to allocate sufficient memory for signal delay computation. When you set this property to 'Auto', the System object automatically allocates memory. When you set this property to 'Property', you specify the maximum one-way propagation distance using the value of the MaximumDistance property.

Data Types: char

`MaximumDistance` — Maximum one-way propagation distance
`10000` (default) | positive real-valued scalar

Maximum one-way propagation distance, specified as a positive real-valued scalar. Units are in meters. Any signal that propagates more than the maximum one-way distance is ignored. The maximum distance must be greater than or equal to the largest position-to-position distance.

Example: 5000

Dependencies

To enable this property, set the MaximumDistanceSource property to 'Property'.

Data Types: double

`MaximumNumInputSamplesSource` — Source of maximum number of samples
`'Auto'` (default) | `'Property'`

The source of the maximum number of samples of the input signal, specified as 'Auto' or 'Property'. When you set this property to 'Auto', the propagation model automatically allocates enough memory to buffer the input signal. When you set this property to 'Property', you specify the maximum number of samples in the input signal using the MaximumNumInputSamples property. Any input signal longer than that value is truncated.

To use this object with variable-size signals in a MATLAB^® Function Block in Simulink^®, set the MaximumNumInputSamplesSource property to 'Property' and set a value for the MaximumNumInputSamples property.

Example: 'Property'

Dependencies

To enable this property, set MaximumDistanceSource to 'Property'.

Data Types: char

`MaximumNumInputSamples` — Maximum number of input signal samples
`100` (default) | positive integer

Maximum number of input signal samples, specified as a positive integer. The input signal is the first argument of the step method, after the System object itself. The size of the input signal is the number of rows in the input matrix. Any input signal longer than this number is truncated. To process signals completely, ensure that this property value is greater than any maximum input signal length.

The waveform-generating System objects determine the maximum signal size:

For any waveform, if the waveform OutputFormat property is set to 'Samples', the maximum signal length is the value specified in the NumSamples property.
For pulse waveforms, if the OutputFormat is set to 'Pulses', the signal length is the product of the smallest pulse repetition frequency, the number of pulses, and the sample rate.
For continuous waveforms, if the OutputFormat is set to 'Sweeps', the signal length is the product of the sweep time, the number of sweeps, and the sample rate.

Example: 2048

Dependencies

To enable this property, set MaximumNumInputSamplesSource to 'Property'.

Data Types: double

Methods

reset	Reset states of System object
step	Propagate signal in Wideband LOS channel

Common to All System Objects
`release`	Allow System object property value changes

Examples

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Spectrum of Propagated Signal in Wideband LOS Channel

Open Live Script

Propagate a wideband signal in a line-of-sight (LOS) channel from a radar at (0,0,0) meters to a target at (35,0,0) meters in medium fog. Set the fog liquid water density to 0.05 gm/m3. Assume rain is falling at 5 mm/hr. The signal carrier frequency is 20 GHz. The signal is a sum of four cw tones at 19.75, 19.875, 20.125, and 20.25 GHz. Set the signal duration to 0.5 μs and the sample rate to 2.0 GHz. Assume the radar is stationary and the target approaches the radar at 40 m/s. The atmospheric temperature is 12°C.

Set the signal parameters and create the transmitted signal.

c = physconst('LightSpeed');
fs = 2e9;
freq = [-0.25,-.125,0.125,0.25]*1e9;
fc = 20.0e9;
dt = 1/fs;
t = [0:dt:.5e-6];
sig = sum(exp(1i*2*pi*t.'*freq),2);

Specify the atmosphere parameters and create the phased.WidebandChannel System object™.

lwd = 0.05;
rainrate = 5.0;
temp = 12.0;
loschannel = phased.WidebandLOSChannel('SampleRate',fs,'PropagationSpeed',c,...
    'SpecifyAtmosphere',true,'OperatingFrequency',fc,'RainRate',rainrate,...
    'LiquidWaterDensity',lwd,'Temperature',temp);

Specify the radar and target positions and velocities.

xradar = [0,0,0].';
vradar = [0,0,0].';
xtgt = [35,0,0].';
vtgt = [-40,0,0].';

Propagated the signal using the step method.

prop_sig = loschannel(sig,xradar,xtgt,vradar,vtgt);

Plot the propagated signal. For a target range of 35 m, the propagation delay is 0.11 μs as seen in the plot.

plot(t*1e6,real(prop_sig))
grid
xlabel('Time ({\mu}s)')
ylabel('Amplitude')

Using the periodogram function with a Taylor window, plot the spectra of the original and propagated signals.

nfft = 1024;
nsamp = size(sig,1);
periodogram([sig prop_sig],taylorwin(nsamp),nfft,fs,'centered')
ylim([-200 0])
legend('transmitted','propagated')

More About

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Attenuation and Loss Factors

Attenuation or path loss in the Wideband LOS channel consists of four components. L = L_fspL_gL_cL_r, where

L_fsp is the free-space path attenuation
L_g is the atmospheric path attenuation
L_c is the fog and cloud path attenuation
L_r is the rain path attenuation

Each component is in magnitude units, not in dB.

Free-space Time Delay and Loss

When the origin and destination are stationary relative to each other, you can write the output signal of a free-space channel as Y(t) = x(t-τ)/L_fsp. The quantity τ is the signal delay and L_fsp is the free-space path loss. The delay τ is given by R/c, where R is the propagation distance and c is the propagation speed. The free-space path loss is given by

$L_{f s p} = \frac{{(4 π R)}^{2}}{λ^{2}},$

where λ is the signal wavelength.

This formula assumes that the target is in the far field of the transmitting element or array. In the near field, the free-space path loss formula is not valid and can result in a loss smaller than one, equivalent to a signal gain. Therefore, the loss is set to unity for range values, R ≤ λ/4π.

When the origin and destination have relative motion, the processing also introduces a Doppler frequency shift. The frequency shift is v/λ for one-way propagation and 2v/λ for two-way propagation. The quantity v is the relative speed of the destination with respect to the origin.

For more details on free space channel propagation, see [5].

Atmospheric Gas Attenuation Model

This model calculates the attenuation of signals that propagate through atmospheric gases.

Electromagnetic signals attenuate when they propagate through the atmosphere. This effect is due primarily to the absorption resonance lines of oxygen and water vapor, with smaller contributions coming from nitrogen gas. The model also includes a continuous absorption spectrum below 10 GHz. The ITU model Recommendation ITU-R P.676-10: Attenuation by atmospheric gases is used. The model computes the specific attenuation (attenuation per kilometer) as a function of temperature, pressure, water vapor density, and signal frequency. The atmospheric gas model is valid for frequencies from 1–1000 GHz and applies to polarized and nonpolarized fields.

The formula for specific attenuation at each frequency is

$γ = γ_{o} (f) + γ_{w} (f) = 0.1820 f N^{″} (f) .$

The quantity N"() is the imaginary part of the complex atmospheric refractivity and consists of a spectral line component and a continuous component:

$N^{″} (f) = \sum_{i} S_{i} F_{i} + {N^{″}}_{D}^{} (f)$

The spectral component consists of a sum of discrete spectrum terms composed of a localized frequency bandwidth function, F(f)_i, multiplied by a spectral line strength, S_i. For atmospheric oxygen, each spectral line strength is

$S_{i} = a_{1} \times 10^{- 7} {(\frac{300}{T})}^{3} \exp [a_{2} (1 - (\frac{300}{T})] P .$

For atmospheric water vapor, each spectral line strength is

$S_{i} = b_{1} \times 10^{- 1} {(\frac{300}{T})}^{3.5} \exp [b_{2} (1 - (\frac{300}{T})] W .$

P is the dry air pressure, W is the water vapor partial pressure, and T is the ambient temperature. Pressure units are in hectoPascals (hPa) and temperature is in degrees Kelvin. The water vapor partial pressure, W, is related to the water vapor density, ρ, by

$W = \frac{ρ T}{216.7} .$

The total atmospheric pressure is P + W.

For each oxygen line, S_i depends on two parameters, a₁ and a₂. Similarly, each water vapor line depends on two parameters, b₁ and b₂. The ITU documentation cited at the end of this section contains tabulations of these parameters as functions of frequency.

The localized frequency bandwidth functions F_i(f) are complicated functions of frequency described in the ITU references cited below. The functions depend on empirical model parameters that are also tabulated in the reference.

To compute the total attenuation for narrowband signals along a path, the function multiplies the specific attenuation by the path length, R. Then, the total attenuation is L_g= R(γ_o + γ_w).

You can apply the attenuation model to wideband signals. First, divide the wideband signal into frequency subbands, and apply attenuation to each subband. Then, sum all attenuated subband signals into the total attenuated signal.

Fog and Cloud Attenuation Model

This model calculates the attenuation of signals that propagate through fog or clouds.

Fog and cloud attenuation are the same atmospheric phenomenon. The ITU model, Recommendation ITU-R P.840-6: Attenuation due to clouds and fog is used. The model computes the specific attenuation (attenuation per kilometer), of a signal as a function of liquid water density, signal frequency, and temperature. The model applies to polarized and nonpolarized fields. The formula for specific attenuation at each frequency is

$γ_{c} = K_{l} (f) M,$

where M is the liquid water density in gm/m³. The quantity K_l(f) is the specific attenuation coefficient and depends on frequency. The cloud and fog attenuation model is valid for frequencies 10–1000 GHz. Units for the specific attenuation coefficient are (dB/km)/(g/m³).

To compute the total attenuation for narrowband signals along a path, the function multiplies the specific attenuation by the path length R. Total attenuation is L_c = Rγ_c.

You can apply the attenuation model to wideband signals. First, divide the wideband signal into frequency subbands, and apply narrowband attenuation to each subband. Then, sum all attenuated subband signals into the total attenuated signal.

Rainfall Attenuation Model

This model calculates the attenuation of signals that propagate through regions of rainfall. Rain attenuation is a dominant fading mechanism and can vary from location-to-location and from year-to-year.

Electromagnetic signals are attenuated when propagating through a region of rainfall. Rainfall attenuation is computed according to the ITU rainfall model Recommendation ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods. The model computes the specific attenuation (attenuation per kilometer) of a signal as a function of rainfall rate, signal frequency, polarization, and path elevation angle. The specific attenuation, ɣ_R, is modeled as a power law with respect to rain rate

$γ_{R} = k R^{α},$

where R is rain rate. Units are in mm/hr. The parameter k and exponent α depend on the frequency, the polarization state, and the elevation angle of the signal path. The specific attenuation model is valid for frequencies from 1–1000 GHz.

To compute the total attenuation for narrowband signals along a path, the function multiplies the specific attenuation by the an effective propagation distance, d_eff. Then, the total attenuation is L = d_effγ_R.

The effective distance is the geometric distance, d, multiplied by a scale factor

$r = \frac{1}{0.477 d^{0.633} R_{0.01}^{0.073 α} f^{0.123} - 10.579 (1 - \exp (- 0.024 d))}$

where f is the frequency. The article Recommendation ITU-R P.530-17 (12/2017): Propagation data and prediction methods required for the design of terrestrial line-of-sight systems presents a complete discussion for computing attenuation.

The rain rate, R, used in these computations is the long-term statistical rain rate, R_0.01. This is the rain rate that is exceeded 0.01% of the time. The calculation of the statistical rain rate is discussed in Recommendation ITU-R P.837-7 (06/2017): Characteristics of precipitation for propagation modelling. This article also explains how to compute the attenuation for other percentages from the 0.01% value.

You can apply the attenuation model to wideband signals. First, divide the wideband signal into frequency subbands and apply attenuation to each subband. Then, sum all attenuated subband signals into the total attenuated signal.

Subband Frequency Processing

Subband processing decomposes a wideband signal into multiple subbands and applies narrowband processing to the signal in each subband. The signals for all subbands are summed to form the output signal.

When using wideband frequency System objects or blocks, you specify the number of subbands, N_B, in which to decompose the wideband signal. Subband center frequencies and widths are automatically computed from the total bandwidth and number of subbands. The total frequency band is centered on the carrier or operating frequency, f_c. The overall bandwidth is given by the sample rate, f_s. Frequency subband widths are Δf = f _s/N_B. The center frequencies of the subbands are

$f_{m} = {\begin{matrix} f_{c} - \frac{f_{s}}{2} + (m - 1) Δ f, N_{B} even \\ f_{c} - \frac{(N_{B} - 1) f_{s}}{2 N_{B}} + (m - 1) Δ f, N_{B} odd \end{matrix}, m = 1, \dots, N_{B}$

Some System objects let you obtain the subband center frequencies as output when you run the object. The returned subband frequencies are ordered consistently with the ordering of the discrete Fourier transform. Frequencies above the carrier appear first, followed by frequencies below the carrier.

The phased.WidebandLOSChannel System object uses narrowband time delay and attenuation algorithms for each subband.

References

[1] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.676-10: Attenuation by atmospheric gases. 2013.

[2] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.840-6: Attenuation due to clouds and fog. 2013.

[3] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods. 2005.

[4] Seybold, J. Introduction to RF Propagation. New York: Wiley & Sons, 2005.

[5] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.

Documentation

phased.WidebandLOSChannel

Description

Construction

Properties

PropagationSpeed — Signal propagation speed physconst('LightSpeed') (default) | positive scalar

OperatingFrequency — Operating frequency 300e6 (default) | positive scalar

SpecifyAtmosphere — Enable atmospheric attenuation model false (default) | true

Temperature — Ambient temperature 15 (default) | real-valued scalar

Dependencies

DryAirPressure — Atmospheric dry air pressure 101.325e3 (default) | positive real-valued scalar

Dependencies

WaterVapourDensity — Atmospheric water vapor density 7.5 (default) | positive real-valued scalar

Dependencies

LiquidWaterDensity — Liquid water density 0.0 (default) | nonnegative real-valued scalar

Dependencies

RainRate — Rainfall rate 0.0 (default) | non-negative real-valued scalar

TwoWayPropagation — Enable two-way propagation false (default) | true

SampleRate — Sample rate of signal 1e6 (default) | positive scalar

NumSubbands — Number of processing subbands 64 (default) | positive integer

MaximumDistanceSource — Source of maximum one-way propagation distance 'Auto' (default) | 'Property'

MaximumDistance — Maximum one-way propagation distance 10000 (default) | positive real-valued scalar

Dependencies

MaximumNumInputSamplesSource — Source of maximum number of samples 'Auto' (default) | 'Property'

Dependencies

MaximumNumInputSamples — Maximum number of input signal samples 100 (default) | positive integer

Dependencies

Methods

Examples

Spectrum of Propagated Signal in Wideband LOS Channel

More About

Attenuation and Loss Factors

Free-space Time Delay and Loss

Atmospheric Gas Attenuation Model

Fog and Cloud Attenuation Model

Rainfall Attenuation Model

Subband Frequency Processing

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Functions

Objects

Phased Array System Toolbox Documentation

Support

`PropagationSpeed` — Signal propagation speed
`physconst('LightSpeed')` (default) | positive scalar

`OperatingFrequency` — Operating frequency
`300e6` (default) | positive scalar

`SpecifyAtmosphere` — Enable atmospheric attenuation model
`false` (default) | `true`

`Temperature` — Ambient temperature
`15` (default) | real-valued scalar

`DryAirPressure` — Atmospheric dry air pressure
`101.325e3` (default) | positive real-valued scalar

`WaterVapourDensity` — Atmospheric water vapor density
`7.5` (default) | positive real-valued scalar

`LiquidWaterDensity` — Liquid water density
`0.0` (default) | nonnegative real-valued scalar

`RainRate` — Rainfall rate
`0.0` (default) | non-negative real-valued scalar

`TwoWayPropagation` — Enable two-way propagation
`false` (default) | `true`

`SampleRate` — Sample rate of signal
`1e6` (default) | positive scalar

`NumSubbands` — Number of processing subbands
`64` (default) | positive integer

`MaximumDistanceSource` — Source of maximum one-way propagation distance
`'Auto'` (default) | `'Property'`

`MaximumDistance` — Maximum one-way propagation distance
`10000` (default) | positive real-valued scalar

`MaximumNumInputSamplesSource` — Source of maximum number of samples
`'Auto'` (default) | `'Property'`

`MaximumNumInputSamples` — Maximum number of input signal samples
`100` (default) | positive integer

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.