Filter input signal through multipath Rayleigh fading channel
The comm.RayleighChannel
System object™ filters an input signal through the multipath Rayleigh fading channel. For
more information on fading model processing, see the Methodology for Simulating
Multipath Fading Channels section.
To filter an input signal through a multipath Rayleigh fading channel:
Create the comm.RayleighChannel
object and set its properties.
Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?
creates a
frequencyselective or frequencyflat multipath Rayleigh fading channel System
object. This object filters a real or complex input signal through the multipath
channel to obtain a channelimpaired signal.rayleighchan
= comm.RayleighChannel
sets properties using one or more namevalue arguments. For example,
rayleighchan
= comm.RayleighChannel(Name,Value)'SampleRate',2
sets the input signal sample rate to 2.
Unless otherwise indicated, properties are nontunable, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
release
function unlocks them.
If a property is tunable, you can change its value at any time.
For more information on changing property values, see System Design in MATLAB Using System Objects.
SampleRate
— Input signal sample rate1
(default)  positive scalarInput signal sample rate in hertz, specified as a positive scalar.
Data Types: double
PathDelays
— Discrete path delay0
(default)  scalar  row vectorDiscrete path delay in seconds, specified as a scalar or row vector.
When you set PathDelays
to a
scalar, the channel is frequency flat.
When you set PathDelays
to a
vector, the channel is frequency selective.
The PathDelays
and AveragePathGains
properties must be the same length.
Data Types: double
AveragePathGains
— Average gains of discrete paths0
(default)  scalar  row vectorAverage gains of the discrete paths in decibels, specified as a scalar or row
vector. The AveragePathGains
and PathDelays
properties
must be the same length.
Data Types: double
NormalizePathGains
— Normalize average path gainstrue
or 1
(default)  false
or 0
Normalize average path gains, specified as one of these logical values:
1
(true
) — The fading processes
are normalized so that the total power of the path gains, averaged over
time, is 0 dB.
0
(false
) — The total power of
the path gains is not normalized.
The AveragePathGains
property specifies the average powers of the path gains.
Data Types: logical
MaximumDopplerShift
— Maximum Doppler shift for all channel paths0.001
(default)  nonnegative scalarMaximum Doppler shift for all channel paths, specified as a nonnegative scalar. Units are in hertz.
The maximum Doppler shift limit applies to each channel path. When you set this
property to 0
, the channel remains static for the entire input.
You can use the reset
object function to
generate a new channel realization. The MaximumDopplerShift
property value must be smaller than SampleRate
/10/f_{c} for each
path. f_{c} is the cutoff frequency factor
of the path. For most Doppler spectrum types, the value of
f_{c} is 1. For Gaussian and biGaussian
Doppler spectrum types, f_{c} is dependent
on the Doppler spectrum structure fields. For more details about how
f_{c} is defined, see the Cutoff Frequency Factor
section.
Data Types: double
DopplerSpectrum
— Doppler spectrum shape for all channel pathsdoppler('Jakes')
(default)  Doppler spectrum structure  1byN_{P} cell array of Doppler
spectrum structuresDoppler spectrum shape for all channel paths, specified as a Doppler spectrum
structure or a 1byN_{P} cell array of
Doppler spectrum structures. These Doppler spectrum structures must be outputs of
the form returned from the doppler
function.
N_{P} is the number of discrete delay
paths specified by the PathDelays
property. The
MaximumDopplerShift
property defines the maximum Doppler shift
value that the DopplerSpectrum
property permits when you
specify the Doppler spectrum..
When you set DopplerSpectrum
to a single Doppler
spectrum structure, all paths have the same specified Doppler
spectrum.
When you set DopplerSpectrum
to a cell array of
Doppler spectrum structures, each path has the Doppler spectrum specified
by the corresponding structure in the cell array.
Specify options for the spectrum type by using the
specType
input to the doppler
function. If you set the
FadingTechnique
property to 'Sum of sinusoids'
, you must set
DopplerSpectrum
to
doppler('Jakes')
.
To enable this property, set the MaximumDopplerShift
property to a positive scalar.
Data Types: struct
 cell
ChannelFiltering
— Channel filteringtrue
or 1
(default)  false
or 0
Channel filtering, specified as one of these logical values:
1
(true
) — The channel accepts
an input signal and produces a filtered output signal.
0
(false
) — The object does not
accept an input signal, produces no filtered output signal, and outputs
only channel path gains. You must specify the duration of the fading
process by using the NumSamples
property.
Data Types: logical
PathGainsOutputPort
— Output channel path gainsfalse
or 0
(default)  true
or 1
Output channel path gains, specified as a logical 0
(false
) or 1
(true
).
Set this property to true
to output the channel path gains of
the underlying fading process.
To enable this property, set the ChannelFiltering
property to true
.
Data Types: logical
NumSamples
— Number of samples100
(default)  nonnegative integerNumber of samples used for the duration of the fading process, specified as a nonnegative integer.
Tunable: Yes
To enable this property, set the ChannelFiltering
property to false
.
Data Types: double
OutputDataType
— Path gain output data type'double'
(default)  'single'
Path gain output data type, specified as 'double'
or
'single'
.
To enable this property, set the ChannelFiltering
property to false
.
Data Types: char
 string
FadingTechnique
— Channel model fading technique'Filtered Gaussian noise'
(default)  'Sum of sinusoids'
Channel model fading technique, specified as 'Filtered Gaussian
noise'
or 'Sum of sinusoids'
.
Data Types: char
 string
NumSinusoids
— Number of sinusoids used48
(default)  positive integerNumber of sinusoids used to model the fading process, specified as a positive integer.
To enable this property, set the FadingTechnique
property to 'Sum of sinusoids'
.
Data Types: double
InitialTimeSource
— Source to control start time of fading process'Property'
(default)  'Input port'
Source to control the start time of the fading process, specified as
'Property'
or 'Input port'
.
When you set InitialTimeSource
to
'Property'
, set the initial time offset by using
the InitialTime
property.
When you set InitialTimeSource
to 'Input
port'
, specify the start time of the fading process by using
the inittime
input argument. The input value can change in
consecutive calls to the object.
To enable this property, set the FadingTechnique
property to 'Sum of sinusoids'
.
Data Types: char
 string
InitialTime
— Initial time offset0
(default)  nonnegative scalarInitial time offset for the fading model in seconds, specified as a nonnegative scalar.
When mod
(InitialTime
/SampleRate
) is nonzero, the initial time offset is rounded up to the nearest
sample position.
To enable this property, set the FadingTechnique
property to 'Sum of sinusoids'
and the InitialTimeSource
property to
'Property'
.
Data Types: double
RandomStream
— Source of random number stream'Global stream'
(default)  'mt19937ar with seed'
Source of the random number stream, specified as 'Global
stream'
or 'mt19937ar with seed'
.
When you specify 'Global stream'
, the object uses
the current global random number stream for normally distributed random
number generation. In this case, the reset
object function resets only the filters.
When you specify 'mt19937ar with seed'
, the object
uses the mt19937ar algorithm for normally distributed random number
generation. In this case, the reset
object function resets the filters and reinitializes the random number
stream to the value of the Seed
property.
Data Types: char
 string
Seed
— Initial seed of mt19937ar random number stream73
(default)  nonnegative integerInitial seed of the mt19937ar random number stream generator algorithm,
specified as a nonnegative integer. When you call the reset
object function, it reinitializes the mt19937ar random number stream to the
Seed
value.
To enable this property, set the RandomStream
property to 'mt19937ar with seed'
.
Data Types: double
Visualization
— Channel visualization'Off'
(default)  'Impulse response'
 'Frequency response'
 'Impulse and frequency responses'
 'Doppler spectrum'
Channel visualization, specified as 'Off'
, 'Impulse
response'
, 'Frequency response'
, 'Impulse
and frequency responses'
, or 'Doppler spectrum'
.
For more information, see the Channel Visualization section.
To enable this property, set the FadingTechnique
property to 'Filtered Gaussian noise'
.
Data Types: char
 string
PathsForDopplerDisplay
— Path used for displaying Doppler spectrum1
(default)  positive integer Path used for displaying the Doppler spectrum, specified as a positive integer
in the range [1, N_{P}].
N_{P} is the number of discrete delay
paths specified by the PathDelays
property. Use
this property to select the discrete path used in constructing a Doppler spectrum
plot.
To enable this property, set the Visualization
property to 'Doppler spectrum'
.
Data Types: double
SamplesToDisplay
— Percentage of samples to display'25%'
(default)  '10%'
 '50%'
 '100%'
Percentage of samples to display, specified as '25%'
,
'10%'
, '50%'
, or
'100%'
. Increasing the percentage improves display accuracy
at the expense of simulation speed.
To enable this property, set the Visualization
property to 'Impulse response'
, 'Frequency
response'
, or 'Impulse and frequency
responses'
.
Data Types: char
 string
filters the input signal y
= rayleighchan(x
)x
through a multipath Rayleigh
fading channel and returns the result in y
.
To enable this syntax, set the ChannelFiltering
property to true
.
specifies a start time for the fading process.y
= rayleighchan(x
,inittime
)
To enable this syntax, set the FadingTechnique
property to 'Sum of sinusoids'
and the InitialTimeSource
property to 'Input port'
.
[
also returns the channel path gains of the underlying multipath Rayleigh fading
process in y
,pathgains
] = rayleighchan(___)pathgains
using any of the input argument
combinations in the previous syntaxes.
To enable this syntax, set the PathGainsOutputPort
property set to true
.
returns
the channel path gains of the underlying fading process. In this case, the channel
requires no input signal and acts as a source of path gains.pathgains
= rayleighchan()
To enable this syntax, set the ChannelFiltering
property to false
.
returns the channel path gains of the underlying fading process beginning at the
specified initial time. In this case, the channel requires no input signal and
acts as a source of path gains.pathgains
= rayleighchan(inittime
)
To enable this syntax, set the FadingTechnique
property to 'Sum of sinusoids'
, the InitialTimeSource
property to 'Input port'
, and the ChannelFiltering
property to false
.
x
— Input signalInput signal, specified as an N_{S}by1 vector, where N_{S} is the number of samples.
Data Types: single
 double
Complex Number Support: Yes
inittime
— Initial time offset0
 nonnegative scalarInitial time offset in seconds, specified as a nonnegative scalar.
When mod
(inittime
/SampleRate
) is nonzero, the initial time offset is rounded up to the
nearest sample position.
Data Types: single
 double
y
— Output signalOutput signal, returned as an
N_{S}by1 vector of complex values with
the same data precision as the input signal x
.
N_{S} is the number of
samples.
pathgains
— Output path gainsOutput path gains, returned as an
N_{S}byN_{P}
matrix. N_{S} is the number of samples.
N_{P} is the number of discrete delay
paths specified by the PathDelays
property.
pathgains
contains complex values.
When you set the ChannelFiltering
property to false
, the data type of this output has the same
precision as the input signal x
.
When you set the ChannelFiltering
property to true
, the data type of this output is specified
by the OutputDataType
property.
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj
, use
this syntax:
release(obj)
Produce the same multipath Rayleigh fading channel response by using two different methods for random number generation. The multipath Rayleigh fading channel System object includes two methods for random number generation. You can use the current global stream or the mt19937ar algorithm with a specified seed. By interacting with the global stream, the System object can produce the same outputs from these two methods.
Create a PSK modulator System object to modulate randomly generated data.
pskModulator = comm.PSKModulator; insig = randi([0,pskModulator.ModulationOrder1],1024,1); channelInput = pskModulator(insig);
Create a multipath Rayleigh fading channel System object, specifying the random number generation method as the my19937ar algorithm and the random number seed as 22.
rayleighchan = comm.RayleighChannel( ... 'SampleRate',10e3, ... 'PathDelays',[0 1.5e4], ... 'AveragePathGains',[2 3], ... 'NormalizePathGains',true, ... 'MaximumDopplerShift',30, ... 'DopplerSpectrum',{doppler('Gaussian',0.6),doppler('Flat')}, ... 'RandomStream','mt19937ar with seed', ... 'Seed',22, ... 'PathGainsOutputPort',true);
Filter the modulated data by using the multipath Rayleigh fading channel System object.
[chanOut1,pathGains1] = rayleighchan(channelInput);
Set the System object to use the global stream for random number generation.
release(rayleighchan);
rayleighchan.RandomStream = 'Global stream';
Set the global stream to have the same seed that you specified when creating the multipath Rayleigh fading channel System object.
rng(22)
Filter the modulated data by using the multipath Rayleigh fading channel System object again.
[chanOut2,pathGains2] = rayleighchan(channelInput);
Verify that the channel and path gain outputs are the same for each of the two methods.
isequal(chanOut1,chanOut2)
ans = logical
1
isequal(pathGains1,pathGains2)
ans = logical
1
Display the impulse and frequency responses of a frequencyselective multipath Rayleigh fading channel that is configured to disable channel filtering.
Define simulation variables. Specify path delays and gains by using the ITU pedestrian B channel configuration.
fs = 3.84e6; % Sample rate in Hz pathDelays = [0 200 800 1200 2300 3700]*1e9; % in seconds avgPathGains = [0 0.9 4.9 8 7.8 23.9]; % dB fD = 50; % Max Doppler shift in Hz
Create a multipath Rayleigh fading channel System object to visualize the impulse response and frequency response plots.
rayleighchan = comm.RayleighChannel('SampleRate',fs, ... 'PathDelays',pathDelays, ... 'AveragePathGains',avgPathGains, ... 'MaximumDopplerShift',fD, ... 'ChannelFiltering',false, ... 'Visualization','Impulse and frequency responses');
Visualize the channel response by running the multipath Rayleigh fading channel System object with no input signal. The impulse response plot enables you to identify the individual paths and their corresponding filter coefficients. The frequency response plot shows the frequencyselective nature of the ITU pedestrian B channel.
rayleighchan();
Show that the channel state is maintained for discontinuous transmissions by using multipath Rayleigh fading channel System objects that use the sumofsinusoids technique. Observe discontinuous channel response segments overlaid on a continuous channel response.
Set the channel properties.
fs = 1000; % Sample rate (Hz) pathDelays = [0 2.5e3]; % In seconds pathPower = [0 6]; % In dB fD = 5; % Maximum Doppler shift (Hz) ns = 1000; % Number of samples nsdel = 100; % Number of samples for delayed paths
Define a continuous time span and three discontinuous time segments over which to plot and view the channel response. View a 1000sample continuous channel response that start at time 0 and three 100sample channel responses that start at times 0.1, 0.4, and 0.7 seconds, respectively.
to0 = 0.0; to1 = 0.1; to2 = 0.4; to3 = 0.7; t0 = (to0:ns1)/fs; % Transmission 0 t1 = to1+(0:nsdel1)/fs; % Transmission 1 t2 = to2+(0:nsdel1)/fs; % Transmission 2 t3 = to3+(0:nsdel1)/fs; % Transmission 3
Create a frequencyflat multipath Rayleigh fading System object, specifying a 1000 Hz sampling rate, the sumofsinusoids fading technique, disabled channel filtering, and the number of samples to view. Specify a seed value so that results can be repeated. Use the default InitialTime
property setting so that the fading channel is simulated from time 0.
rayleighchan1 = comm.RayleighChannel('SampleRate',fs, ... 'MaximumDopplerShift',fD, ... 'RandomStream','mt19937ar with seed', ... 'Seed',17, ... 'FadingTechnique','Sum of sinusoids', ... 'ChannelFiltering',false, ... 'NumSamples',ns);
Create a clone of the multipath Rayleigh fading channel System object. Set the number of samples for the delayed paths you specify the source for the initial time so that you can specify the fading channel offset time can be specified as an input argument when using the System object.
rayleighchan2 = clone(rayleighchan1);
rayleighchan2.InitialTimeSource = 'Input port';
rayleighchan2.NumSamples = nsdel;
Save the path gain output for the continuous channel response by using the rayleighchan1
object and for the discontinuous delayed channel responses by using the rayleighchan2
object with initial time offsets are provided as input arguments.
pg0 = rayleighchan1(); pg1 = rayleighchan2(to1); pg2 = rayleighchan2(to2); pg3 = rayleighchan2(to3);
Compare the number of samples processed by the two channels by using the info
object function. The rayleighchan1
object processed 1000 samples, while the rayleighchan2
object processed only 300 samples.
G = info(rayleighchan1); H = info(rayleighchan2); [G.NumSamplesProcessed H.NumSamplesProcessed]
ans = 1×2
1000 300
Convert the path gains into decibels.
pathGain0 = 20*log10(abs(pg0)); pathGain1 = 20*log10(abs(pg1)); pathGain2 = 20*log10(abs(pg2)); pathGain3 = 20*log10(abs(pg3));
Plot the path gains for the continuous and discontinuous cases. The gains for the three segments match the gain for the continuous case. Because the channel characteristics are maintained even when data is not transmitted, the alignment of the two plots shows that the sumofsinusoids technique is suited to the simulation of packetized data.
plot(t0,pathGain0,'r') hold on plot(t1,pathGain1,'b') plot(t2,pathGain2,'b') plot(t3,pathGain3,'b') grid xlabel('Time (sec)') ylabel('Path Gain (dB)') legend('Continuous','Discontinuous','location','nw') title('Continuous and Discontinuous Transmission Path Gains')
Reproduce the multipath Rayleigh fading channel output across multiple frames by using the ChannelFilterCoefficients
property returned by the info object function of the comm.RayleighChannel
System object.
Create a multipath Rayleigh fading channel System object, defining two paths. Generate data to pass through the channel.
rayleighchan = comm.RayleighChannel( ... 'SampleRate',1000, ... 'PathDelays',[0 1.5e3], ... 'AveragePathGains',[0 3], ... 'PathGainsOutputPort',true)
rayleighchan = comm.RayleighChannel with properties: SampleRate: 1000 PathDelays: [0 0.0015] AveragePathGains: [0 3] NormalizePathGains: true MaximumDopplerShift: 1.0000e03 DopplerSpectrum: [1x1 struct] ChannelFiltering: true PathGainsOutputPort: true Show all properties
data = randi([0 1],600,1);
Pass data through the channel. Assign the ChannelFilterCoefficients
property value to the variable coeff
. Within a for
loop, calculate the fractional delayed input signal at the path delay locations stored in coeff
, apply the path gains, and sum the results for all of the paths. Compare the output of the multipath Rayleigh fading channel System object (chanout1
) to the output reproduced using the path gains and the ChannelFilterCoefficients
property of the multipath Rayleigh fading channel System object (chanout2
).
chaninfo = info(rayleighchan); coeff = chaninfo.ChannelFilterCoefficients; Np = length(rayleighchan.PathDelays); state = zeros(size(coeff,2)1,size(coeff,1)); nFrames = 10; chkChan = zeros(nFrames,1); for jj = 1 : nFrames data = randi([0 1],600,1); [chanout1,pg] = rayleighchan(data); fracdelaydata = zeros(size(data,1),Np); % Calculate the fractional delayed input signal. for ii = 1:Np [fracdelaydata(:,ii),state(:,ii)] = ... filter(coeff(ii,:),1,data,state(:,ii)); end % Apply the path gains and sum the results for all of the paths. % Compare the channel outputs. chanout2 = sum(pg .* fracdelaydata,2); chkChan(jj) = isequal(chanout1,chanout2); end chkChan'
ans = 1×10
1 1 1 1 1 1 1 1 1 1
Verify that the autocorrelation of the path gain output from the Rayleigh channel System object is a Bessel function. The results in [ 1 ] and Appendix A of [ 2 ], show that when the autocorrelation of the path gain outputs is a Bessel function, the Doppler spectrum is Jakesshaped.
Initialize simulation parameters.
Rsym = 9600; % Input symbol rate (symbols/s) sps = 10; % Number of samples per input symbol Fs = sps*Rsym; % Input sampling frequency (samples/s) Ts = 1/Fs; % Input sampling period (s) numsym = 1e6; % Number of input symbols to simulate numsamp = numsym*sps; % Number of channel samples to simulate fd = 100; % Maximum Doppler frequency shift (Hz) num_acsamp = 5000; % Number of samples of autocovariance % of complex fading process calculated numtx = 1; % Number of transmit antennas numrx = 1; % Number of receive antennas numsin = 48; % Number of sinusoids frmLen = 10000; numFrames = numsamp/frmLen;
Configure a Rayleigh channel System object.
chan = comm.RayleighChannel( ... 'FadingTechnique','Sum of sinusoids', ... 'NumSinusoids',numsin, ... 'RandomStream','mt19937ar with seed', ... 'PathDelays',0, ... 'AveragePathGains',0, ... 'SampleRate',Fs, ... 'MaximumDopplerShift',fd, ... 'PathGainsOutputPort',true);
Apply DPSK modulation to a random bit stream.
tx = randi([0 1],numsamp,numtx); % Random bit stream dpskSig = dpskmod(tx,2); % DPSK signal
Pass the modulated signal through the channel.
outsig = zeros(numsamp,numrx); pg_rx = zeros(numsamp,numrx,numtx); for frmNum = 1:numFrames [outsig((1:frmLen)+(frmNum1)*frmLen,:),pathGains] = ... chan(dpskSig((1:frmLen)+(frmNum1)*frmLen,:)); for i = 1:numrx pg_rx((1:frmLen)+(frmNum1)*frmLen,i,:) = ... pathGains(:,:,:,i); end end
Using the channel path gains received per antenna, compute the autocovariance of the fading process for each transmitreceive path.
autocov = zeros(frmLen+1,numrx,numtx); autocov_normalized_real = zeros(num_acsamp+1,numrx,numtx); autocov_normalized_imag = zeros(num_acsamp+1,numrx,numtx); for i = 1:numrx % Compute autocovariance of simulated complex fading process for j = 1:numtx autocov(:,i,j) = xcov(pg_rx(:,i,j),num_acsamp); % Real part of normalized autocovariance autocov_normalized_real(:,i,j) = ... real(autocov(num_acsamp+1:end,i,j) ... / autocov(num_acsamp+1,i,j)); % Imaginary part of normalized autocovariance autocov_normalized_imag(:,i,j) = ... imag(autocov(num_acsamp+1:end,i,j) ... / autocov(num_acsamp+1,i,j)); end end
Compute the theoretical autocovariance of the complex fading process by using the besselj
function.
Rrr = zeros(1,num_acsamp+1); for n = 1:1:num_acsamp+1 Rrr(n) = besselj(0,2*pi*fd*(n1)*Ts); end Rrr_normalized = Rrr/Rrr(1);
Display the autocovariance to compare the results from the Rayleigh channel System object and the besselj
function.
subplot(2,1,1) plot(autocov_normalized_real,'b') hold on plot(Rrr_normalized,'r') hold off legend('comm.RayleighChannel', ... 'Bessel function of the first kind') title('Autocovariance of Real Part of Rayleigh Process') subplot(2,1,2) plot(autocov_normalized_imag) legend('comm.RayleighChannel') title('Autocovariance of Imaginary Part of Rayleigh Process')
As computed below, the mean square error comparing the results from the Rayleigh channel object versus the Bessel function is insignificant.
act_mse_real = ... sum((autocov_normalized_realrepmat(Rrr_normalized.',1,numrx,numtx)).^2,1) ... / size(autocov_normalized_real,1)
act_mse_real = 7.0043e08
act_mse_imag = sum((autocov_normalized_imag0).^2,1) ...
/ size(autocov_normalized_imag,1)
act_mse_imag = 4.1064e07
References
1. Dent, P., G.E. Bottomley, and T. Croft. “Jakes Fading Model Revisited.” Electronics Letters 29, no. 13 (1993): 1162. https://doi.org/10.1049/el:19930777.
2. Pätzold, Matthias. Mobile Fading Channels. Chichester, UK: John Wiley & Sons, Ltd, 2002. https://doi.org/10.1002/0470847808.
Compute and plot the empirical and theoretical probability density function (PDF) for a Rayleigh channel with one path.
Initialize parameters and create a Rayleigh channel System object that does not apply channel filtering.
Ns = 1.92e6; Rs = 1.92e6; dopplerShift = 2000; chan = comm.RayleighChannel( ... 'SampleRate',Rs, ... 'PathDelays',0, ... 'AveragePathGains',0, ... 'MaximumDopplerShift',dopplerShift, ... 'ChannelFiltering',false, ... 'NumSamples',Ns, ... 'FadingTechnique','Sum of sinusoids');
Compute and plot the empirical and theoretical PDF for the Rayleigh channel.
figure; hold on; % Empirical PDF plot gain = chan(); pd = fitdist(abs(gain),'Kernel','BandWidth',.01); r = 0:.1:3; y = pdf(pd,r); plot(r,y) % Theoretical PDF plot exp_pdf_amplitude = raylpdf(r,0.7); plot(r,exp_pdf_amplitude') legend('Empirical','Theoretical') title('Empirical and Theoretical PDF Curves')
The cutoff frequency factor, f_{c}, is dependent on the type of Doppler spectrum.
For any Doppler spectrum type other than Gaussian and biGaussian, f_{c} equals 1.
For a doppler
('Gaussian')
spectrum type,
f_{c} equals NormalizedStandardDeviation
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.
For a doppler
('BiGaussian')
spectrum type:
If the PowerGains
(1)
and
NormalizedCenterFrequencies
(2)
field values are both 0
, then
f_{c} equals NormalizedStandardDeviation
(1)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.
If the PowerGains
(2)
and
NormalizedCenterFrequencies
(1)
field values are both 0
, then
f_{c} equals NormalizedStandardDeviation
(2)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.
If the NormalizedCenterFrequencies
field value is
[0,0]
and the
NormalizedStandardDeviation
field has two identical
elements, then f_{c} equals NormalizedStandardDeviation
(1)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.
In all other cases, f_{c} equals 1.
The comm.RayleighChannel
System object enables visualization of the channel impulse response, frequency response,
and Doppler spectrum.
Note
The displayed and specified path gain locations can differ by as much as 5% of the input sample time.
The visualization display speed is controlled by the combination of
the SamplesToDisplay
property and the
Reduce Updates to Improve Performance
scope menu item found in Playback . Reducing the
percentage of samples to display and enabling reduced updates can speed
up the rendering of the visualization scope.
If you close the visualization scopes, calls to the System object execute at normal speed.
Code generation is available only when you set the
Visualization
property to
'Off'
.
Impulse Response
The impulse response scope displays the path gains, channel filter coefficients, and
interpolated path gains. The path gains occur at time instances that correspond to the
specified PathDelays
property and might not be aligned with the
input sampling time. The scope uses channel filter coefficients to model the channel.
The coefficients are interpolated from the actual path gains and are aligned with the
input sampling time. The path gains overlap the filter coefficients for cases where the
path gains are aligned with the sampling time. Sinc interpolation is used to connect the
channel filter coefficients and is shown as the interpolated path gains. These points
are used solely for display purposes and not used in subsequent channel filtering. For a
flat fading channel (one path), the sinc interpolation curve is not displayed. For all
impulse response plots, the frame and sample numbers are shown in the upperleft corner
of the scope.
The impulse response plot shares the same toolbar and menus as the dsp.ArrayPlot
System object.
When the specified path gains align with the sample rate, the path gains and the channel filter coefficients overlap. In this figure, the impulse response shows that the path gains overlap the filter coefficients.
If the specified path gains are not aligned with the sample rate, the path gains and the channel filter coefficients do not overlap. In this figure, the filter coefficients are equally distributed. Because the path gains are not aligned with the sample rate, the path gains do not overlap with the channel filter coefficients.
This figure shows the impulse response for a frequencyflat channel without displaying the interpolated path gains.
Frequency response
The frequency response scope displays the multipath Rayleigh fading channel spectrum
by taking a discrete Fourier transform of the channel filter coefficients. The frequency
response plot shares the same toolbar and menus as the dsp.SpectrumAnalyzer
System object.
The yaxis limits of the plot are computed based on the
NormalizePathGains
and AveragePathGains
properties of the comm.RayleighChannel
System object.
This table shows other selected default spectrum settings. You can change these settings from their default values by using the Spectrum Settings in View .
Spectrum Settings  Value 

Type in Main options 

Window length in Main options  Channel filter length 
NFFT in Main options 

Window in Window options 

Units in Trace options 

This figure shows the frequency response plot for a frequencyselective channel.
Doppler Spectrum
The Doppler spectrum plot displays the theoretical Doppler spectrum and the
empirically determined data points. The theoretical data is displayed as a line for the
case of nonstatic channels and as a point for static channels. The empirical data is
shown as * symbols. Before the empirical plot is updated, the internal buffer must be
completely filled with filtered Gaussian samples. The empirical plot is the running mean
of the spectrum that is calculated from each full buffer. For nonstatic channels, the
number of input samples that is needed before the next update is displayed in the
upperleft corner of the plot. The number of samples that is needed is a function of the
sample rate and the maximum Doppler shift. For static channels, the text "Reset
fading channel for next update
" is displayed.
[1] Oestges, Claude, and Bruno Clerckx. MIMO Wireless Communications: From RealWorld Propagation to SpaceTime Code Design. 1st ed. Boston, MA: Elsevier, 2007.
[2] Correia, Luis M., and European Cooperation in the Field of Scientific and Technical Research (Organization), eds. Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G. 1st ed. Amsterdam ; Boston: Elsevier/Academic Press, 2006.
[3] Kermoal, J.P., L. Schumacher, K.I. Pedersen, P.E. Mogensen, and F. Frederiksen. “A Stochastic MIMO Radio Channel Model with Experimental Validation.” IEEE Journal on Selected Areas in Communications 20, no. 6 (August 2002): 1211–26. https://doi.org/10.1109/JSAC.2002.801223.
[4] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan. Simulation of Communication Systems. Second edition. Boston, MA: Springer US, 2000.
[5] Patzold, M., ChengXiang Wang, and B. Hogstad. “Two New SumofSinusoidsBased Methods for the Efficient Generation of Multiple Uncorrelated Rayleigh Fading Waveforms.” IEEE Transactions on Wireless Communications 8, no. 6 (June 2009): 3122–31. https://doi.org/10.1109/TWC.2009.080769.
Usage notes and limitations:
To generate C code, set the DopplerSpectrum
property to a single Doppler spectrum structure.
Code generation is available only when you set the
Visualization
property to 'Off'
.
See System Objects in MATLAB Code Generation (MATLAB Coder).
comm.AWGNChannel
 comm.MIMOChannel
 comm.RicianChannel
 comm.RayTracingChannel
 comm.ChannelFilter
 comm.WINNER2Channel
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