comm.RayleighChannel

Filter input signal through multipath Rayleigh fading channel

Description

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:

1. Create the comm.RayleighChannel object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

rayleighchan = comm.RayleighChannel

rayleighchan = comm.RayleighChannel(Name=Value)

Description

rayleighchan = comm.RayleighChannel creates a frequency-selective or frequency-flat multipath Rayleigh fading channel System object. This object filters a real or complex input signal through the multipath channel to obtain a channel-impaired signal.

rayleighchan = comm.RayleighChannel(Name=Value) sets properties using one or more name-value arguments. For example, comm.RayleighChannel(SampleRate=2) sets the input signal sample rate to 2.

Properties

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 rate

1 (default) | positive scalar

Input signal sample rate in hertz, specified as a positive scalar.

Data Types: double

PathDelays — Discrete path delay

0 (default) | scalar | row vector

Discrete 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 paths

0 (default) | scalar | row vector

Average 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 gains

trueor 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 paths

0.001 (default) | nonnegative scalar

Maximum 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 less than or equal to 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 bi-Gaussian 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 paths

doppler('Jakes') (default) | Doppler spectrum structure | 1-by-N_P cell array of Doppler spectrum structures

Doppler spectrum shape for all channel paths, specified as a Doppler spectrum structure or a 1-by-N_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').

Dependencies

To enable this property, set the MaximumDopplerShift property to a positive scalar.

Data Types: struct | cell

ChannelFiltering — Channel filtering

trueor 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 gains

false 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.

Dependencies

To enable this property, set the ChannelFiltering property to true.

Data Types: logical

NumSamples — Number of samples

100 (default) | nonnegative integer

Number of samples used for the duration of the fading process, specified as a nonnegative integer.

Tunable: Yes

Dependencies

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'.

Dependencies

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 used

48 (default) | positive integer

Number of sinusoids used to model the fading process, specified as a positive integer.

Dependencies

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.

Dependencies

To enable this property, set the FadingTechnique property to 'Sum of sinusoids'.

Data Types: char | string

InitialTime — Initial time offset

0 (default) | nonnegative scalar

Initial 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.

Dependencies

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 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 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 stream

73 (default) | nonnegative integer

Initial 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.

Dependencies

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 topic.

Data Types: char | string

PathsForDopplerDisplay — Path used for displaying Doppler spectrum

1 (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.

Dependencies

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.

Dependencies

To enable this property, set the Visualization property to 'Impulse response', 'Frequency response', or 'Impulse and frequency responses'.

Data Types: char | string

Usage

Syntax

Y = rayleighchan(X)

Y = rayleighchan(X,inittime)

[Y,pathgains] = rayleighchan(___)

pathgains = rayleighchan()

pathgains = rayleighchan(inittime)

Description

Y = rayleighchan(X) filters the input signal X through a multipath Rayleigh fading channel and returns the result in Y.

To enable this syntax, set the ChannelFiltering property to true.

Y = rayleighchan(X,inittime) specifies a start time for the fading process.

To enable this syntax, set the FadingTechnique property to 'Sum of sinusoids' and the InitialTimeSource property to 'Input port'.

[Y,pathgains] = rayleighchan(___) also returns the channel path gains of the underlying multipath Rayleigh fading process in pathgains using any of the input argument combinations in the previous syntaxes.

To enable this syntax, set the PathGainsOutputPort property set to true.

pathgains = rayleighchan() 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.

To enable this syntax, set the ChannelFiltering property to false.

pathgains = rayleighchan(inittime) 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.

To enable this syntax, set the FadingTechnique property to 'Sum of sinusoids', the InitialTimeSource property to 'Input port', and the ChannelFiltering property to false.

Input Arguments

X — Input signal

N_S-by-1 vector

Input signal, specified as an N_S-by-1 vector, where N_S is the number of samples.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: single | double
Complex Number Support: Yes

inittime — Initial time offset

0 | nonnegative scalar

Initial 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

Output Arguments

Y — Output signal

N_S-by-1 vector

Output signal, returned as an N_S-by-1 vector of complex values with the same data precision as the input signal X. N_S is the number of samples.

pathgains — Output path gains

N_S-by-N_P matrix

Output path gains, returned as an N_S-by-N_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.

Object Functions

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)

Specific to comm.RayleighChannel

info	Characteristic information about fading channel object

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Produce Same Rayleigh Channel Outputs Using Two Random Number Generation Methods

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.ModulationOrder-1],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 1.5e-4], ...
    '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 Impulse and Frequency Responses of Multipath Rayleigh Fading Channel

Display the impulse and frequency responses of a frequency-selective 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]*1e-9; % 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 frequency-selective nature of the ITU pedestrian B channel.

rayleighchan();

Model Multipath Rayleigh Fading Channel by Using Sum-of-Sinusoids Technique

Show that the channel state is maintained for discontinuous transmissions by using multipath Rayleigh fading channel System objects that use the sum-of-sinusoids technique. Observe discontinuous channel response segments overlaid on a continuous channel response.

Set the channel properties.

fs = 1000;               % Sample rate (Hz)
pathDelays = [0 2.5e-3]; % 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 1000-sample continuous channel response that starts at time 0 and three 100-sample 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:ns-1)/fs;      % Transmission 0
t1 = to1+(0:nsdel-1)/fs; % Transmission 1
t2 = to2+(0:nsdel-1)/fs; % Transmission 2
t3 = to3+(0:nsdel-1)/fs; % Transmission 3

Create a frequency-flat multipath Rayleigh fading System object, specifying a 1000 Hz sampling rate, the sum-of-sinusoids 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. In the cloned object, set the number of samples to view for the delayed paths. Also configure the initial time source as an input so that you can specify the fading channel offset time as an input argument when using the System object.

rayleighchan2 = clone(rayleighchan1);
rayleighchan2.NumSamples = nsdel;
rayleighchan2.InitialTimeSource = 'Input port';

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 sum-of-sinusoids 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 Multipath Rayleigh Fading Channel Response

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 1.5e-3], ...
    'AveragePathGains',[0 -3], ...
    'PathGainsOutputPort',true)

rayleighchan = 
  comm.RayleighChannel with properties:

             SampleRate: 1000
             PathDelays: [0 0.0015]
       AveragePathGains: [0 -3]
     NormalizePathGains: true
    MaximumDopplerShift: 1.0000e-03
        DopplerSpectrum: [1x1 struct]
       ChannelFiltering: true
    PathGainsOutputPort: true

  Use get to 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 Autocorrelation of Rayleigh Channel Path Gains

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 Jakes-shaped.

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)+(frmNum-1)*frmLen,:),pathGains] = ...
        chan(dpskSig((1:frmLen)+(frmNum-1)*frmLen,:));
    for i = 1:numrx 
        pg_rx((1:frmLen)+(frmNum-1)*frmLen,i,:) = ... 
        pathGains(:,:,:,i);
    end 
end 

Using the channel path gains received per antenna, compute the autocovariance of the fading process for each transmit-receive 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*(n-1)*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_real-repmat(Rrr_normalized.',1,numrx,numtx)).^2,1) ...
    / size(autocov_normalized_real,1) 

act_mse_real = 
7.0043e-08

act_mse_imag = sum((autocov_normalized_imag-0).^2,1) ...
    / size(autocov_normalized_imag,1)

act_mse_imag = 
4.1064e-07

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.

Compare PDF of Empirical and Theoretical Rayleigh Channel

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, by using the fitdist (Statistics and Machine Learning Toolbox) and pdf (Statistics and Machine Learning Toolbox) functions.

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')

More About

Cutoff Frequency Factor

The cutoff frequency factor, f_c, is dependent on the type of Doppler spectrum.

• For any Doppler spectrum type other than Gaussian and bi-Gaussian, f_c equals 1.

• For a doppler('Gaussian') spectrum type, f_c equals NormalizedStandardDeviation$$\times \sqrt{2\log 2}$$.

• For a doppler('BiGaussian') spectrum type:

  • If the PowerGains(1) and NormalizedCenterFrequencies(2) field values are both 0, then f_c equals NormalizedStandardDeviation(1)$$\times \sqrt{2\log 2}$$.

  • If the PowerGains(2) and NormalizedCenterFrequencies(1) field values are both 0, then f_c equals NormalizedStandardDeviation(2)$$\times \sqrt{2\log 2}$$.

  • If the NormalizedCenterFrequencies field value is [0,0] and the NormalizedStandardDeviation field has two identical elements, then f_c equals NormalizedStandardDeviation(1)$$\times \sqrt{2\log 2}$$.

  • In all other cases, f_c equals 1.

References

[1] Oestges, Claude, and Bruno Clerckx., MIMO Wireless Communications: From Real-World Propagation to Space-Time 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., Cheng-Xiang Wang, and B. Hogstad. “Two New Sum-of-Sinusoids-Based 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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

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).

Version History

Introduced in R2013b

R2022b: Updates to channel visualization display

The channel visualization feature now presents:

• Configuration settings in the bottom toolbar on the plot window.

• Plots side-by-side in one window when you select the Impulse and frequency response channel visualization option.