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:
Create the
comm.RayleighChannelobject 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?
Creation
Description
rayleighchan = comm.RayleighChannel
rayleighchan = comm.RayleighChannel(Name=Value)comm.RayleighChannel(SampleRate=2) sets the input signal sample
rate to 2.
Properties
Usage
Syntax
Description
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.
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.
pathgains = rayleighchan()
To enable this syntax, set the ChannelFiltering
property to false.
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.
Input Arguments
Output Arguments
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)
Examples
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.
Apply 8-PSK modulation to randomly generated data.
M = 8; phaseOffset = pi/M; insig = randi([0,M-1],1024,1); channelInput = pskmod(insig,M,phaseOffset);
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 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();
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 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: [1×1 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 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.
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
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.
