comm.RicianChannel

Filter input signal through multipath Rician fading channel

Description

The comm.RicianChannel System object™ filters an input signal through a multipath Rician fading channel. For more information on fading model processing, see Methodology for Simulating Multipath Fading Channels.

To filter an input signal using a multipath Rician fading channel:

1. Create the comm.RicianChannel 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

ricianlchan = comm.RicianChannel

ricianlchan = comm.RicianChannel(Name,Value)

Description

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

ricianlchan = comm.RicianChannel(Name,Value) sets properties using one or more name-value pair arguments. Enclose each property name in quotes. For example, comm.RicianChannel('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 Hz, 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 PathDelays is a scalar, the channel is frequency flat.

• When PathDelays is a vector, the channel is frequency selective.

Data Types: double

AveragePathGains — Average of the discrete paths

0 (default) | scalar | row vector

Average gains of the discrete paths in decibels, specified as a scalar or row vector. AveragePathGains must be of the same size as the PathDelays property.

Data Types: double

NormalizePathGains — Normalize average path gains to 0 dB

true or 1 (default) | false or 0

Normalize average path gains to 0 dB, specified as a logical 1 (true) or 0 (false).

• When NormalizePathGains is true, the fading processes are normalized so that the total power of the path gains, averaged over time, is 0 dB.

• When NormalizePathGains is false, the total power of the path gains is not normalized.

Data Types: logical

KFactor — Rician K-factor

3 (default) | positive scalar | row vector of nonnegative values

Rician K-factor, specified as a positive scalar or row vector of nonnegative values. The vector must be the same length as the PathDelays property value.

• When KFactor is a scalar, the first discrete path is a Rician fading process with a Rician K-factor of KFactor. Any remaining discrete paths are independent Rayleigh fading processes.

• When KFactor is a row vector, the discrete path corresponding to a positive element of the KFactor vector is a Rician fading process with a Rician K-factor specified by that element. The discrete path corresponding to any zero-valued elements of the KFactor vector are Rayleigh fading processes. At least one element value must be nonzero.

Data Types: double

DirectPathDopplerShift — Doppler shift

0 (default) | scalar | row vector

Doppler shift of the line-of-sight components of a multipath Rician fading channel, specified as a scalar or row vector. Units are in hertz. The DirectPathDopplerShift property must be of the same size as the KFactor property.

• When DirectPathDopplerShift is a scalar, the value represents the line-of-sight component Doppler shift of the first discrete path. This path exhibits a Rician fading process.

• When DirectPathDopplerShift is a row vector, the discrete path corresponding to a positive element of the KFactor vector is a Rician fading process. The corresponding element of DirectPathDopplerShift specifies the line-of-sight component Doppler shift of that discrete path.

Data Types: double

DirectPathInitialPhase — Initial phase

0 (default) | scalar | row vector

Initial phase of the line-of-sight components of a multipath Rician fading channel, specified as a scalar or row vector. Units are in radians. The DirectPathInitialPhase property must be of the same size as the KFactor property.

• When DirectPathInitialPhase is a scalar, the value represents the line-of-sight component initial phase of the first discrete path. This path exhibits a Rician fading process.

• When DirectPathInitialPhase is a row vector, the discrete path corresponding to a positive element of the KFactor vector is a Rician fading process. The corresponding element of DirectPathInitialPhase specifies the line-of-sight component initial phase of that discrete path.

Data Types: double

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 smaller than SampleRate/10/f_c for each path. f_c represents 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 Cutoff Frequency Factor.

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, that is, the length of the PathDelays property.

• When DopplerSpectrum is defined by a single Doppler spectrum structure, all paths have the same specified Doppler spectrum.

• When DopplerSpectrum is defined by a cell array of Doppler spectrum structures, each path has the Doppler spectrum specified by the corresponding structure in the cell array.

Options for the spectrum type are specified by 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 value. The MaximumDopplerShift property defines the maximum Doppler shift value permitted when specifying the Doppler spectrum.

Data Types: struct | cell

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 InitialTimeSource is set to 'Property', use the InitialTime property to set the initial time offset.

• When InitialTimeSource is set to 'Input port', specify the start time of the fading process by using the itime input to the System object. The input value can change in consecutive calls to the System object.

Dependencies

This property applies when the FadingTechnique property to 'Sum of sinusoids'.

Data Types: string | char

InitialTime — Initial time offset

0 (default) | nonnegative scalar

Initial time offset, in seconds, for the fading model, specified as a nonnegative scalar. InitialTime must be greater than end time of the last frame. InitialTime is rounded up to the nearest sample position when it is not a multiple of 1/SampleRate.

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 random number stream, specified as 'Global stream' or 'mt19937ar with seed'.

• 'Global stream' — The current global random number stream is used for normally distributed random number generation. In this case, the reset object function resets the channel filters only.

• 'mt19937ar with seed' — The mt19937ar algorithm is used for normally distributed random number generation. In this case, the reset object function resets the channel filters and reinitializes the random number stream to the value of the Seed property.

Data Types: string | char

Seed — Initial seed of mt19937ar random number stream

73 (default) | nonnegative integer

Initial seed of mt19937ar random number stream generator algorithm, specified as a nonnegative integer. When the reset object function is called, the mt19937ar random number stream is reinitialized to the Seedproperty value.

Dependencies

This property applies when you set the RandomStream property to 'mt19937ar with seed'.

Data Types: double

PathGainsOutputPort — Option to output path gains

false or 0 (default) | true or 1

Option to output path gains, specified as 0 (false) or 1 (true). Set this property to 1 (true) to output the channel path gains of the underlying fading process.

Data Types: logical

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 Channel Visualization.

Data Types: string | char

SamplesToDisplay — Percentage of samples to display

'25%' (default) | '10%' | '50%' | '100%'

Percentage of samples to display, specified as '25%', '10%', '50%', or '100%'. Displaying fewer samples improves (decreases) the display update rate at the expense of decreasing the visualized precision.

Dependencies

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

Data Types: string | char

PathsForDopplerDisplay — Path for Doppler display

1 (default) | positive integer

Path for Doppler display, specified as a positive integer. Use this property to select the discrete path used in constructing a Doppler spectrum plot. The specified path must be an element of {1, 2, ..., N_P}. In this set, N_P is the number of discrete delay paths, that is, the length of the PathDelays property value.

Dependencies

To enable this property, set the Visualization property to 'Doppler spectrum'.

Data Types: double

Usage

Syntax

y = rayleighchan(x)

[y,pathgains] = rayleighchan(x)

___ = rayleighchan(x,itime)

Description

y = rayleighchan(x) filters input signal x through a multipath Rician fading channel and returns the output signal in y.

[y,pathgains] = rayleighchan(x) returns the channel path gains of the underlying multipath Rician fading process in pathgains. To enable this syntax set the PathGainsOutputPort property set to 1 (true).

___ = rayleighchan(x,itime) passes data through the multipath Rician fading channel beginning at the initial time specified by itime. To enable this syntax, set the FadingTechnique property to 'Sum of sinusoids' and the InitialTimeSource property to 'Input port'.

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.

Data Types: single | double
Complex Number Support: Yes

itime — Initial time

0 | nonnegative scalar

Initial time in seconds, specified as a nonnegative scalar. The itime input must be greater than the end time of the last frame. When itime is not a multiple of 1/SampleRate, it 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 — Path gains

N_S-by-N_P array

Path gains, returned as an N_S-by-N_P array. N_S is the number of samples. N_P is the number of discrete delay paths, that is, the length of the PathDelays property value. pathgains contains complex values with the same precision as the input signal x.

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.RicianChannel

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 Rician Channel Outputs Using two Random Number Generation Methods

This example shows how to produce the same multipath Rician fading channel response by using two different methods for random number generation. The multipath Rician 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 the two methods.

Create a PSK modulator System object to modulate randomly generated data.

pskModulator = comm.PSKModulator;
channelInput = pskModulator(randi([0 pskModulator.ModulationOrder-1],1024,1));

Create a multipath Rician fading channel System object, specifying the random number generation method as the my19937ar algorithm and the random number seed as 73.

ricianchan = comm.RicianChannel(...
    'SampleRate',1e6,...
    'PathDelays',[0.0 0.5 1.2]*1e-6,...
    'AveragePathGains',[0.1 0.5 0.2],...
    'KFactor',2.8,...
    'DirectPathDopplerShift',5.0,...
    'DirectPathInitialPhase',0.5,...
    'MaximumDopplerShift',50,...
    'DopplerSpectrum',doppler('Bell', 8),...
    'RandomStream','mt19937ar with seed', ...
    'Seed',73, ...
    'PathGainsOutputPort',true);

Filter the modulated data by using the multipath Rician fading channel System object.

[RicianChanOut1, RicianPathGains1] = ricianchan(channelInput);

Set the System object to use the global stream for random number generation.

release(ricianchan);
ricianchan.RandomStream = 'Global stream';

Set the global stream to have the same seed that was specified when creating the multipath Rician fading channel System object.

rng(73)

Filter the modulated data by using the multipath Rician fading channel System object again.

[RicianChanOut2,RicianPathGains2] = ricianchan(channelInput);

Verify that the channel and path gain outputs are the same for each of the two methods.

isequal(RicianChanOut1,RicianChanOut2)

ans = logical
   1

isequal(RicianPathGains1,RicianPathGains2)

ans = logical
   1

Display Impulse and Frequency Responses of Multipath Rician Fading Channel

This example shows how to create a frequency-selective multipath Rician fading channel and display its impulse and frequency responses.

Set the sample rate to 3.84 MHz. Specify path delays and gains by using the ITU pedestrian B channel configuration. Set the Rician K-factor to 10 and the maximum Doppler shift to 50 Hz.

fs = 3.84e6; % Hz
pathDelays = [0 200 800 1200 2300 3700]*1e-9; % sec
avgPathGains = [0 -0.9 -4.9 -8 -7.8 -23.9]; % dB
fD = 50; % Hz

Create a multipath Rician fading channel System object by using the previously defined properties and to visualize the impulse response and frequency response plots.

ricianChan = comm.RicianChannel('SampleRate',fs, ...
    'PathDelays',pathDelays, ...
    'AveragePathGains',avgPathGains, ...
    'KFactor',10, ...
    'MaximumDopplerShift',fD, ...
    'Visualization','Impulse and frequency responses');

Generate random binary data and pass it through the multipath Rician fading channel. 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.

x = randi([0 1],1000,1);
y = ricianChan(x);

Model a Rician Channel Using Sum-of-Sinusoids Technique

The example shows how the channel state is maintained in cases in which data is discontinuously transmitted. Create a Rician channel object and pass data through it using the sum-of-sinusoids technique.

Set the channel properties.

fs = 1000; % Sample rate (Hz)
pathDelays = [0 2.5e-3]; % Path delays (s)
pathPower = [0 -6]; % Path power (dB)
fD = 5; % Maximum Doppler shift (Hz)
ns = 1000; % Number of samples
nsdel = 100; % Number of samples for delayed paths

Define the overall simulation time and three time segments for which data is to be transmitted. In this case, the channel is simulated for 1s with a 1000 Hz sampling rate. One 1000-sample continuous data sequence is transmitted at time 0. Three 100-sample data packets are transmitted at times 0.1 s, 0.5 s, and 0.8 s, respectively.

to0 = 0.0;
to1 = 0.1;
to2 = 0.5;
to3 = 0.8;
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

Generate random binary data corresponding to the previously defined time intervals.

d0 = randi([0 1],ns,1);
d1 = randi([0 1],nsdel,1);
d2 = randi([0 1],nsdel,1);
d3 = randi([0 1],nsdel,1);

Create a frequency-flat multipath Rician fading System object, specifying the sum-of-sinusoids fading technique. So that results can be repeated, specify a seed value. Use the default InitialTime property setting so that the fading channel will be simulated from time 0. Enable the path gains output.

ricianchan1 = comm.RicianChannel('SampleRate',fs, ...
    'MaximumDopplerShift',5, ...
    'RandomStream','mt19937ar with seed', ...
    'Seed',17, ...
    'FadingTechnique','Sum of sinusoids', ...
    'PathGainsOutputPort',true);

Create a clone of the multipath Rician fading channel System object. Set the source for initial time so that the fading channel offset time can be specified as an input argument when using the System object.

ricianchan2 = clone(ricianchan1);
ricianchan2.InitialTimeSource = 'Input port';

Pass random binary data through the first multipath Rician fading channel System object, ricianchan1. Data is transmitted over all 1000 time samples. For this example, only the complex path gain is needed.

[~,pg0] = ricianchan1(d0);

Pass random data through the second multipath Rician fading channel System object, ricianchan2, where the initial time offsets are provided as input arguments.

[~,pg1] = ricianchan2(d1,to1);
[~,pg2] = ricianchan2(d2,to2);
[~,pg3] = ricianchan2(d3,to3);

Compare the number of samples processed by the two channels by using the info object function. The ricianchan1 object processed 1000 samples, while the ricianhan2 object only processed 300 samples.

G = info(ricianchan1);
H = info(ricianchan2);
[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. The alignment of the two highlights that the sum-of-sinusoids technique is suited to the simulation of packetized data, as the channel characteristics are maintained even when data is not transmitted.

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')

Use Info Method to Reproduce Multipath Rican Fading Channel Response

The example show how to use the ChannelFilterCoefficients property returned by the info object function of the comm.RicianChannel System object to reproduce the multipath Rician fading channel output.

Create a multipath Rician fading channel System object, defining two paths and specifying data to pass through the channel.

ricianchan = comm.RicianChannel('SampleRate',1000,'PathDelays',[0 1e-3], ...
    'AveragePathGains',[0 -2],'PathGainsOutputPort',true)

ricianchan = 
  comm.RicianChannel with properties:

                SampleRate: 1000
                PathDelays: [0 1.0000e-03]
          AveragePathGains: [0 -2]
        NormalizePathGains: true
                   KFactor: 3
    DirectPathDopplerShift: 0
    DirectPathInitialPhase: 0
       MaximumDopplerShift: 1.0000e-03
           DopplerSpectrum: [1x1 struct]

  Show all properties

data = randi([0 1],600,1);

Pass data through the channel. Assign the ChannelFilterCoefficients property value to the variable coeff.

[chanout1,pg] = ricianchan(data);
chaninfo = info(ricianchan)

chaninfo = struct with fields:
           ChannelFilterDelay: 0
    ChannelFilterCoefficients: [2x2 double]
          NumSamplesProcessed: 600

coeff = chaninfo.ChannelFilterCoefficients;

Calculate the fractional delayed input signal at the path delay locations stored in coeff.

Np = length(ricianchan.PathDelays);
fracdelaydata = zeros(size(data,1),Np);
for ii = 1:Np
    fracdelaydata(:,ii) = filter(coeff(ii,:),1,data);
end

Apply the path gains and sum the results for all paths.

chanout2 = sum(pg .* fracdelaydata,2);

Compare the output of the multipath Rician fading channel System object to the output reproduced using the path gains and the ChannelFilterCoefficients property of the multipath Rician fading channel System object.

isequal(chanout1,chanout2)

ans = logical
   1

Compare CDF of Empirical and Theoretical Rician Channel

Compute and plot the empirical and theoretical CDF for a Rician channel with one path.

Initialize parameters and create a System object for the Rician channel.

Ns = 1.92e6;
Rs = 1.92e6;
dopplerShift = 2000;
KFactor = -3;                  % dB
KFactorLin = 10.^(KFactor/10); % linear

chan = comm.RicianChannel( ...
    "SampleRate",Rs, ...
    "PathDelays",0, ...
    "KFactor",KFactorLin, ...
    "AveragePathGains",0, ...
    "MaximumDopplerShift",dopplerShift, ...
    "FadingTechnique","Sum of sinusoids", ...
    "PathGainsOutputPort",true);

Compute and plot the empirical and theoretical CDF for the Rician channel. Compute empirical CDF by using the path gains.

% Empirical CDF plot
[~, g] = chan(ones(Ns,1));
ecdf(abs(g));
hold on;
% Theoretical CDF plot
r = 0:.1:3;
s = sqrt(KFactorLin)/sqrt(KFactorLin+1);
sigma = sqrt(1/2)/sqrt(KFactorLin+1);
exp_cdf_amplitude = cdf('Rician',r,s,sigma);
plot(r,exp_cdf_amplitude')   
legend('Emp','Theor')

Compare PDF of Empirical and Theoretical Rician Channel

Compute and plot the empirical and theoretical PDF for a Rician channel with one path.

Initialize parameters and create a System object for the Rician channel.

Ns = 1.92e6;
Rs = 1.92e6;
dopplerShift = 2000;
KFactor = -3;                  % dB
KFactorLin = 10.^(KFactor/10); % linear
sig = complex(randn(Ns,1),randn(Ns,1));

chan = comm.RicianChannel( ...
    "SampleRate",Rs, ...
    "PathDelays",0, ...
    "KFactor",KFactorLin, ...
    "AveragePathGains",0, ...
    "MaximumDopplerShift",dopplerShift, ...
    "FadingTechnique",'Sum of sinusoids', ...
    "PathGainsOutputPort",true);

Compute and plot the empirical and theoretical PDF for the Rician channel.

figure;
hold on;
% Empirical PDF plot
[~, gain] = chan(sig);
pd = fitdist(abs(gain),'Kernel','BandWidth',.01);
r = 0:.1:3;
y = pdf(pd,r);
plot(r,y)
% Theoretical PDF plot
s = sqrt(KFactorLin)/sqrt(KFactorLin+1);
sigma = sqrt(1/2)/sqrt(KFactorLin+1);
exp_pdf_amplitude = pdf('Rician',r,s,sigma);
plot(r,exp_pdf_amplitude')
legend('Empirical','Theoretical')

More About

Cutoff Frequency Factor

The cutoff frequency factor, f_c, is determined for different Doppler spectrum types.

• For any Doppler spectrum type other than Gaussian and biGaussian, 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.

Channel Visualization

The comm.RicianChannel 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 Playback > Reduce Updates to Improve Performance scope menu item. Reducing the percentage of samples to display and enabling reduced updates can speed up the rendering of the visualization scope.

• After the visualization scopes are manually closed, calls to the System object are executed at its normal speed.

• Code generation is available only when the Visualization property is set 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 which correspond to the specified PathDelays property and might not be aligned with the input sampling time. The channel filter coefficients are used to model the channel. They are interpolated from the actual path gains and are aligned with the input sampling time. In cases in which the path gains are aligned with the sampling time, the path gains overlap the filter coefficients. 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 upper-left 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 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. The path gains do not overlap with the channel filter coefficients because the path gains are not aligned with the sample rate.

This figure shows the impulse response for a frequency-flat channel. In this case, the interpolated path gains are not displayed.

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 y-axis limits of the plot are computed based on the NormalizePathGains and AveragePathGains properties of the comm.RicianChannel System object.

This table shows other selected default spectrum settings. These settings can be changed from their default values by using the View > Spectrum Settings menu.

Spectrum Settings	Value
Main options>Type	Power
Main options>Window length	Channel filter length
Main options>NFFT	512
Window options>Window	Rectangular
Trace options>Units	dBW

This figure shows the frequency response plot for a frequency selective 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 calculated from each full buffer. For nonstatic channels, the number of input samples needed before the next update is displayed in the upper-left corner of the plot. The number of samples 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.

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 the Visualization property is 'Off'.

• See System Objects in MATLAB Code Generation (MATLAB Coder).