phased.MultipathChannel

Propagate signals in multipath channel

Description

The phased.MultipathChannel System object™ propagates a signal through a multipath channel. To run the object, you must provide characteristics for each path: time delay, gain, Doppler factor, reflection loss, and spreading loss.

For sonar applications, you can use the phased.IsoSpeedUnderwaterPaths System object to generate channel path characteristics. You can also supply these characteristics independently.

To model signal propagation through a multipath channel:

1. Create the phased.MultipathChannel 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

propagator = phased.MultipathChannel

propagator = phased.MultipathChannel

Description

propagator = phased.MultipathChannel creates a signal propagator System object for a multipath underwater channel.

propagator = phased.MultipathChannel sets properties using one or more optional name-value arguments. For example, OperatingFrequency=40e3 sets the operating frequency to 40e3.

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.

OperatingFrequency — Signal carrier frequency

20e3 (default) | positive real-valued scalar

Signal carrier frequency, specified as a positive real-valued scalar. Units are in Hz.

Example: 10000

Data Types: double

SampleRate — Signal sample rate

1e3 (default) | positive real-valued scalar

Signal sample rate, specified as a positive real-valued scalar. Units are in Hz. The object uses this quantity to calculate the propagation delay in units of samples.

Example: 3e3

Data Types: double

MaximumDelaySource — Source of maximum delay

"Auto" (default) | "Property"

Source of the maximum delay value, specified as one of these options.

• "Auto" — The channel automatically allocates enough memory to simulate the propagation delay.

• "Property" — You can specify the maximum delay by using the MaximumDelay property. The object ignores signals arriving after the maximum delay.

MaximumDelay — Maximum signal delay

1 (default) | positive scalar

Maximum signal delay, specified as a positive scalar. The object ignores delays greater than this value. Units are in seconds.

Dependencies

To enable this property, set the MaximumDelaySource property to "Property".

InterpolationMethod — Interpolation method to implement fractional delay

"Linear" (default) | "Oversample"

Interpolation method used to implement the signal fractional delay and the Doppler time-dilation and compression, specified as one of these options.

• "Linear" — The object linearly interpolates the input signal onto a uniform grid to propagate the signal.

• "Oversample" — The object resamples the input signal to a higher rate before linear interpolation. For broadband signals, oversampling preserves spectral shape.

Usage

Syntax

propSig = propagator(sig,propPaths,dopplerFactor,absorptionLoss)

Description

propSig = propagator(sig,propPaths,dopplerFactor,absorptionLoss) returns a signal, propSig, propagated through a multipath channel. sig is the input signal to the channel. The propPaths matrix can describe one-way or two-way propagation from the signal source position to the signal destination position.

• When you use this object for one-way propagation, the source refers to the origin of the signal and the destination refers to the receiver. You can use one-way propagation modeling to model passive sonar and underwater communications.

• When you use this object for two-way propagation, the destination refers to the reflecting target, not the sonar receiver. A two-way path consists of a two identical one-way paths from source to target and back to receiver (collocated with the source). You can use two-way propagation to model active sonar systems.

Note

The object performs an initialization the first time the object is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first call the release method to unlock the object.

Input Arguments

sig — Channel input signal

matrix

Channel input signal, specified as a complex-valued M-by-N matrix. M is the number of samples in the signal and N is the number of paths.

Data Types: double
Complex Number Support: Yes

propPaths — Propagation paths

real-valued 3-by-N matrix

Propagation paths, specified as a real-valued 3-by-N matrix. N is the number of paths in the channel. Each column represents a path. The matrix rows represent:

Row	Data
1	Propagation delays for each path. Units are in seconds.
2	Total reflection coefficient for each path. Units are dimensionless
3	Spreading loss for each path. Units are in dB.

Except for the direct path, paths consist of alternating surface and bottom reflections. The losses for multiple reflections at the boundaries are multiplied. When you use phased.IsoSpeedUnderwaterPaths to create a path matrix, some of the columns can contain NaN values. phased.MultipathChannel ignores these paths.

Data Types: double

dopplerFactor — Doppler factor

row vector

Doppler factor, specified as a real-valued N-by-1 row vector. N is the number of paths. The Doppler factor multiplies the transmitted frequency to produce the Doppler-shifted frequency for each path. The factor also defines the time contraction or dilation of a signal. Units are dimensionless.

Data Types: double

absorptionLoss — Frequency-dependent absorption loss

matrix

Frequency-dependent absorption loss, specified as a real-valued K-by-N+1 matrix. K is the number of frequencies and N is the number of paths. The first column of aloss contains the absorption-loss frequencies in Hz. The remaining columns contain the absorption losses for the corresponding frequency. Units are in dB.

Data Types: double

Output Arguments

propSig — Channel output signal

matrix

Channel output signal, returned as a complex-valued M-by-N matrix. M is the number of samples in the signal and N is the number of paths. The output is the signal propagated through the channel. propSig has the same dimensions as the input signal, sig.

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)

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

One-Way Signal Propagation in Multipath Underwater Sound Channel

Create a five-path underwater sound channel and compute the propagation path matrix, the Doppler factor, and the absorption loss. Assume that the source is stationary and the receiver is moving along the x-axis toward the source at 20 km/h. Assume the default one-way propagation.

Create the channel and specify the source and receiver locations and velocities.

numpaths = 5;
channel = phased.IsoSpeedUnderwaterPaths(ChannelDepth=200,BottomLoss=10, ...
    NumPathsSource="Property",NumPaths=numpaths);
tstep = 1;
srcpos = [0;0;-160];
rcvpos = [100;0;-50];
speed = -20*1000/3600;
srcvel = [0;0;0];
rcvvel = [speed;0;0];

Compute the path matrix, Doppler factor, and losses.

[pathmat,dop,absloss] = channel(srcpos,rcvpos,srcvel,rcvvel,tstep);

Create 500 samples of a 100 Hz signal. Assume all the paths have the same signal. Propagate the signals to the receiver.

fs = 1e3;
nsamp = 500;
propagator = phased.MultipathChannel(OperatingFrequency=10e3,SampleRate=fs);
t = [0:(nsamp-1)]'/fs;
sig0 = sin(2*pi*100*t);
sig = repmat(sig0,1,numpaths);
propsig = propagator(sig,pathmat,dop,absloss);

Plot the real part of the coherent sum of the propagated signals.

plot(t*1000,real(sum(propsig,2)))
xlabel('Time (millisec)')

Two-Way Signal Propagation in Multipath Underwater Sound Channel

Create a seven-path underwater sound channel and display the propagation path matrix. Assume that the source is stationary and that the receiver is moving along the x-axis toward the source at 20 km/h. Assume two-way propagation.

speed = -20*1000/3600;
numpaths = 7;
csound = 1515.0;
channel = phased.IsoSpeedUnderwaterPaths(ChannelDepth=200, ...
    PropagationSpeed=csound,BottomLoss=10,NumPathsSource="Property", ...
    NumPaths=numpaths,TwoWayPropagation=true);
tstep = 1;
srcpos = [0;0;-160];
tgtpos = [500;0;-50];
srcvel = [0;0;0];
tgtvel = [speed;0;0];

Obtain the path matrix, Doppler factor, loss, and target reflection and transmit angles.

[pathmat,dop,aloss,tgtangs,srcangs] = channel(srcpos,tgtpos,srcvel,tgtvel,tstep);

Create a 100 Hz signal with 500 samples. Assume that all the paths have the same signal but with different amplitudes. Then, propagate the signals to the target and back. You can use the angle information to calculate any angular dependence of the source and target responses. Each channel can have a different amplitude. This example uses a simple cosine model.

fs = 1e3;
nsamp = 500;
propagator = phased.MultipathChannel(OperatingFrequency=10e3,SampleRate=fs);
t = [0:(nsamp-1)]'/fs;
ampsrc = cosd(srcangs(2,:));
amptgt = cosd(tgtangs(2,:));
sig0 = sin(2*pi*100*t);
sig = repmat(sig0,1,numpaths);
amptotal = ampsrc.^2.*amptgt;
sig = bsxfun(@times,amptotal,sig);

Because of the finite propagation delay, the first call to the propagator does not return the signal. Call propagator twice to obtain the returned signal.

propsig = propagator(sig,pathmat,dop,aloss);
propsig = propagator(sig,pathmat,dop,aloss);

Plot the real part of the coherent sum of the propagated signals. Compute the round trip time.

rng = rangeangle(srcpos,tgtpos);
tr = rng/csound;
plot((t+tr)*1000,real(sum(propsig,2)))
xlabel("Time (millisec)")

Propagate Sound in Channel Having Unknown Number of Paths

Create an underwater sound channel and plot the combined received signal. Automatically find the number of paths. Assume that the source is stationary and that the receiver is moving along the x-axis toward the source at 20 km/h. Assume the default one-way propagation.

speed = -20*1000/3600;
channel = phased.IsoSpeedUnderwaterPaths(ChannelDepth=200,BottomLoss=5, ...
    NumPathsSource="Auto",CoherenceTime=5);
tstep = 1;
srcpos = [0;0;-160];
rcvpos = [500;0;-50];
srcvel = [0;0;0];
rcvvel = [speed;0;0];

Compute the path matrix, Doppler factor, and losses. The propagator outputs 51 paths output but some paths can contain Nan values.

[pathmat,dop,absloss,rcvangs,srcangs] = channel(srcpos,rcvpos,srcvel,rcvvel,tstep);

Create of a 100 Hz signal with 500 samples. Assume that all the paths have the same signal. Use a phased.MultipathChannel System object™ to propagate the signals to the receiver. phased.MultipathChannel accepts as input all paths produced by phased.IsoSpeedUnderwaterPaths but ignores paths that have NaN values.

fs = 1e3;
nsamp = 500;
propagator = phased.MultipathChannel(OperatingFrequency=10e3,SampleRate=fs);
t = [0:(nsamp-1)]'/fs;
sig0 = sin(2*pi*100*t);
numpaths = size(pathmat,2);
sig = repmat(sig0,1,numpaths);
propsig = propagator(sig,pathmat,dop,absloss);

Plot the real part of the coherent sum of the propagated signals.

plot(t*1000,real(sum(propsig,2)))
xlabel("Time (millisec)")

Doppler Stretching of Sonar Signal

Compare the duration of a propagated signal from a stationary sonar to that of a moving sonar. The moving sonar has a radial velocity of 25 m/s away from the target. In each case, propagate the signal along a single path. Assume one-way propagation.

Define the sonar system parameters: maximum unambiguous range, required range resolution, operating frequency, and propagation speed.

maxrange = 5000.0;
rngres = 10.0;
fc = 20.0e3;
csound = 1520.0;

Use a rectangular waveform for the transmitted signal.

prf = csound/(2*maxrange);
pulseWidth = 8*rngres/csound;
pulseBW = 1/pulseWidth;
fs = 80*pulseBW;
waveform = phased.RectangularWaveform(PulseWidth=pulseWidth,PRF=prf, ...
    SampleRate=fs);

Specify the sonar positions.

sonarplatform1 = phased.Platform(InitialPosition=[0;0;-60],Velocity=[0;0;0]);
sonarplatform2 = phased.Platform(InitialPosition=[0;0;-60],Velocity=[0;-25;0]);

Specify the target position.

targetplatform = phased.Platform(InitialPosition=[0;500;-60],Velocity=[0;0;0]);

Define the underwater path and propagation channel objects.

paths = phased.IsoSpeedUnderwaterPaths(ChannelDepth=100, ...
    CoherenceTime=0,NumPathsSource="Property",NumPaths=1, ...
    PropagationSpeed=csound);
propagator = phased.MultipathChannel(SampleRate=fs,OperatingFrequency=fc);

Create the transmitted waveform.

wav = waveform();
nsamp = size(wav,1);
rxpulses = zeros(nsamp,2);
t = (0:nsamp-1)/fs;

Transmit the signal and then receive the echo at the stationary sonar.

[pathmat,dop,aloss,~,~] = paths(sonarplatform1.InitialPosition, ...
    targetplatform.InitialPosition,sonarplatform1.InitialVelocity, ...
    targetplatform.InitialVelocity,1/prf);
rxpulses(:,1) = propagator(wav,pathmat,dop,aloss);

Transmit and receive at the moving sonar.

[pathmat,dop,aloss,~,~] = paths(sonarplatform2.InitialPosition, ...
    targetplatform.InitialPosition,sonarplatform2.Velocity, ...
    targetplatform.Velocity,1/prf);
rxpulses(:,2) = propagator(wav,pathmat,dop,aloss);

Plot the received pulses.

plot(abs(rxpulses))
xlim([490 650])
ylim([0 1.65e-3])
legend("Stationary sonar","Moving sonar")
xlabel("Received Sample Time (sec)")
ylabel("Integrated Received Pulses")

The signal received at the moving sonar has increased in duration compared to the stationary sonar.

References

[1] Urick, R.J. Principles of Underwater Sound, 3rd Edition. New York: Peninsula Publishing, 1996.

[2] Sherman, C.S. and J. Butler Transducers and Arrays for Underwater Sound. New York: Springer, 2007.

[3] Allen, J.B. and D. Berkely, “Image method for efficiently simulating small-room acoustics”, J. Acoust. Soc. Am, Vol 65, No. 4. April 1979.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

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

Version History

Introduced in R2017a