Doppler estimation

The `phased.DopplerEstimator`

System
object™ estimates
Doppler frequencies of targets. Input to the estimator consists of
detection locations output from a detector, and a range-Doppler response
data cube. When detections are clustered, the Doppler frequencies
are computed using cluster information. Clustering associates multiple
detections into one extended detection.

To compute Doppler values for detections:

Define and set up your Doppler estimator using the Construction procedure that follows.

Call the

`step`

method to compute the Doppler of detections, using the properties you specify for the`phased.DopplerEstimator`

System object.

Instead of using the `step`

method to perform
the operation defined by the System
object, you can call the object
with arguments, as if it were a function. For example, ```
y
= step(obj,x)
```

and `y = obj(x)`

perform
equivalent operations.

`estimator = phased.DopplerEstimator`

creates
a Doppler estimator System
object, `estimator`

.

`estimator = phased.DopplerEstimator(`

creates
a System
object, `Name`

,`Value`

)`estimator`

, with each specified
property `Name`

set to the specified `Value`

.
You can specify additional name and value pair arguments in any order
as (`Name1,Value1`

,...,`NameN,ValueN`

).

`NumEstimatesSource`

— Source of requested number of Doppler estimates`'Auto'`

(default) | `'Property'`

Source of the number of requested Doppler estimates, specified
as `'Auto'`

or `'Property'`

.

If you set this property to `'Auto'`

, the number
of estimates equals the number of columns in the `detidx`

input
argument of the `step`

method. If cluster IDs are provided,
the number of estimates equals the number of unique cluster IDs.

If you set this property to `'Property'`

, the
number of reported estimates is obtained from the value of the `NumEstimates`

property.

**Data Types: **`char`

`NumEstimates`

— Maximum number of estimates`1`

(default) | positive integerThe maximum number of estimates to report, specified as a positive
integer. When the number of requested estimates is greater than the
number of columns in the `detidx`

argument of the `step`

method,
the remainder is filled with `NaN`

.

To enable this property, set the `NumEstimatesSource`

property
to `'Property'`

.

**Data Types: **`c`

| `double`

`ClusterInputPort`

— Accept `clusterids`

as input`false`

(default) | `true`

Option to accept `clusterids`

as an input argument
to the `step`

method, specified as `false`

or `true`

.
Setting this property to `true`

enables the `clusterid`

input
argument of the `step`

method.

**Data Types: **`logical`

`VarianceOutputPort`

— Enable output of Doppler variance estimates`false`

(default) | `true`

Option to enable output of Doppler variance estimate, specified
as `false`

or `true`

. Doppler variances
estimates are returned in the `dopvar`

output argument
of the `step`

method.

**Data Types: **`logical`

`NumPulses`

— Number of pulses in Doppler-processed waveform`2`

(default) | positive integerThe number of pulses in the Doppler processed data cube, specified as a positive integer.

To enable this property, set the `VarianceOutputPort`

property
to `true`

.

**Data Types: **`single`

| `double`

`NoisePowerSource`

— Source of noise power values`'Property'`

(default) | `'Input port'`

Source of noise power values, specified as `'Property'`

or ```
'Input
port'
```

. Noise power is used to compute Doppler estimation
variance and SNR. If you set this property to `'Property'`

,
the value of the `NoisePower`

property represents the
noise power at the detection locations. If you set this property to
`'Input port'`

, you can specify noise power using the
`noisepower`

input argument of the `step`

method.

**Data Types: **`char`

`NoisePower`

— Noise power`1.0`

(default) | positive scalarConstant noise power value over the range-Doppler data cube, specified as a positive scalar. Noise power units are linear. The same noise power value is applied to all detections.

To enable this property, set the `VarianceOutputPort`

property
to `true`

and set `NoisePowerSource`

to `'Property'`

.

**Data Types: **`single`

| `double`

step | Estimate target Doppler |

Common to All System Objects | |
---|---|

`release` | Allow System object property value changes |

To estimate the range and speed of three targets, create a range-Doppler map using the `phased.RangeDopplerResponse`

System object™. Then use the `phased.RangeEstimator`

and `phased.DopplerEstimator`

System objects to estimate range and speed. The transmitter and receiver are collocated isotropic antenna elements forming a monostatic radar system.

The transmitted signal is a linear FM waveform with a pulse repetition interval (PRI) of 7.0 μs and a duty cycle of 2%. The operating frequency is 77 GHz and the sample rate is 150 MHz.

```
fs = 150e6;
c = physconst('LightSpeed');
fc = 77.0e9;
pri = 7e-6;
prf = 1/pri;
```

Set up the scenario parameters. The transmitter and receiver are stationary and located at the origin. The targets are 500, 530, and 750 meters from the radar along the *x*-axis. The targets move along the *x*-axis at speeds of –60, 20, and 40 m/s. All three targets have a nonfluctuating radar cross-section (RCS) of 10 dB. Create the target and radar platforms.

Numtgts = 3; tgtpos = zeros(Numtgts); tgtpos(1,:) = [500 530 750]; tgtvel = zeros(3,Numtgts); tgtvel(1,:) = [-60 20 40]; tgtrcs = db2pow(10)*[1 1 1]; tgtmotion = phased.Platform(tgtpos,tgtvel); target = phased.RadarTarget('PropagationSpeed',c,'OperatingFrequency',fc, ... 'MeanRCS',tgtrcs); radarpos = [0;0;0]; radarvel = [0;0;0]; radarmotion = phased.Platform(radarpos,radarvel);

Create the transmitter and receiver antennas.

txantenna = phased.IsotropicAntennaElement; rxantenna = clone(txantenna);

Set up the transmitter-end signal processing. Create an upsweep linear FM signal with a bandwidth of one half the sample rate. Find the length of the PRI in samples and then estimate the rms bandwidth and range resolution.

bw = fs/2; waveform = phased.LinearFMWaveform('SampleRate',fs, ... 'PRF',prf,'OutputFormat','Pulses','NumPulses',1,'SweepBandwidth',fs/2, ... 'DurationSpecification','Duty cycle','DutyCycle',0.02); sig = waveform(); Nr = length(sig); bwrms = bandwidth(waveform)/sqrt(12); rngrms = c/bwrms;

Set up the transmitter and radiator System object properties. The peak output power is 10 W and the transmitter gain is 36 dB.

peakpower = 10; txgain = 36.0; txgain = 36.0; transmitter = phased.Transmitter( ... 'PeakPower',peakpower, ... 'Gain',txgain, ... 'InUseOutputPort',true); radiator = phased.Radiator( ... 'Sensor',txantenna,... 'PropagationSpeed',c,... 'OperatingFrequency',fc);

Set up the free-space channel in two-way propagation mode.

channel = phased.FreeSpace( ... 'SampleRate',fs, ... 'PropagationSpeed',c, ... 'OperatingFrequency',fc, ... 'TwoWayPropagation',true);

Set up the receiver-end processing. Set the receiver gain and noise figure.

collector = phased.Collector( ... 'Sensor',rxantenna, ... 'PropagationSpeed',c, ... 'OperatingFrequency',fc); rxgain = 42.0; noisefig = 1; receiver = phased.ReceiverPreamp( ... 'SampleRate',fs, ... 'Gain',rxgain, ... 'NoiseFigure',noisefig);

Loop over the pulses to create a data cube of 128 pulses. For each step of the loop, move the target and propagate the signal. Then put the received signal into the data cube. The data cube contains the received signal per pulse. Ordinarily, a data cube has three dimensions where the last dimension corresponds to antennas or beams. Because only one sensor is used, the cube has only two dimensions.

The processing steps are:

Move the radar and targets.

Transmit a waveform.

Propagate the waveform signal to the target.

Reflect the signal from the target.

Propagate the waveform back to the radar. Two-way propagation enables enables you to combine the return propagation with the outbound propagation.

Receive the signal at the radar.

Load the signal into the data cube.

Np = 128; dt = pri; cube = zeros(Nr,Np); for n = 1:Np [sensorpos,sensorvel] = radarmotion(dt); [tgtpos,tgtvel] = tgtmotion(dt); [tgtrng,tgtang] = rangeangle(tgtpos,sensorpos); sig = waveform(); [txsig,txstatus] = transmitter(sig); txsig = radiator(txsig,tgtang); txsig = channel(txsig,sensorpos,tgtpos,sensorvel,tgtvel); tgtsig = target(txsig); rxcol = collector(tgtsig,tgtang); rxsig = receiver(rxcol); cube(:,n) = rxsig; end

Display the data cube containing signals per pulse.

imagesc([0:(Np-1)]*pri*1e6,[0:(Nr-1)]/fs*1e6,abs(cube)) xlabel('Slow Time {\mu}s') ylabel('Fast Time {\mu}s') axis xy

Create and display the range-Doppler image for 128 Doppler bins. The image shows range vertically and speed horizontally. Use the linear FM waveform for match filtering. The image is here is the range-Doppler map.

ndop = 128; rangedopresp = phased.RangeDopplerResponse('SampleRate',fs, ... 'PropagationSpeed',c,'DopplerFFTLengthSource','Property', ... 'DopplerFFTLength',ndop,'DopplerOutput','Speed', ... 'OperatingFrequency',fc); matchingcoeff = getMatchedFilter(waveform); [rngdopresp,rnggrid,dopgrid] = rangedopresp(cube,matchingcoeff); imagesc(dopgrid,rnggrid,10*log10(abs(rngdopresp))) xlabel('Closing Speed (m/s)') ylabel('Range (m)') axis xy

Because the targets lie along the positive *x*-axis, positive velocity in the global coordinate system corresponds to negative closing speed. Negative velocity in the global coordinate system corresponds to positive closing speed.

Estimate the noise power after matched filtering. Create a constant noise background image for simulation purposes.

mfgain = matchingcoeff'*matchingcoeff; dopgain = Np; noisebw = fs; noisepower = noisepow(noisebw,receiver.NoiseFigure,receiver.ReferenceTemperature); noisepowerprc = mfgain*dopgain*noisepower; noise = noisepowerprc*ones(size(rngdopresp));

Create the range and Doppler estimator objects.

rangeestimator = phased.RangeEstimator('NumEstimatesSource','Auto', ... 'VarianceOutputPort',true,'NoisePowerSource','Input port', ... 'RMSResolution',rngrms); dopestimator = phased.DopplerEstimator('VarianceOutputPort',true, ... 'NoisePowerSource','Input port','NumPulses',Np);

Locate the target indices in the range-Doppler image. Instead of using a CFAR detector, for simplicity, use the known locations and speeds of the targets to obtain the corresponding index in the range-Doppler image.

detidx = NaN(2,Numtgts); tgtrng = rangeangle(tgtpos,radarpos); tgtspd = radialspeed(tgtpos,tgtvel,radarpos,radarvel); tgtdop = 2*speed2dop(tgtspd,c/fc); for m = 1:numel(tgtrng) [~,iMin] = min(abs(rnggrid-tgtrng(m))); detidx(1,m) = iMin; [~,iMin] = min(abs(dopgrid-tgtspd(m))); detidx(2,m) = iMin; end

Find the noise power at the detection locations.

ind = sub2ind(size(noise),detidx(1,:),detidx(2,:));

Estimate the range and range variance at the detection locations. The estimated ranges agree with the postulated ranges.

[rngest,rngvar] = rangeestimator(rngdopresp,rnggrid,detidx,noise(ind))

`rngest = `*3×1*
499.7911
529.8380
750.0983

rngvar =3×110^{-4}× 0.0273 0.0276 0.2094

Estimate the speed and speed variance at the detection locations. The estimated speeds agree with the predicted speeds.

[spdest,spdvar] = dopestimator(rngdopresp,dopgrid,detidx,noise(ind))

`spdest = `*3×1*
60.5241
-19.6167
-39.5838

spdvar =3×110^{-5}× 0.0806 0.0816 0.6188

The `phased.DopplerEstimator`

System
object estimates the Doppler frequency of a detection by following these
steps of the Doppler estimator are

Input a Doppler-processed response data cube obtained from the

`phased.RangeDopplerResponse`

System object. The first dimension of the cube represents the fast-time or equivalent range of the returned signal samples. The second dimension represents the spatial information, such as sensors or beams. The last dimension represents the response as a function of Doppler frequency. Only this dimension is used to estimate detection Doppler frequency. All others are ignored. See Radar Data Cube.Input the matrix of detection indices that specify the location of detections in the data cube. Each column denotes a separate detection. The row entries designate indices into the data cube. To return these detection indices as an output of the

`phased.CFARDetector`

or`phased.CFARDetector2D`

detectors. To return these indices, set the detector`OutputFormat`

property of either CFAR detector to`'Detection index'`

.Optionally input a row vector of cluster IDs. This vector is equal in length to the number of detections. Each element of this vector assigns an ID to a corresponding detection. To form clusters of detections, the same ID can be assigned to more than one detection. To enable this option, set the

`ClusterInputPort`

property to`true`

.When

`ClusterInputPort`

is`false`

, the object computes Doppler frequencies for each detection. The algorithm finds the response values at the detection index and at two adjacent indices in the cube along the Doppler dimension. Then, the algorithm fits a quadratic curve to the magnitudes of the Doppler response at these three indices. The peak of the curve indicates the detection location. When detections occur at the first or last sample in the Doppler dimension, the object estimates the detection location from a two-point centroid. The centroid is formed using the location of the detection index and the sample next to the detection index.When the object computes Doppler frequencies for each cluster. The algorithm finds the indices of the largest response value in the cluster. Then, the algorithm fits a quadratic curve to that detection in the same way as for individual detections.

The object converts the fractional index values to Doppler frequency or speed by using appropriate units from the

`dopgrid`

input argument of the`step`

method. You can obtain values for`dopgrid`

using the`phased.RangeDopplerResponse`

System object.

This System
object supports single and double precision for input data, properties, and arguments. If
the input data `X`

is single precision, the output data is single precision.
If the input data `X`

is double precision, the output data is double
precision. The precision of the output is independent of the precision of the properties and
other arguments.

[1] Richards, M. *Fundamentals of Radar Signal
Processing.* 2nd ed. McGraw-Hill Professional Engineering,
2014.

[2] Richards, M., J. Scheer, and W. Holm, * Principles
of Modern Radar: Basic Principles*. SciTech Publishing,
2010.

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

Usage notes and limitations:

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

This System
object supports single and double precision for input data, properties, and arguments. If
the input data `X`

is single precision, the output data is single precision.
If the input data `X`

is double precision, the output data is double
precision. The precision of the output is independent of the precision of the properties and
other arguments.

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