phased.GLRTDetector
Description
The generalized likelihood ratio test detector (GLRT) can detect signals with unknown parameters in the presence of noise. Unknown parameters include signal amplitude, phase, frequency, and arrival times. The detector replaces unknown parameters with their maximum likelihood estimates under the signal absent hypothesis H0 or the alternative signal present hypothesis H1 and then uses the LRT detector to output detection results.
Create the
phased.GLRTDetector
object 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
creates a
generalized likelihood ratio test detector
= phased.GLRTDetectordetector
System object™ with default properties.
creates a likelihood ratio test detector
= phased.GLRTDetector(Name
= Value
)detector
System object with the specified property Name
set to the specified
Value
. You can specify additional name-value pair arguments in any
order as (Name1
= Value1
, …
,NameN
= ValueN
).
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.
DataComplexity
— Data complexity
'Complex'
(default) | 'Real'
Data complexity, specified as 'Complex'
or 'Real'
.
Complexity defines the format used to report output data. When
DataComplexity
is 'Complex'
, data is
complex-valued. When DataComplexity
is 'Real'
,
data is real-valued.
Example: 'Real'
Data Types: char
| string
ProbabilityFalseAlarm
— Probability of false alarm
1e-1
(default) | nonnegative scalar
Probability of false alarm, specified as a positive scalar between 0 and 1, inclusive.
Example: 1e-6
Data Types: single
| double
OutputFormat
— Format of output data
'Detection result'
(default) | 'Detection index'
Format of output data, specified as 'Detection result'
or 'Detection index'
. Output data is returned in the Y
argument.
Example: 'Detection index'
Data Types: char
| string
ThresholdOutputPort
— Output detection statistics and threshold
false
(default) | true
Output detection statistics and detection threshold, specified as false
or true
. Set this property to true
to output the detection statistics in the stat
argument and the detection threshold in the th
argument. Set this property to false
to suppress the output of detection statistics and threshold.
Data Types: logical
NoiseInputPort
— Enable input of known noise power
false
(default) | true
Enable the input of noise power, specified as false
or
true
. You can input known or estimated noise power from a reference
source. When true
, use the input argument ncov
to specify noise power. When false
, the noise input port is disabled
and the noise power is estimated by the GLRT detector.
Data Types: logical
SignalParameterOutputPort
— Output maximum likelihood estimate of unknown signal parameters
false
(default) | true
Output the maximum likelihood estimates of the unknown signal parameters under the
alternative hypothesis (H1), specified as
false
or true
. Parameters are output in the
estparam
argument.
Data Types: logical
NoisePowerOutputPort
— Output estimated noise power
false
(default) | true
Output the estimated noise power, under the alternative hypothesis. Noise power is
output in the estnoise
argument.
Dependencies
To enable this property, set the NoiseInputPort
property to
false
.
Data Types: logical
Usage
Syntax
Description
You can combine optional input and output arguments when their enabling properties are
set. Optional inputs and outputs must be listed in the same order as the order of the
enabling properties. For example, [Y,stat,th,estparam] =
detector(X,hyp,obs,ncov)
.
Input Arguments
X
— Input data
N-by-1 real-valued vector | N-by-1 complex-valued vector | N-by-M real-valued matrix | N-by-M complex-valued matrix
Input data, specified as a real-valued or complex-valued N-by-1
vector, or an N-by-M real-valued or
complex-valued matrix. N is the signal length and
M is the number of data channels. Detection is performed along
the columns of X
. The size of each row M
cannot change during simulation. When M = 1, X
represents a single channel of data. When M > 1,
X
can represent N samples from
M data channels. Data streams can later be combined, for example,
by beamforming.
The input data has a general interpretation. For example, the data can be interpreted as:
Time series – N samples of a time series
Sensor - N represents a snapshot of data samples from a set of sensors
Data Types: single
| double
Complex Number Support: Yes
hyp
— Augmented linear equality constraint matrix
real-valued R-by-(P + 1) matrix | complex-valued R-by-(P + 1) matrix
Augmented linear equality constraint matrix, specified as a real-valued or
complex-valued R-by-(P + 1) matrix. The matrix
takes the form [A,b]
representing the equation:
where the unknown parameters are represented by ϴ.
A
has the rank R ≥ 1. The augmented linear
equality constraint matrix expresses the null hypothesis
H0.
For this signal model, the GLRT detector determines whether to reject the null
hypothesis which is expressed in the form A*θ = b
where
A
is an R-by-P matrix with
R ≤ P and rank R ≥ 1. b
is
an R-by-1 vector. A
and b
are
carried in the augmented linear equality constraint matrix hyp =
[A,b]
. Because there are D signal models, the GLRT
detector outputs D detection results for each column of
X
Data Types: single
| double
Complex Number Support: Yes
obs
— Observation matrix
N-by-P-by-D
array
Observation matrix for the linear deterministic signal model, specified as an
N-by-P-by-D array
N > p and rank P, D is the
number of signal models, and the white Gaussian noise
is a
N-by-1 vector determined by the covariance
ncov
argument. The observation matrix is defined by
X
= obs
*param
+
noise
,
Example: 20.0
Data Types: single
| double
Complex Number Support: Yes
ncov
— Known noise power
positive scalar
Known noise power, specified as a scalar or a row vector of length
D. When ncov
is a scalar, it represents
equal known noise power for D models. When
ncov
is a row vector of length D, it
represents the known noise power for the D models,
respectively.
Example: 20.0
Dependencies
To enable this argument, set the NoiseInputPort
property to
true
.
Data Types: single
| double
Output Arguments
Y
— Detection results
D-by-M logical-valued vector | 1-by-L integer-valued vector | 2-by-L integer-valued matrix
Detection results of D models for M
independent data samples returned as a D-by-M
logical-valued vector, 1-by-L integer-valued vector, or
2-by-L integer-valued matrix. The format of
Y
depends on how the OutputFormat
property
is specified. By default, the OutputFormat
property is set to
'Detection result'
.
When OutputFormat
is 'Detection result'
,
Y
is a D-by-M matrix
containing logical detection results, where D is the number of
signal models and M is the number of columns of
X
. For each row, Y is
true
in a column if there is a detection in the corresponding
column of arg
. Otherwise, Y
is
false
.
When OutputFormat
is 'Detection index'
,
Y
is a 1-by-L
vector or a
2-by-L matrix containing detection indices, where
L is the number of detection found in the M
data samples and D models. When X
is a column
vector, Y is a 1-by-L vector and contains the
index of the detections found in the D models. When
X
is a matrix, Y
is a
2-by-L matrix, and each column of Y
has the
form [detrow;detcol]
, where detrow
is the index
of the model and detcol
is the column index of
X
.
stat
— detection statistic
N-by-M (default) | 1-by-L
Detection statistics, returned as a N-by-M
matrix or 1-by-L vector. The format of stat
depends on the OutputFormat
property.
When
OutputFormat
is'Detection result'
,stat
has the same size asY
.When
OutputFormat
is'Detection index'
,stat
is a 1-by-L vector containing detection statistics for each corresponding detection inY
.
th
— Detection threshold
scalar
Detection threshold, returned as a scalar.
Dependencies
To enable this argument, set the ThresholdOutputPort
property to true
.
estparam
— Maximum likelihood estimates of signal parameters
P-by-M-by-D
array
Maximum likelihood estimates (MLE) of unknown signal parameters, returned as a P-by-M-by-D array.
Dependencies
To enable this argument, set the SignalParameterOutputPort
property to true
.
estnoise
— Estimated noise power
positive scalar
Estimated noise power, returned as a positive scalar. When the
OutputFormat
property is 'Detection result'
,
estnoise
has the same size as Y
. When
OutputFormat
property is 'Detection index'
,
estnoise
returns a noise power estimate of size
1-by-L for each corresponding detection in
Y
.
Dependencies
To enable this argument, set the NoisePowerOutputPort
property to true
.
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
Generalized Likelihood Ratio Test Detection on Real Data
Perform GLRT detection on a real Gaussian noise matrix with a desired probability of false alarm of 0.1. Assume that the signal dimension is 4, the noise power is unknown, and there are 2 unknown signal parameters with true values 0. Use a 3-model observation matrix. Perform the detection on all samples of the input and evaluate the probability of false alarm.
rng(10031); glrt = phased.GLRTDetector( ... DataComplexity = 'Real', ... ProbabilityFalseAlarm = 0.1); N = 4; M = 1000; p = 2; D = 3; x = randn(N,M); hyp = [eye(p) zeros(p,1)]; obs = randn(N,p,D); dresult = glrt(x,hyp,obs); Pfa = sum(dresult,2)/M
Pfa = 3×1
0.0970
0.1030
0.1110
Generalized Likelihood Ratio Threshold Detection on Complex Data
Perform Generalized Likelihood Ratio Threshold detection on complex Gaussian noise matrix with a desired probability of false alarm of 0.1. Assume that the signal dimension is 5. Also assume that the noise power is unknown. Assume there is only one unknown signal parameter with a true value zero. Use a single-model observation matrix. Perform the detection on all samples of the input and evaluate the probability of false alarm.
rng default glrt = phased.GLRTDetector(DataComplexity = 'Complex', ... ProbabilityFalseAlarm = 0.1); N = 5; M = 1000; x = 1/sqrt(2)*(randn(N,M)+1i*randn(N,M)); hyp = [1 0]; obs = ones(N,1); dresult = glrt(x,hyp,obs); Pfa = sum(dresult)/M
Pfa = 0.1060
Perform Generalized Likelihood Ratio Test Detection
Perform GLRT detection on a complex Gaussian noise matrix with a desired probability of false alarm of 0.1. Assume that the signal dimension is 2 and that the noise power is unknown. There is only 1 unknown signal parameter with true value 0. Use a single-model observation matrix. Perform the detection on all samples of the input and evaluate the probability of false alarm.
Create the 1000 samples of Gaussian random data.
rng default
N = 2;
M = 1000;
x = 1/sqrt(2)*(randn(N,M) + 1i*randn(N,M));
Create the GLRT detector System object™.
glrt = phased.GLRTDetector(DataComplexity = 'complex', ... ProbabilityFalseAlarm = 0.1);
Specify the observation and hypotheses matrices.
hyp = [1 0]; obs = ones(N,1);
Solve and display the first 15 of the detection results.
dresult = glrt(x,hyp,obs); disp(dresult(1:15))
0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
Estimate the probability of false alarm.
Pfa = sum(dresult)/M
Pfa = 0.0930
The probability of false alarm is close to the desired probability of 0.1.
Perform Generalized Likelihood Ratio Test Detection For Two Parameters
Perform GLRT detection on a given complex Gaussian noise matrix with a desired probability of false alarm of 0.1. Assume that the signal dimension is 4 and the noise power is unknown. There are 2 unknown signal parameters with true values 0. Use a 3-model observation matrix. Perform the detection on all samples of the input and evaluate the probability of false alarm.
Create the random data.
rng default
N = 4;
M = 1000;
P = 2;
D = 3;
x = 1/sqrt(2)*(randn(N,M)+1i*randn(N,M));
Create the phased.GLRTDetector
System object™.
glrt = phased.GLRTDetector(DataComplexity = 'complex', ... ProbabilityFalseAlarm = 0.1); hyp = [eye(P) zeros(P,1)]
hyp = 2×3
1 0 0
0 1 0
obs = randn(N,P,D) + 1i*randn(N,P,D);
Run the detector and compute the probability of false alarm.
dresult = glrt(x,hyp,obs); pfa = sum(dresult,2)/M
pfa = 3×1
0.0890
0.0980
0.0970
Perform Angle-Domain GLRT Detection of Two Targets
Perform angle-domain GLRT detection for two targets located at 11 and -47 degrees with a desired probability of false alarm of 0.01. Use a ULA of dimension 128 to receive a single-snapshot signal with complex white Gaussian noise. The noise power and target complex amplitudes are unknown. Use a 256-model observation matrix, where each model checks the existence of a target following that model. Perform the detection on the input and plot the detection result.
rng default glrt = phased.GLRTDetector(DataComplexity = 'complex', ... ProbabilityFalseAlarm = 0.01);
Create two targets located at 11 and -47 degrees.
tarAng = [11,-47]; tarNum = length(tarAng);
Start with a ULA array with 128 elements having 1/2-wavelength element spacing.
N = 128;
fc = 3e8;
elementPos = (0:N-1)*physconst('LightSpeed')/fc/2;
Create single-snapshot received signal from two targets at the ULA.
tarAmp = 1/sqrt(2)*(randn(tarNum,1) + 1i*randn(tarNum,1)); signal = steervec(elementPos,tarAng)*tarAmp;
Single-snapshot of complex white Gaussian noise at the ULA.
noise = 1/sqrt(2)*(randn(N,1) + 1i*randn(N,1));
Add the noise to the signal.
x = signal + noise;
Partition angle into 256 angle bins
D = 256; angGrid = asind(2*(-D/2:D/2-1)/D);
Perform GLRT detection on 256 signal models. Each model assumes one target. % N-by-1-by-D
obs = permute(steervec(elementPos,angGrid),[1 3 2]); hyp = [1,0]; dresult = glrt(x,hyp,obs);
Plot the GLRT detection results at the 256 angle bins.
plot(angGrid,dresult) xlabel('Angle (degrees)') ylabel('Detection Result') grid on
Perform Angle-Doppler-Domain GLRT Detection
Perform angle-Doppler-domain GLRT detection for a target located at 28 degree at a Doppler of 10 Hz with a desired probability of false alarm of 1e-6. Use a ULA of dimension 128 to receive a 32-pulse signal under complex white Gaussian noise. The noise power and target complex amplitude are unknown. Use an observation matrix with 256-by-64 angle-Doppler models, where each model checks the existence of a target following that model. Perform the detection on the input and plot the spatial-temporal detection map.
rng default glrt = phased.GLRTDetector('DataComplexity','complex',... 'ProbabilityFalseAlarm',1e-6,... 'ThresholdOutputPort',true);
Target is located at 28 degree at a Doppler of 10 Hz.
tarAng = -28; tarDop = 10;
Create a ULA with 128 elements and with elements spaced at 1/20-wavelength.
elementNum = 128;
fc = 3e8;
elementPos = (0:elementNum-1)*physconst('LightSpeed')/fc/2;
ULA observes 32 pulses at a PRF of 50 Hz
fPRF = 50; pulseNum = 32;
Create the spatial-temporal signal from the target at the ULA.
tarAmp = 1/sqrt(2)*(randn + 1i*randn); dopSv = dopsteeringvec(tarDop,pulseNum,fPRF); angSv = steervec(elementPos,tarAng); signal = kron(dopSv,angSv)*tarAmp;
Add the spatial-temporal complex white Gaussian noise at the ULA.
noisePow = 0.01; N = elementNum*pulseNum; noise = sqrt(noisePow/2)*(randn(N,1) + 1i*randn(N,1)); x = signal + noise;
Partition angle into 256 angle bins and Doppler into 64 Doppler bins
angNum = 256; dopNum = 64; angGrid = asind(2*(-angNum/2:angNum/2-1)/angNum); dopGrid = fPRF*(-dopNum/2:dopNum/2-1)/dopNum; D = angNum*dopNum;
Perform GLRT detection on 256-by-64 angle-Doppler models, each assuming 1 target.
obs = zeros(N,1,D); for dopBin = 1:dopNum dopGridSv = dopsteeringvec(dopGrid(dopBin),pulseNum,fPRF); for angBin = 1:angNum angGridSv = steervec(elementPos,angGrid(angBin)); angDopGridSv = kron(dopGridSv,angGridSv); obs(:,:,(dopBin-1)*angNum+angBin) = angDopGridSv; end end hyp = [1,0]; [dresult,stat,th] = glrt(x,hyp,obs); stat = reshape(stat,angNum,dopNum);
Plot a spatial-temporal GLRT detection map.
[dopMesh,angMesh] = meshgrid(dopGrid,angGrid); surf(angMesh,dopMesh,pow2db(stat)) hold on mesh(angMesh,dopMesh,pow2db(th)*ones(angNum,dopNum)) xlabel('Angle (degrees)') ylabel('Doppler (Hz)') zlabel('Power (dB)')
More About
Data Precision
This System object supports single and double precision for input data, properties and arguments. If input data is single precision, all the non-logical outputs are also single precision. If input data is double precision, the non-logical outputs are double precision. The precision of the non-logical output is independent of the precision of the properties and other arguments.
Signal Model
The GLRT detector assumes D linear deterministic signals in each
column of X
. The GLRT detector assumes that the data follows the linear
deterministic signal model X = H*param + noise
where
X
is an N-by-1 data vector, H
the observation matrix given as an
N-by-P-by-D array.
param
is a P-by-1 vector that contains P unknown signal parameters.H
is an N-by-P-by-D array that summarizes D observation matrices of size N-by-P with N > p\P and rank P.noise
is an N-by-1 noise vector assumed to be white Gaussian.
For this signal model, the GLRT detector determines whether to reject the
null hypothesis. The null hypothesis is expressed in the form A*param = b
where A
is an R-by-P matrix with
R ≤ P and rank R ≥ 1, and b
is an
R-by-1 vector. A
and b
are form
the augmented linear equality constraint matrix hyp = [A,b]
. Because
there are D signal models, the GLRT detector outputs D
detection results for each column of X
.
H
is the observation matrix for a linear deterministic signal model
X = H*param + noise
. obs
is an
N-by-P-by-D array with N
> p
and with rank p
, D is the number of
signal models, and noise
is a white Gaussian noise
N-by-1 vector.
The GLRT algorithm replaces the unknown parameters by their maximum likelihood estimates under the H0 or H1 hypotheses. Subsequently, the algorithm applies the likelihood ratio test. For a data vector x with unknown model parameters ϴ, the GLRT decides H1 if the likelihood ratio is greater than the threshold η
for the estimated ϴ.
Detection Statistics and Threshold
For a real data model with known Gaussian white noise, the test statistic is given by
where represents the maximum likelihood estimate of θ given by
For a complex data model with known Gaussian noise, the test statistic is given by
where H† denotes the adjoint of H where
For the real data model with unknown white Gaussian noise. the test statistic is
where again the maximum likelihood estimate of θ is represented by
. but here σ² is estimated by
For complex data with unknown Gaussian noise, the test statistic is
where
and the estimate of σ² is
The detection threshold for real data with known white Gaussian noise and a given theoretical probability of false alarm Pfa is calculated from the chi-square inverse cumulative distribution function (CDF) with r degrees of freedom.
For complex data with known white Gaussian noise and a given theoretical probability of false alarm Pfa, the theoretical detection threshold is calculated from the chi-square inverse cumulative distribution function (CDF) with 2r degrees of freedom
For real data with unknown white Gaussian noise and a given theoretical probability of
false alarm Pfa, the theoretical detection
threshold calculated from the f-inverse cumulative distribution function
(CDF) with r degrees of freedom
For complex data with unknown white Gaussian noise and a given theoretical probability
of false alarm Pfa, the theoretical detection
threshold is calculated from the f-inverse cumulative distribution
function
(CDF) with 2r degrees of freedom
References
[1] Steven M. Kay, Fundamentals of Statistical Signal Processing, Detection Theory, Prentice-Hall PTR, 1993.
[2] Mark A. Richards, Fundamentals of Radar Signal Processing, Third edition, McGraw-Hill Education, 2022.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2023b
See Also
phased.LRTDetector
| npwgnthresh
| rocsnr
| rocpfa
| phased.CFARDetector
| phased.CFARDetector2D
MATLAB コマンド
次の MATLAB コマンドに対応するリンクがクリックされました。
コマンドを MATLAB コマンド ウィンドウに入力して実行してください。Web ブラウザーは MATLAB コマンドをサポートしていません。
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)