GLRT Detector
GLRT receiver detection algorithm block.
Description
The GLRT Detector detects signals with unknown parameters in the presence of noise. Unknown parameters include amplitude, phase, frequency and time of arrival. The detector replaces the unknown parameters with their maximum likelihood estimates under the hypothesis of no signal and the alternative hypothesis of signal presence . The binary detector then chooses between the null hypothesis and the alternative hypothesis based on the measurements. If hypothesis best accounts for the data, the detector determines that the target is absent. If the hypothesis best fits the data, the detector determines that the target is present.
Ports
Input
#
X
—
input signal
real vector N by 1 | real vector N by 1 | real matrix N by M | complex matrix N by M
Details
The input data, given as a real or complex vector to or a real or complex matrix to . - is the signal length and is the number of data channels. Detection is performed along the X columns. The size of each row of cannot change during simulation.
-
If , X represents one data channel.
-
If , X may represent sampling samples from data channels. The data streams can be combined later, e.g. by beamforming.
The input data has a common interpretation. For example, the data may be interpreted as:
-
Time series - samples of a time series.
-
Sensor - represents a snapshot of a sample of samples from a set of sensors.
| Data types |
|
| Complex numbers support |
Yes |
#
Hyp
—
augmented linear matrix of equality constraints
` real matrix R on (P+1)` | ` complex matrix R on (P+1)`
Details
The augmented constraint matrix of a linear equality given as a real or complex matrix at . The matrix has the form [A, b] and is an equation:
where the unknown parameters are contained in the variable . A has rank . The augmented linear equality constraint matrix expresses the null hypothesis .
For this signal model, the GLRT detector determines whether to reject the null hypothesis, which is expressed in the form AΘ = b, where A is the matrix on with rank and rank , and b is the vector on . A and b are in the augmented constraint matrix of linear equality constraints hyp = [A, b]. Since there are signal models, the GLRT detector outputs the detection results for each column X.
| Data types |
|
| Complex numbers support |
Yes |
#
Obs
—
observation matrix
`array N on P on D
Details
The observation matrix for a linear deterministic signal model given as an array on on , where , rank , is the number of signal models, and white Gaussian noise is a vector on , defined by the covariance argument ncov. The observation matrix is defined as X =obs*param+ noise.
- Example
-
30.0
| Data types |
|
| Complex numbers support |
Yes |
#
NCov
—
specified noise power
`positive scalar
Details
The noise power given as a scalar or string vector of length .
-
If NCov is a scalar, it represents the equal known noise power for models.
If NCov is a string vector of length , it represents the specified noise power for models respectively.
Dependencies
To use this port, check the Enable known noise power input parameters.
| Data types |
|
| Complex numbers support |
No |
Output
#
Y
—
detection results
logical vector D on M | ` vector of integer values 1 on L` | ` matrix of integer values 2 on L`
Details
The results of detecting patterns for independent data samples, returned as a logical vector on pr. The Y format depends on the value of the Output format parameters. By default, the Output format parameter is set to Detection result.
-
If the Output format parameters are set to
Detection result, Y is a matrix , containing the results of logical detection, where is the number of signal models and is the number of X columns. For each row, istruein a column if there is a detection in the correspondingargcolumn. Otherwise, Y isfalse. -
If the Output format parameters are set to
Detection index, Y is a vector to or a matrix to , containing detection indices, where is the number of detections found in data samples and models . When X is a column vector, is a vector by , containing an index of detections found in models . When X is a matrix, Y is a matrix to , and each column is[detrow;detcol], wheredetrowis the model index anddetcolis the column index .
| Data types |
|
| Complex numbers support |
No |
#
Stat
—
detection statistics
` matrix N on (by default)` | ` vector 1 on L`
Details
Detection statistics returned as a matrix to or a vector to . The value of Stat depends on the value of the Output format parameters.
-
If the Output format parameters are set to
Detection result, Stat has the same size as Y. -
If the Output format parameters are set to
Detection index, Stat is a vector of at , containing the detection statistics for each relevant detection in Y.
Dependencies
To use this port, check the Output detection statistics and threshold parameters.
| Data types |
|
| Complex numbers support |
No |
#
Th
—
calculated detection threshold
scalar
Details
The detection threshold returned as a scalar.
Dependencies
To use this port, select the Output detection statistics and threshold parameters check box.
| Data types |
|
| Complex numbers support |
No |
#
Param
—
maximum likelihood estimates of signal parameters
`array P on N on D
Details
Maximum likelihood estimates (MLE) of unknown signal parameters returned as an array on on .
Dependencies
To use this port, select the Output MLEs of unknown signal parameters checkbox.
| Data types |
|
| Complex numbers support |
No |
#
N
—
noise power
`positive scalar
Details
Estimated noise power returned as a positive scalar.
-
If the Output format parameters are set to
Detection result, N is the same size as Y. -
If the Output format parameters are set to
Detection index, N returns a noise power estimate of size at for each corresponding detection in Y.
Dependencies
To use this port, select the Output estimated noise power parameters check box.
| Data types |
|
| Complex numbers support |
No |
Parameters
Main
#
Probability of false alarm —
false alarm probability
Real number
Details
The probability of a false alarm, given as a positive scalar from 0 to 1 inclusive.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Output format —
detection result format
Detection result | Detection index
Details
The format of detection results returned to output port Y is specified as Detection result or Detection index.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Output detection statistics and threshold —
output of detection statistics and threshold
Logical
Details
Select this check box to output detection statistics and detection threshold through Stat and Th ports.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Enable known noise power input (NCov) —
switching on the input noise power
Logical
Details
Select this check box to enable noise power input through the NCov port.
Dependencies
Clear the Output estimated noise power checkbox to enable this checkbox.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Output MLEs of unknown signal parameters —
inclusion of maximum likelihood estimation output
Logical
Details
Select this check box to output the maximum likelihood estimate of the signal parameters through the Param port.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Output estimated noise power —
switching on the output of the estimated noise power
Logical
Details
Select this check box to output the estimated noise power through the N port.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |