LRT Detector
Receiver detection algorithm LRT block.
Description
The LRT Detector block implements an algorithm for binary detection of signals in the presence of noise by the likelihood ratio test (LRT). The binary detector chooses between the null hypothesis and the alternative hypothesis based on data measurements. The null hypothesis means there is no signal and the alternative hypothesis means there is some signal present.
Ports
Input
#
X
—
input signal
real vector N by 1 | complex vector N by 1 | real matrix N by M | complex matrix N by M
Details
The input signal given as a real or complex vector to or a real or complex matrix to . - is the length of the signal, and is the number of data channels. Each data channel has samples to produce a matrix by . Each row represents the components of a data vector of length .
-
If , X represents one data channel.
-
If , X can represent samples from data channels.
Detection is performed on the columns of X. The size of each row cannot change during the simulation.
The LRT Detector block assumes the same signal model in each X column. The noise-free signal is contained in the -dimensional data vector XK. A Gaussian noise defined by the noise power NCov is added to each column. For this signal model, the LRT Detector determines whether or not to reject the null hypothesis Xk = 0. Since there is only one known signal model, the LRT Detector produces one detection result for each X column.
| Data types |
|
| Complex numbers support |
Yes |
#
XK
—
known signal
real vector N by 1 | complex vector N by 1
Details
A known noiseless signal given as a real or complex vector at .
| Data types |
|
| Complex numbers support |
Yes |
#
NCov
—
noise power
`positive scalar
Details
The power or covariance of noise, given as a positive scalar.
| Data types |
|
| Complex numbers support |
No |
Output
#
Y
—
detected output signal
logical vector 1 on M | numerical vector 1 on L
Details
Detection results returned as a vector of logical values to or an integer vector to . The value of Y depends on the value of the Output format parameters. By default, the Output format parameter is set to Detection result.
-
If the Output format parameter is set to
Detection result, Y is a vector to , containing the logical detection results, where is the number of columns of the X signal. Y is true if there is a detection in the corresponding column X. Otherwise Y is false. -
If the Output format parameters are set to
Detection index, Y is an integer vector to , containing detection indices, where is the number of detections found across all channels.
| Data types |
|
| Complex numbers support |
Yes |
#
Stat
—
detection statistics
matrix D on M | vector 1 on L
Details
Detection statistics returned as a matrix to or a vector to . The value of Stat depends on the setting of the Output format parameters.
-
If the Output format parameters are set to
Detection result, Stat is a matrix to . -
If the Output format parameters are set to
Detection index, Stat is a vector of to , containing the detection statistics for each relevant detection in Y.
Dependencies
To use this port, select the Output detection statistics and threshold checkbox.
| Data types |
|
| Complex numbers support |
Yes |
#
Th
—
detection threshold
scalar
Details
The detection threshold returned as a scalar.
| Data types |
|
| Complex numbers support |
Yes |
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.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Output format —
output format
Detection result | Detection index
Details
The output data format, is specified as Detection result or Detection index. The output data is returned to the Y port.
| 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 |