LRT Detector

Likelihood ratio test detector

Since R2023b

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Libraries:
Phased Array System Toolbox / Detection

Description

The likelihood ratio test (LRT) detector performs binary signal detection in the presence of noise. The binary detector chooses between the null hypothesis H₀ and the alternative hypothesis H₁ based on data measurements. The null hypothesis denotes the absence of any signal while the alternative hypothesis denotes the presence of some signal.

Ports

Input

X — Input data

real-valued N-by-1 vector | complex-valued N-by-1 vector | real-valued N-by-M matrix | complex-valued N-by-M 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. Each data channel has N samples to yield an N-by-M matrix. Each row represents the components of a length-M data vector. When M = 1, X represents a single channel of data. When M > 1, X can represent N samples from M data channels. Detection is performed along the columns of X. The size of each row M cannot change during the simulation.

The LRT detector assumes the same signal model in each column of X. The noise-free signal is contained in the N-dimensional data vector Xknown. 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 Xknown = 0. Because there is only one known signal model, the LRT detector outputs one detection result for each column of X.

Data Types: single | double
Complex Number Support: Yes

XK — Known signal

real-valued N-by-1 vector | complex-valued N-by-1 vector

Known noise-free signal, specified as a real-valued or complex-valued N-by-1 vector.

Data Types: single | double
Complex Number Support: Yes

NCov — Noise power

positive scalar

Noise power or covariance, specified as a positive scalar.

Example: 2.0

Data Types: single | double

Output

Y — Detection results

1-by-M logical-valued vector | 1-by-L integer-valued vector

Detection results, returned as a 1-by-M logical-valued vector or a 1-by-L integer-valued vector. The format of Y depends on the value of the Output format parameter. By default, the Output format parameter is set to 'Detection result'.

• When the Output format parameter is set to 'Detection result', Y is a 1-by-M vector containing logical detection results, where M is the number of columns of X. Y is true if there is a detection in the corresponding column of X. Otherwise, Y is false.

• When the Output format parameter is set to 'Detection index', Y is a 1-by-L integer-valued vector containing detection indices, where L is the number of detections found over all M channels.

Data Types: single | double | Boolean
Complex Number Support: Yes

Stat — Detection statistics

D-by-M (default) | matrix | 1-by-L vector

Detection statistics, returned as a D-by-M matrix or as a 1-by-L vector. The format of stat depends on the setting of the Output format parameter.

• When Output format parameter is 'Detection result', stat is a D-by-M matrix.

• When Output format parameter is 'Detection index', stat is a 1-by-L vector containing detection statistics for each corresponding detection in Y.

Dependencies

To enable this port, select the Output detection statistics and threshold check box.

Data Types: single | double
Complex Number Support: Yes

Th — Detection threshold

scalar

Detection threshold, returned as a scalar.

Dependencies

To enable this port, select the Output detection statistics and threshold check box.

Data Types: single | double

Parameters

Probability of false alarm — Probability of false alarm

0.1 (default) | nonnegative scalar

Probability of false alarm, specified as positive scalar between 0 and 1, inclusive.

Programmatic Use

Block Parameter:ProbabilityFalseAlarm

Type:double, single

Values:scalar |

Default:0.1

Data Types: single | double

Output format — 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 port.

Example: Detection index

Programmatic Use

Block Parameter:OutputFormat

Type:char, string

Values:Detection result | Detection index

Default:Detection result

Data Types: char | string

Output detection statistics and threshold — Output detection statistics and threshold

false (default) | true

Select this checkbox to output detection statistics and detection threshold using the Stat and Th ports.

Programmatic Use

Block Parameter:ThresholdOutputPort

Type:check box

Values:0 | 1

Default:0

Simulate using — Block simulation method

Interpreted Execution (default) | Code Generation

Block simulation, specified as Interpreted Execution or Code Generation. If you want your block to use the MATLAB^® interpreter, choose Interpreted Execution. If you want your block to run as compiled code, choose Code Generation. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using Code Generation. Long simulations run faster with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

When the Simulink^® model is in Accelerator mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

Block Simulation	Simulation Behavior
	Normal	Accelerator	Rapid Accelerator
Interpreted Execution	The block executes using the MATLAB interpreter.	The block executes using the MATLAB interpreter.	Creates a standalone executable from the model.
Code Generation	The block is compiled.	All blocks in the model are compiled.

For more information, see Choosing a Simulation Mode (Simulink).

Programmatic Use

Block Parameter:SimulateUsing

Type:enum

Values:Interpreted Execution, Code Generation

Default:Interpreted Execution

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b