# Detection

The Phased Array System Toolbox™ includes System objects and Simulink^{®} blocks for performing matched filtering, constant false
alarm rate (CFAR) detection in one or two dimensions, stretch-processing
pulse compression and coherent and noncoherent pulse integration.
Utility functions let you compute and visualize receiver operating
characteristic (ROC) curves for various signal-to-noise ratio (SNR)
levels or probabilities of false alarm. A suite of functions and an app
let you perform radar analysis using the radar equation. You can
estimate, for example, received SNR or maximum target detection range. A
similar set of capabilities are provided for the sonar equation. Blake
charts let you visualize radar coverage.

## Objects

`phased.AlphaBetaFilter` | Alpha-beta filter for object tracking |

`phased.CFARDetector` | Constant false alarm rate (CFAR) detector |

`phased.CFARDetector2D` | Two-dimensional CFAR detector |

`phased.GLRTDetector` | Generalized likelihood ratio detector (Since R2023b) |

`phased.LRTDetector` | Likelihood ratio test detector (Since R2023b) |

`phased.MatchedFilter` | Matched filter |

`phased.StretchProcessor` | Stretch processor for linear FM waveform |

`phased.TimeVaryingGain` | Time varying gain control |

## Blocks

2-D CFAR Detector | Two-dimensional constant false alarm rate (CFAR) detector |

CFAR Detector | Constant false alarm rate (CFAR) detector |

Dechirp Mixer | Dechirping operation on input signal |

GLRT Detector | Perform generalized likelihood ratio test detection (Since R2023b) |

LRT Detector | Likelihood ratio test detector (Since R2023b) |

Matched Filter | Matched filter |

Pulse Integrator | Coherent or noncoherent pulse integration |

Stretch Processor | Stretch processor for linear FM waveforms |

Time Varying Gain | Time varying gain (TVG) control |

## Functions

## Apps

Sonar Equation Calculator | Estimate maximum range, SNR, transmission loss and source level of a sonar system |

Sensor Array Analyzer | Analyze beam patterns and performance characteristics of linear, planar, 3-D, and arbitrary sensor arrays |

## Topics

### Detection and Estimation

**Neyman-Pearson Hypothesis Testing**

In phased-array applications, you sometimes need to decide between two competing hypotheses to determine the reality underlying the data the array receives.**Constant False-Alarm Rate (CFAR) Detectors**

CFAR detectors apply the Neyman-Pearson criterion to target detection. The detectors estimate noise statistics from data.**Receiver Operating Characteristics**

Receiver operating characteristic (ROC) curves describe a detector’s performance by relating probability of false alarm to probability of detection.**Matched Filtering**

Matched filtering increases SNR and improves detection.**Stretch Processing**

Stretch processing, also known as deramping or dechirping, is an alternative to matched filtering.**FMCW Range Estimation**

FMCW range estimation dechirps the received signal, extracts beat frequencies, and computes the target range.**Range-Doppler Response**

Perform range-Doppler processing and visualize range-Doppler maps.

### Phased Array Conventions

**Standards and Conventions**

This section introduces the concept of baseband signals and defines the local and global coordinate systems used in the toolbox.**Units of Measure and Physical Constants**

Phased Array System Toolbox uses the International System of Units (SI).

### Sonar Equation

**Sonar Equation**

The sonar equation is used in underwater signal processing to relate received signal power to transmitted signal power for one-way or two-way sound propagation.**Doppler Effect for Sound**

The Doppler effect is the change in the observed frequency of a source due to the motion of either the source or receiver or both.