Detection

Target detection, CFAR, 2-D CFAR, ROC curves, sonar equation

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

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ROC Estimation

`albersheim`	Required SNR using Albersheim’s equation
`dechirp`	Perform dechirp operation on FMCW signal
`npwgnthresh`	Detection SNR threshold for signal in white Gaussian noise
`pulsint`	Pulse integration
`rocpfa`	Receiver operating characteristic curves by false-alarm probability
`rocsnr`	Receiver operating characteristic curves by SNR
`shnidman`	Required SNR using Shnidman’s equation

Radar Performance

`bw2rangeres`	Convert bandwidth to range resolution (Since R2021a)
`coincidence`	Coincidence algorithm (Since R2021a)
`crt`	Chinese remainder theorem (Since R2021a)
`freq2wavelen`	Convert frequency to wavelength (Since R2021a)
`iscoprime`	Check coprime relation (Since R2021a)
`physconst`	Physical constants
`rangeres2bw`	Convert range resolution to bandwidth (Since R2021a)
`wavelen2freq`	Convert wavelength to frequency (Since R2021a)

Sonar Performance

`bw2rangeres`	Convert bandwidth to range resolution (Since R2021a)
`freq2wavelen`	Convert frequency to wavelength (Since R2021a)
`physconst`	Physical constants
`rangeres2bw`	Convert range resolution to bandwidth (Since R2021a)
`range2tl`	Compute underwater sound transmission loss from range
`sonareqsl`	Compute source level using the sonar equation
`sonareqsnr`	Compute SNR using the sonar equation
`sonareqtl`	Compute transmission loss using the sonar equation
`tl2range`	Compute range from underwater transmission loss
`wavelen2freq`	Convert wavelength to frequency (Since R2021a)

SAR Image Formation

`rangeMigrationSFM`	Range migration image formation algorithm for stepped FM waveform (Since R2022a)
`rangeMigrationLFM`	Range migration image formation algorithm for linear FM waveform (Since R2022a)
`rangeMigrationFMCW`	Range migration image formation algorithm for frequency-modulated CW waveform (Since R2022a)
`rangeDopplerImagerLFM`	Range Doppler image formation algorithm for linear FM waveform (Since R2022a)

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.