## Phased Array System Toolbox |

- Multifunction radar system modeling, including actively electronically scanned array (AESA) and passively electronically scanned array (PESA)
- Radar theater models with moving targets, propagation channels, and interference such as clutter and jammers
- URA, ULA, UCA, and conformal sensor arrays with perturbation and polarization effects
- Continuous and pulsed waveforms, including frequency modulated and phased coded pulses
- Digital beamforming algorithms for broadband and narrowband waveforms, including Capon and Frost
- Direction of arrival (DOA) algorithms, including monopulse, beamscan, MVDR, Root MUSIC, and ESPRIT
- Range and Doppler estimation and detection algorithms, including CFAR processing
- Space-time adaptive processing (STAP) algorithms, including sample matrix inversion (SMI) and adaptive DPCA pulse canceller

Phased Array System Toolbox provides narrowband and broadband digital beamforming algorithms. It enables you to suppress interferences and avoid self-nulling with adaptive beamformers, such as minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV) beamformers. You can use STAP techniques to remove clutter and jammer. The system toolbox lets you beamform in a region of interest to estimate the direction of arrival (DOA) of incident signals for any array geometry. Alternatively, you can use efficient sum-and-difference monopulse trackers for a uniform linear (ULA) or rectangular array (URA) and super resolution techniques such as MUSIC and ESPRIT.

**Conventional and Adaptive Beamformers** (Example)

Compare phase shift, Capon, or MVDR, and LCMV beamformers.

**Wideband Beamforming** (Example)

Compare subband phase shift, Frost, and time delay beamformers.

**Space-Time Adaptive Processing (STAP)** (Example)

Suppress clutter and jammer interference with a conventional or adaptive DPCA canceller and an SMI beamformer.

**Beamscan and MVDR DOA Estimation** (Example)

Estimate broadside angles of signals received by a linear array, and azimuth and elevation angles of signals received by a planar array.

**High Resolution DOA Estimation** (Example)

Estimate angles of arrival from two signal sources with super resolution MUSIC and ESPRIT techniques.

**Monopulse Trackers** (Example)

Estimate the DOA of a signal using a sum-and-difference monopulse algorithm.

Phased Array System Toolbox provides common waveforms used in active sensor array systems. You can define the parameters of constant frequency (PCW), frequency modulated continuous wave (FMCW), and multiple frequency-shift keying (MFSK) continuous waveforms. The system toolbox lets you specify pulse repetition frequency (PRF), pulse duration, and bandwidth of linear frequency modulation (LFM), stepped FM, and phased coded pulse waveforms. You can also use Phased Array System Toolbox to analyze spectral properties, range resolution, Doppler resolution, and the coupling between range and Doppler.

**Radar Waveform Analyzer** (Example)

Explore properties of continuous and frequency modulated and phase-coded pulse waveforms.

**Ambiguity Function of Pulse Waveforms** (Example)

Compare range and Doppler capabilities of rectangular, linear, and stepped FM pulse waveforms.

**Staggered PRF Waveforms** (Example)

Avoid blind speed problems with staggered PRF waveforms.

**FMCW Waveforms** (Example)

Estimate range and Doppler and compensate for range Doppler coupling effect in FMCW signals.

**MFSK Waveforms** (Example)

Compare MFSK and FMCW waveforms to estimate range and speed in multitarget scenarios.

Phased Array System Toolbox lets you model and analyze the behavior of active or passive electronically scanned arrays (AESA or PESA) with arbitrary geometries including uniform linear array (ULA), uniform circular array (UCA), and uniform rectangular array (URA). You can define your own array geometry by specifying the position and orientation of each element in 3D space. You can model common antenna and microphone elements whose radiation pattern can be described by an analytic function or defined by frequency-dependent measured data. The system toolbox lets you model array perturbations and mutual coupling between elements, specify polarization, define subarrays, and model heterogeneous arrays with multiple element patterns.

**Sensor Array Analyzer App** (Example)

Visualize directivity patterns of microphone and antenna arrays in rectangular, spherical, and u/v space.

**Grating Lobe Diagrams** (Example)

Analyze grating lobes of a wavefield due to spatial undersampling.

**Phased Array Gallery** (Example)

Model and visualize various array and subarray geometries.

**Calibrate Arrays with Perturbations** (Example)

Calibrate antenna arrays with electrical and geometrical uncertainties using pilot signals.

**Antenna Array with Custom Pattern** (Example)

Import measured antenna patterns and model effects on arrays.

**Modeling Mutual Coupling** (Example)

Model mutual coupling in large arrays by replacing isolated element patterns with embedded element patterns.

**Array Pattern Synthesis** (Example)

Match desired beam patterns, synthesize beam patterns with nulls, and thin arrays using genetic algorithms.

**Polarized Antennas** (Example)

Analyze polarized fields and model signal transmission between polarized antennas and targets.

Phased Array System Toolbox provides matched filtering and stretch processing pulse compression, coherent and noncoherent pulse integration, range and Doppler estimation, and constant false alarm rate (CFAR) detection algorithms. You can use these algorithms to compute and visualize receiver operating characteristic (ROC) curves for various signal-to-noise ratio (SNR) levels or probabilities of false alarm. You can also determine the maximum target range and visualize radar vertical coverage on Blake charts.

**ROC Curves** (Example)

Visualize detection performance by plotting probability of detection (Pd) and probability of false-alarm (Pfa) vs. SNR.

**Constant False Alarm Rate (CFAR) Detectors** (Example)

Compare cell-averaging (CA), greatest, and smallest of cell-averaging (GOCA, SOCA), and order statistic (OS) CFAR detectors.

**Blake Charts** (Example)

Calculate vertical coverage of a radar antenna pattern and plot maximum detection.

**Scan Radar** (Example)

Scan a region with a phased array radar to detect targets.

**Range Estimation Using Stretch Processing** (Example)

Use stretch processing for pulse compression of wideband linear FM waveforms.

**Range-Doppler Estimation** (Example)

Compute and visualize range-Doppler responses of pulsed and FMCW radar systems.

**Radar Equation Calculator** (Example)

Calculate target range, transmit power, or SNR for monostatic and bistatic systems.

Phased Array System Toolbox provides models for polarized point target reflectors defined by the radar cross section (RCS). You can create collections of distributed point reflectors for complex, distributed targets. By specifying position and velocity, you can model target trajectories. The system toolbox also enables you to model the free space propagation of signals including range-dependent time delay, phase shift, Doppler shift, and attenuation, along with clutter and jammer interferences. You can define complex scenarios and analyze behavior of end-to-end systems.

**Simulate End-to-End Radar System**

Generate, transmit, and propagate signals through the environment and process return signals to detect targets.

**GPU Acceleration of Clutter Simulation**

Accelerate clutter simulations using a GPU or code generation (MEX).

**Jammer Modeling** (Example)

Simulate the effect of a barrage jammer on target echo.

**Modeling RF Front End in Radar System Simulation** (Example)

Add fidelity to end-to-end radar system simulation by modeling RF behaviors of transmitters and receivers.

**Target and Platform Motion Modeling** (Example)

Model trajectories of extended bodies such as arrays, targets, and sources of interference.

**Free Space Propagation** (Example)

Model range-dependent time delays, phase shifts, Doppler shifts, and gain effects of a signal propagating through free space.