Phased Array System Toolbox

Key Features

  • Monostatic and multistatic radar system modeling, including point targets, free-space propagation, surface clutter, and barrage jammer
  • Modeling of sensor arrays and subarrays with arbitrary geometries
  • Polarization and platform motion specification for arrays and targets
  • Synthesis and analysis of continuous and pulsed waveforms
  • Broadband and narrowband digital beamforming, including MVDR/Capon, LCMV, time delay, Frost, and subband phase shift
  • Direction of arrival algorithms, including monopulse, beamscan, MVDR, root MUSIC, and ESPRIT
  • Algorithms for TVG, pulse compression, coherent and noncoherent integration, CFAR processing, plotting ROC curves, and estimating range and Doppler
  • Space-time adaptive processing (STAP), including sample matrix inversion (SMI), and angle-Doppler response visualization

The system toolbox includes examples that provide a starting point for implementing user-defined phased array systems.

Phased Array Design and Analysis

Phased Array System Toolbox enables you to model and analyze the behavior of common array geometries and user-defined array geometries. Common array geometries include:

  • Uniform linear array (ULA)
  • Uniform rectangular array (URA)
  • Conformal array

You can define your own array geometry by specifying the number of elements, the element spacing, and each element’s position and orientation in 3D space. The individual element response and radiation pattern can be isotropic, cosine shaded, or specified by your own 3D pattern. Your response and radiation pattern can be either described by an ideal analytic function or defined from measured data. You can apply shading (tapering) across the entire array.

You can also define multiple element patterns in an array to model an inhomogeneous array.

With the system toolbox, you can model common antenna and microphone elements. In a custom antenna or microphone, you can specify wideband, frequency-dependent patterns. You can also specify polarization in polarization-capable antenna elements, such as Dipole or custom antennas.

The system toolbox provides tools to visualize and analyze the radiation pattern of individual elements or of the whole array in aggregate. The visualization can be inspected in rectangular, spherical, and u/v space. With the tools, you can measure or visualize:

  • Array geometry
  • Array gain
  • Array response
  • Delay between elements
  • Steering vector
  • Element response
Three-dimensional beam pattern for a 10 x 10 uniform rectangular array.
Three-dimensional beam pattern for a 10 x 10 uniform rectangular array.

Waveform Design and Analysis

Phased Array System Toolbox supports waveform design and analysis for many common waveforms, including:

  • Constant frequency (PCW)
  • Linear frequency modulation (LFM)
  • Stepped FM
  • Frequency modulation constant waveform (FMCW)
  • Phased coded waveforms

The system toolbox provides a number of configurable parameters for each waveform, such as pulse repetition frequency (PRF), sample rate, pulse duration, and bandwidth. You can also design waveforms with staggered PRFs to address blind-speed problems in moving target indicator (MTI) systems. Waveform envelopes can be either rectangular or Gaussian weighted.

The system toolbox also provides apps and functions to visualize your waveform design, such as the ambiguity function (AF). The AF provides insight into the waveform characteristic in terms of range resolution, Doppler resolution, and the coupling between range and Doppler. It also provides the ideal matched-filter response.

Ambiguity function for a stepped FM waveform.
Ambiguity function for a stepped FM waveform.

Transmitter and Receiver Modeling

Phased Array System Toolbox supports a generalized framework for modeling the physical transmission of a waveform, its propagation through the environment, and its ultimate reception. This framework allows for monostatic and bistatic system models. In addition, you can model array elements as part of a platform whose dynamics (initial position and velocity) are user-defined. You can deploy transmitter elements and receiver elements either on a common platform for monostatic modeling or on separate platforms for bistatic modeling. You can also model stationary system geometries by specifying a zero-velocity vector.

Transmitter Modeling

The system toolbox provides tools to model transmitter behavior by specifying parameters such as:

  • Gain
  • Peak power
  • Loss factor
  • Platform motion

Receiver Modeling

You can also model the reception of a signal at the receiver array to accommodate a variety of situations. You can control the receiver array’s behavior using the following attributes:

  • Narrowband or broadband model
  • Far-field or near-field model
  • Array shading
  • Platform motion

After a signal has been received across the array elements, you can configure the receiver front-end model parameters such as:

  • Gain
  • Loss factor
  • Noise bandwidth
  • Noise figure
  • Reference temperature

You can also configure receiver models for either coherent or noncoherent processing.

Target and Environment Modeling

Target Modeling

You can model targets as point reflectors, which are principally defined by the radar cross section (RCS) or the RCS matrix if polarization is considered. Phased Array System Toolbox target models support the following target types:

  • Nonfluctuating RCS models (Swerling 0 or 5)
  • Fluctuating RCS models (Swerling 1–4)

With the system toolbox you can model more complex, distributed targets by creating a collection of distributed point reflectors. You can also model target motion by specifying the appropriate dynamics, such as initial position and velocity.

Environment Modeling

The system toolbox includes free-space environment models that simulate one-way or two-way propagation delays. It models both time delay and phase shift incurred during propagation. One-way propagation is useful for modeling bistatic systems. Two-way propagation enables you to model monostatic systems. You can model user-specified complex models with MATLAB algorithms. Alternatively, you can integrate third-party and proprietary environment models with the system toolbox’s environment model.

The system toolbox also provides a barrage-jammer model to generate a wideband interference signal with user-specified radiated power. You can use multiple jammers to model complex electromagnetic environments.

The system toolbox offers a constant gamma clutter model you can use to generate surface clutter from land or sea. The surface is divided into small patches during the simulation, and the responses from patches are assembled at the end to form the clutter echo. You can accelerate the clutter simulation using GPUs (requires Parallel Computing Toolbox™).

Spatial Signal Processing

Digital Beamforming

Beamforming is a fundamental spatial signal processing operation of a phased array system. Phased Array System Toolbox supports 1D and 2D beamforming techniques, as well as conventional and adaptive beamforming techniques.

The system toolbox provides the Capon algorithm, a common adaptive beamformer for suppressing interference, and the linearly constrained minimum variance (LCMV) beamformer, for avoiding situations where self-nulling can occur. For broadband signals, the system toolbox offers adaptive algorithms such as the Frost and time delay LCMV beamformers. You can also use subband processing as an alternative to time delays for broadband signals.

The system toolbox supports the following digital beamforming techniques:

  • Narrowband, including conventional (phase shift), MVDR (Capon), and LCMV
  • Broadband, including Frost, time delay, time delay LCMV, and subband phase shift

Direction of Arrival Estimation

Estimating the direction of arrival (DOA) of incident signals is a fundamental spatial signal processing operation. For various array geometries, the system toolbox provides several processing techniques for estimating DOA.

For uniform linear arrays, it provides:

  • Sum and difference monopulse
  • Beamscan
  • MVDR (Capon)
  • High-resolution techniques, including ESPRIT, beamspace ESPRIT, root MUSIC, root WSF 

For uniform rectangular arrays, it provides:

  • Sum and difference monopulse
  • Beamscan
  • MVDR (Capon)

For conformal arrays, it provides:

  • Beamscan
  • MVDR (Capon)

When using high-resolution DOA techniques, you can use either the Akaike information criterion (AIC) or the minimum description length (MDL) criterion to estimate the number of signals.

Plots showing 2D beamscan spatial spectrum and 2D MVDR spatial spectrum.
Plots showing 2D beamscan spatial spectrum (top) and 2D MVDR spatial spectrum (bottom).

Temporal Signal Processing

After a signal has been propagated through the receiver array and receiver front end, you can process the resultant radar cube using a number of temporal signal processing techniques provided by Phased Array System Toolbox, including:

  • Time-varying gain control (TVG)
  • Pulse compression
  • Matched filter with spectrum weighting option
  • Coherent and noncoherent integration
  • Stretch processing
  • Dechirp

At this point in the processing chain, the system toolbox provides algorithms for the detection and estimation of parameters of interest, such as range and Doppler. The following signal processing tools enable you to numerically characterize and visualize the detection performance of your system:

  • Constant false alarm rate (CFAR) processing including cell-averaging (CA), greatest-of cell-averaging (GOCA), smallest-of cell-averaging (SOCA), and order statistic (OS)
  • ROC curve visualization
  • Neyman-Pearson detector threshold
  • Albersheim and Shnidman equations
Receiver operating characteristic (ROC) curves  for various SNR environments.
Receiver operating characteristic (ROC) curves for various SNR environments.

Space-Time Adaptive Processing

For suppressing clutter and jammer interference, Phased Array System Toolbox provides several space-time adaptive processing (STAP) algorithms, including:

  • Displaced phase center array (DPCA)
  • Adaptive DPCA
  • Sample matrix inversion (SMI)

Although the SMI algorithm is computationally intensive and typically not a candidate for real-time implementation, it is useful as an ideal reference, against which you can compare other algorithms. An angle-Doppler response tool provides a useful visualization of the overall performance of the output of the various STAP algorithms.

Target obscured by clutter return at 1000 meters. After SMI STAP processing, the clutter return is suppressed and the target return is detectable.

Target (top, blue vertical line) obscured by clutter return at 1000 meters. After SMI STAP processing (bottom), the clutter return is suppressed and the target return is detectable.

Angle-Doppler response for combined clutter and target returns  and SMI weights  used for clutter suppression that render the target detectable.

Angle-Doppler response for combined clutter and target returns (top) and SMI weights (bottom) used for clutter suppression that render the target detectable.

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