MATLAB Examples

Compute and plot the ambiguity function magnitudes for a rectangular and linear FM pulse waveform. The zero Doppler cut (magnitudes of the autocorrelation sequences) illustrates pulse

To create a conformal array with default properties, use this command:

Plot a linear FM (LFM) pulse waveform. The LFM waveform has a duration of 100 microseconds, a bandwidth of 200 kHz, and a PRF of 4 kHz. Use the default values for the other properties. Compute the

Compute the required peak transmit power using the radar equation. You implement a noncoherent detector with a monostatic radar operating at 5 GHz. Based on the noncoherent integration of

Construct a 60-element uniform circular array. In constructing a uniform circular array, you can use either the phased.UCA or the phased.ConformalArray System objects. The conformal

Apply the basic toolbox workflow to the following scenario: Assume you have a single isotropic antenna operating at 4 GHz. Assume the antenna is located at the origin of your global

Create a linear FM pulse waveform using phased.LinearFMWaveform . The example illustrates how to specify property settings.

Plot the ambiguity function of a linear FM pulse waveform.

Construct and visualize a custom-geometry array containing antenna elements with a custom radiation pattern. The radiation pattern of each element is constant over each azimuth angle and

Use the nonparametric beamscan technique to estimate the direction of arrival (DOA) of signals. The beamscan algorithm estimates the DOAs by scanning the array beam over a region of

Construct and visualize a four-element ULA with custom cardioid microphone elements. Specify the polar pattern frequencies as 500 and 1000 Hz.

Assume that the minimum detectable SNR at the receiver of a monostatic radar operating at 1 GHz is 13 dB. Use the radar equation to determine the maximum detectable range for a target with a

Estimate the output SNR for a target with an RCS of 1m^{2} . The radar is bistatic. The target is located 50 km from the transmitter and 75 km from the receiver. The radar operating frequency is 10

Simulate clutter on a graphical processing unit (GPU) or through code generation (MEX) instead of the MATLAB interpreter. The example applies the sample matrix inversion (SMI) algorithm,

Phased Array System Toolbox can be used to model an end-to-end radar system - generate a transmitted waveform, simulate the target return, and then process the received signal to detect the

Simulates a monostatic radar system. It uses dataflow domain in Simulink® to automatically partition the data-driven portions of the radar system into multiple threads and thereby

How an audio beamforming system simulation model in Simulink® can have improved performance using dataflow domain. It uses the dataflow domain in Simulink® to automatically partition the

How hybrid beamforming is employed at the transmit end of a massive MIMO communications system, using techniques for both multi-user and single-user systems. The example employs full

The design of a moving target indication (MTI) radar to mitigate the clutter and identify moving targets. For a radar system, clutter refers to the received echoes from environmental

Simulates a phased array radar that periodically scans a predefined surveillance region. A 900-element rectangular array is used in this monostatic radar. Steps are introduced to derive

Model frequency agility in radar, communications and EW systems to counter the effects of interference.

How phased arrays are used in a MIMO-OFDM communication system employing beamforming. The example models the radiating elements that comprise a transmitter and the front-end receiver

Simulate an active monostatic sonar scenario with two targets. The sonar system consists of an isotropic projector array and a single hydrophone element. The projector array is spherical

Design a monostatic pulse radar to estimate the target range. A monostatic radar has the transmitter collocated with the receiver. The transmitter generates a pulse which hits the target

Simulate a passive sonar system. A stationary underwater acoustic beacon is detected and localized by a towed passive array in a shallow-water channel. The acoustic beacon transmits a 10

Simulate a polarimetric bistatic radar system to estimate the range and speed of targets. Transmitter, receiver and target kinematics are taken into account. For more information

Model a radar's hardware, signal processing, and propagation environment for a driving scenario. First you develop a model of the radar transmit and receive hardware, signal processing,

Compares triangle sweep FMCW and MFSK waveforms used for simultaneous range and speed estimation for multiple targets. The MFSK waveform is specifically designed for automotive radar

Modern aircraft often carry a radar warning receiver (RWR) with them. The RWR detects the radar emission and warns the pilot when the radar signal shines on the aircraft. An RWR can not only

Use scenario viewer to visualize the radar system theater.

How waveform type affects radar detection performance. The example considers the situation where a new performance goal is set for an existing radar system design . Since the old design can

Model a point-to-point MIMO-OFDM system with beamforming. The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM)

Model an automotive adaptive cruise control system using the frequency modulated continuous wave (FMCW) technique. This example performs range and Doppler estimation of a moving

The goal of a wireless communication system is to serve as many users with the highest possible data rate given constraints such as radiation power limit and operating budget. To improve the

Introduces how forming a virtual array in MIMO radars can help increase angular resolution. It shows how to simulate a coherent MIMO radar signal processing chain using Phased Array System

Model a 77 GHz 2x4 antenna array for Frequency-Modulated Continuous-Wave (FMCW) radar applications. The presence of antennas and antenna arrays in and around vehicles has become a

Simulate beamforming an IEEE® 802.11ad™ DMG waveform with a phased array using WLAN Toolbox™ and Phased Array System Toolbox™.

Introduces the basic concept of hybrid beamforming and shows how to simulate such a system.

Simulates a multifunction phased array radar system. A multifunction radar can perform jobs that usually require multiple traditional radars. For example, scanning radars are

Implements an adaptive DPCA pulse canceller for clutter and interference rejection. The scenario is identical to the one in DPCA Pulse Canceller to Reject Clutter except that a stationary

Implements a DPCA pulse canceller for clutter rejection. Assume you have an airborne radar platform modeled by a six-element ULA operating at 4 GHz. The array elements are spaced at one-half

Create and beamform a 10-element ULA. Assume the carrier frequency is 1 GHz. Set the array element spacing to be one-half the carrier wavelength.

Display the angle-Doppler response of a stationary array to a stationary target. The array is a six-element uniform linear array (ULA) located at the global origin (0,0,0) . The target is

This scenario is identical to the one presented in Adaptive DPCA Pulse Canceller To Reject Clutter and Interference . You can run the code for both examples to compare the ADPCA pulse

Estimate angles of arrival from two separate signal sources when both angles fall within the main lobe of the array response a uniform linear array (ULA). In this case, a beamscan DOA

Illustrates the nonzero Doppler shift exhibited by a stationary target in the presence of array motion. In general, this nonzero shift complicates the detection of slow-moving targets

Perform wideband conventional time-delay beamforming with a microphone array of omnidirectional elements. Create an acoustic (pressure wave) chirp signal. The chirp signal has a

Plot the response of an acoustic microphone element and an array of microphone elements to validate the performance of a beamformer. The array must maintain an acceptable array pattern

Use the phased.SumDifferenceMonopulseTracker System object� to track a moving target. The phased.SumDifferenceMonopulseTracker tracker solves for the direction of a target from

Illustrates how to apply digital beamforming to a narrowband signal received by an antenna array. Three beamforming algorithms are illustrated: the phase shift beamformer (PhaseShift),

Determine the position of the source of a wideband signal using generalized cross-correlation (GCC) and triangulation. For simplicity, this example is confined to a two-dimensional

Use Simulink® to suppress clutter and jammer interference from the received pulses of a monostatic radar. It illustrates how to model clutter and jammer interference as well as how to use the

Convert an azimuth angle of and an elevation angle of to a broadside angle.

Illustrates microphone array beamforming to extract desired speech signals in an interference-dominant, noisy environment. Such operations are useful to enhance speech signal quality

Beamform a plane wave arriving at a 10 element ULA of isotropic antenna elements. The operating frequency of the array is 100 MHz.

Illustrates using beamscan, MVDR, and MUSIC for direction of arrival (DOA) estimation. Beamscan is a technique that forms a conventional beam and scans it over directions of interest to

Apply conventional and adaptive beamforming in Simulink® to a narrowband signal received by an antenna array. The signal model includes noise and interference. This example is based on the

Start with a data set consisting of 200 samples per pulse for ten pulses collected at 6 sensor elements. Your data is organized as a 6-by-10-by-200 Matlab™ array. Reorganize the data into a

Gives a brief introduction to space-time adaptive processing (STAP) techniques and illustrates how to use Phased Array System Toolbox™ to apply STAP algorithms to the received pulses.

Illustrates several high-resolution direction of arrival (DOA) estimation techniques. It introduces variants of the MUSIC, root-MUSIC, ESPRIT and root-WSF algorithms and discusses

Beamform signals received by an array of microphones to extract a desired speech signal in a noisy environment. This Simulink® example is based on the MATLAB® example Acoustic Beamforming

Use beamscan and minimum variance distortionless response (MVDR) techniques for direction of arrival (DOA) estimation in Simulink®. It is based on the MATLAB® example Direction of

Generate a receiver operating characteristic (ROC) curve of a radar system using a Monte-Carlo simulation. The receiver operating characteristic determines how well the system can

Visualize the speed and range of a target in a pulsed radar system that uses a rectangular waveform.

In the Neyman-Pearson framework, the probability of detection is maximized subject to the constraint that the false-alarm probability does not exceed a specified level. The false-alarm

Compute empirically the probability of false alarm for a real-valued signal in white Gaussian noise.

Create a CFAR detector and test its ability to adapt to the statistics of input data. The test uses noise-only trials. By using the default square-law detector, you can determine how close the

Compare the probability of detection resulting from two CFAR algorithms. In this scenario, the order statistic algorithm detects a target that the cell-averaging algorithm does not.

Empirically verify the probability of false alarm in a system that integrates two real-valued pulses. In this scenario, each integrated sample is the sum of two samples, one from each pulse.

Empirically verify the probability of false alarm in a system that uses coherent detection of complex-valued signals. Coherent detection means that the system utilizes information about

To illustrate coherent-on-receive, construct a rectangular pulse waveform with five pulses. The waveform pulse repetition frequency (PRF) is 10 kHz and the pulse width is 50 μs. The pulse

Receiver Operating Characteristic (ROC) curves present graphical summaries of a detector's performance. You can generate ROC curves using the rocpfa and rocsnr functions.

The radarEquationCalculator is a Matlab™ App that lets you determine key radar characteristics such as detection range, required peak transmit power, and SNR. The App works for monostatic

A monostatic pulse radar detecting the radial velocity of moving targets at specific ranges. The speed is derived from the Doppler shift caused by the moving targets. We first identify the

Introduces constant false alarm rate (CFAR) detection and shows how to use CFARDetector and CFARDetector2D in the Phased Array System Toolbox™ to perform cell averaging CFAR detection.

Detect a signal in complex, white Gaussian noise using multiple received signal samples. A matched filter is used to take advantage of the processing gain.

Assess the performance of both coherent and noncoherent systems using receiver operating characteristic (ROC) curves. It assumes the detector operates in an additive complex white

Discusses the detection of a deterministic signal in complex, white, Gaussian noise. This situation is frequently encountered in radar, sonar and communication applications.

Estimate the range of a target using stretch processing in a radar system that uses a linear FM pulse waveform.

Introduces the basic concept of micro-Doppler effect present in the radar return of a target due to the target's rotation. Such micro-Doppler signature can be used in the processing stage to

Create a custom cardioid microphone, and plot the power response pattern at 500 and 800 Hz.

Construct an omnidirectional microphone element having a response within the human audible frequency range of 20 to 20,000 Hz. Baffle the microphone response for azimuth angles outside of

Amplify and transmit a linear FM pulse.

Design a backbaffled isotropic antenna element and obtain its response. First, construct an X-band isotropic antenna element that operates from 8 to 12 GHz setting the Backbaffle property

Models a tracking radar based on a 31-by-31 (961-element) uniform rectangular array (URA). The radar is designed to follow a moving target. At each time instant, the radar points in the known

Set up a rectangular array containing linear subarrays. The example also finds the phase centers of the subarrays.

Plot the grating lobe diagram for an 11-by-9-element uniform rectangular array having element spacing equal to one-half wavelength.

Construct a narrowband collector that models a plane wave impinging on a two-element uniform linear array. The array has an element spacing of 0.5 m (default for a ULA). The operating

Construct an antenna with a cosine-squared response in both azimuth and elevation. The operating frequency range of the antenna is 1 to 10 GHz. Plot the 3-D antenna response at 5 GHz.

Plots the right-handed and left-handed circular polarization components of fields generated by a crossed-dipole antenna at 1.5 GHz. You can see how the circular polarization changes from

Compute the steering vector for a 4-element ULA at an operating frequency of 1 GHz. Assume that the waveform is incident on the array from 45° azimuth and 10° elevation.

Arrange copies of a linear subarray in a triangular layout.

When you create antenna arrays such as a uniform linear array (ULA), you can use antennas that are built into Phased Array System Toolbox™. Alternatively, you can use Antenna Toolbox™

Create a uniform rectangular array (URA) and obtain information about the element positions, the array response, and inter-element time delays. Then, simulate the reception of two sine

Construct a backbaffled isotropic antenna element with a uniform frequency response over a range of azimuth angles from [-180,180] degrees and elevation angles from [-90,90] degrees. The

Simulate the reception of a 100-Hz sine wave modulated by a carrier frequency of 1 GHz at a 4-element ULA. Assume the angle of arrival of the signal is (-90;0) .

The Sensor property of a phased.Collector System object™ can specify a single antenna element. In this example, create a custom antenna element using the phased.CustomAntennaElement

Create and view a ULA having four isotropic antenna elements separated by 0.5 meters

Construct a four-element ULA with elements spaced at 0.25 m. Obtain the array magnitude response (absolute value of the complex-valued array response) for azimuth angles (-180:180) at 1

Computes the delay between elements of a 4-element ULA using the phased.ElementDelay System object™. Assume that the incident waveform satisfies the far-field condition. The delays are

Illustrates adding phase noise to a rectangular pulse waveform having five pulses. A random phase is added to each sample of the waveform. Compute the phase of the output waveform and compare

Obtain the responses of the elements of a 4-element ULA array at 1 GHz.

Arrange copies of a linear subarray to form a rectangular array.

The example illustrates the use of Swerling target models to describe the fluctuations in radar cross-section. The scenario consists of a rotating monostatic radar and a target having a

How several different coordinate systems come into play when modeling a typical radar scenario. The scenario considered here is a bistatic radar system consisting of a transmitting radar

Propagate a signal in free space from a stationary radar to a moving target.

Construct a linear FM pulse waveform of 50 ms duration with a bandwidth of 100 kHz. Model the range-dependent time delay and amplitude loss incurred during two-way propagation. The pulse

Demonstrates how to simulate the effect of a barrage jammer on a target echo. First, create the required objects. You need an array, a transmitter, a radiator, a target, a jammer, a collector,

Assume a transmitter is located at (1000,250,10) in the global coordinate system. Assume a target is located at (3000,750,20) . The transmitter operates at 1 GHz. Determine the free space

Examines the statistical properties of the barrage jammer output and how they relate to the effective radiated power (ERP) . Create a barrage jammer using an effective radiated power of 5000

Assume a target approaches a stationary receiver with a radial speed of 23.0 m/s. The target reflects a narrowband electromagnetic wave with a frequency of 1 GHz. Estimate the one-way

Create a radar target with a nonfluctuating RCS of 1 square meter and an operating frequency of 1 GHz. Specify a wave propagation speed equal to the speed of light.

The TwoWayPropagation property of the phased.FreeSpace System object™ lets you simulate either one- or two-way propagation. The following example demonstrates how to use this property

Creates and transmits a linear FM waveform with a 1 GHz carrier frequency. The waveform is transmitted and collected by an isotropic antenna with a back-baffled response. The waveform

Illustrate pulse-Doppler processing using Phased Array System Toolbox™. Assume that you have a stationary monostatic radar located at the global origin, (0,0,0) . The radar consists of a

Assume you observe a Doppler shift of 400.0 Hz for a waveform with a frequency of 9 GHz. Determine the radial velocity of the target.

Model several RF propagation effects. These include free space path loss, atmospheric attenuation due to rain, fog and gas, and multipath propagation due to bounces on the ground. This

Most platforms in phased array applications do not move with constant velocity. If the time interval described by the number of time steps is small with respect to the platform speed, you can

Classify radar returns using feature extraction followed by a support vector machine (SVM) classifier.

Model radar targets with increasing levels of fidelity. The example introduces the concept of radar cross sections (RCS) for simple point targets and extends it to more complicated cases of

Uses the phased.Platform System object™ to model the change in range between a stationary radar and a moving target. The radar is located at (1000,1000,0) and has a velocity of (0,0,0) . The

Beginning with a simple example, model the motion of a platform over ten time steps. To determine the time step, assume that you have a pulse transmitter with a pulse repetition frequency

Determine the position of a target in local spherical coordinates centered at the phase center of a URA array. The center of the URA defines the origin of the local coordinate system and has the

Determine the position of a target in rectangular coordinates in the global coordinate system. First, specify the local spherical coordinates of a target with respect to a URA. The center of

The following examples show how to use the az2broadside and broadside2az functions.

Simulate a polarimetric Doppler radar return that meets the requirements of weather observations. Radar plays a critical role in weather observation, detection of hazards,

The radarWaveformAnalyzer is a Matlab™ App that lets you explore important properties of a signal such as its waveform, spectrum, and ambiguity function.

Create rectangular pulse waveform signals having different durations. The example plots two pulses of each waveform.

Create and plot a 5-step stepped FM pulse waveform using the phased.SteppedFM System object™. Set the pulse width (duration) to 50 µs, the pulse repetition frequency (PRF) to 10 kHz, and the

Create a rectangular pulse waveform variable using phased.RectangularWaveform . The example also plots the pulse and finds the bandwidth of the pulse.

Instead of the rectangular waveform used in the End-to-End Radar System example, you can use a phase-coded waveform instead of a rectangular waveform. To do so, replace the

Model a linear FM pulse waveform with two PRFs of 1 and 2 kHz. Set the sweep bandwidth to 200 kHz and the duration of 100 μs. The sample rate is 1 MHz. Output 5 pulses.

Improve the SNR by performing matched filtering.

Compares the results of matched filtering with and without spectrum weighting. Spectrum weighting is often used with linear FM waveforms to reduce the sidelobes in the time domain.

Illustrates how to use the ambiguity function to analyze waveforms. It compares the range and Doppler capability of several basic waveforms, e.g., the rectangular waveform and the linear

Model antenna and target motion, and monitor array sidelobes while beamforming.

Model a ground-based monostatic pulse radar to estimate the range and speed of fluctuating targets.

The example presents a scenario consisting of a rotating monostatic radar and a target with a radar cross-section described by a Swerling 1 model. In this example, the radar and target are

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 3 model. In this example, the radar and target are stationary.

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 4 model. In this example, the radar and target are stationary.

Model an end-to-end monostatic radar using Simulink®. A monostatic radar consists of a transmitter colocated with a receiver. The transmitter generates a pulse which hits the target and

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