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Phased array systems use the spatial and temporal characteristics of propagating space-time wavefields to extract information about any sources of the wavefields. By processing data collected over a spatiotemporal aperture using an array of sensors, you can significantly improve performance over a single sensor in a number of areas. These areas include, but are not limited to:

Signal detectability

Spatial selectivity

Source identification and localization

The following figure shows a high-level overview of a phased array system.

Phased array systems in diverse applications, such as radar, sonar, medical ultrasonography, medical imaging, and cellular phone communication share many common elements including:

**Source Array**— The source array transmits a waveform through an environment. The waveform often consists of repeating pulses modulated by a carrier frequency. Depending on the application, the wave may be an acoustic (mechanical), or electromagnetic wave. The source array is often electronically or mechanically steered to transmit in preferred directions.**Environment**— The medium in which the waveform travels to and from the target affects a number of system parameters including propagation speed, absorption loss, and wave dispersion.**Target**— The target reflects a portion of the incident waveform energy from the source array. Some percentage of the reflected energy is backscattered in the direction of the receiver array. In some applications, the target is the source of the waveform energy.**Receiver Array**— The receiver array collects energy from the target representing the*signal*along with external and internal sources of*noise*. The receiver implements algorithms to improve the signal-to-noise ratio and extract space-time information from the signal.

At the receiver, phased array systems implement algorithms to extract temporal and spatial information about the source, or sources of energy. The following figure shows a high-level overview of array signal processing algorithms common to a significant number of phased array systems.

Brief descriptions of the three categories are:

**Temporal Processing**— Phased arrays often operate in poor signal-to-noise (SNR) ratios. Employing temporal integration and matched filtering improves the SNR. Knowing the propagation speed of the transmitted waveform and measuring the time it takes for a pulse to travel to and from a target allows phased array systems to estimate range. Performing Fourier analysis on a time series of pulses enables the phased array to extract Doppler information from moving targets.**Spatial Processing**— Combining weighted information across multiple sensor elements with a known geometry enables phased array systems to spatially filter incoming waveforms. Phased arrays can also estimate the direction of arrival and the number of source waveforms incident on the array.**Space-Time Processing**— Simultaneously analyzing both spatial and temporal information enables phased array systems to produce joint angle-Doppler measurements of incident waveforms. Space-time processing enables phased array systems to distinguish moving targets from stationary targets when the phased array is in motion.

The following figure presents an overview of a radar phased array system. The figure expands on the high-level overview shown in Phased Array System Overview.

To exploit the advantages of array processing, you must first understand how to model and optimize the performance of each component and operation in a phased array system. This software provides models for all the components of the phased array system illustrated in the preceding figure from signal synthesis to signal analysis.

The software supports models in which the transmitter and receiver are collocated or spatially separated. The software also supports models in which both the targets and phased array are in motion.

Phased Array
System Toolbox™ software supports the design of
rectangular, linear frequency-modulated, and linear stepped-frequency
pulsed waveforms. To create such waveforms, you use `phased.RectangularWaveform`

, `phased.LinearFMWaveform`

,
and `phased.SteppedFMWaveform`

.

The software enables you to simulate the physical components of a phased array system, including:

**Transmitter**— You can specify the transmitter peak power, gain, and loss factor. See`phased.Transmitter`

for details.**Antenna elements**— You can create antenna elements with isotropic response patterns or antenna elements with user-specified response patterns. These response patterns can encompass the entire range of azimuth ([-180,180] degrees) and elevation ([-90,90] degrees) angles. See`phased.IsotropicAntennaElement`

,`phased.CosineAntennaElement`

, and`phased.CustomAntennaElement`

for details.**Microphone elements**— For acoustic applications, you can model an omnidirectional or custom microphone with`phased.OmnidirectionalMicrophoneElement`

or`phased.CustomMicrophoneElement`

.**Phased arrays**— There are System objects for three phased array geometries:Uniform linear array (ULA) —

`phased.ULA`

enables you to model a uniform linear array consisting of sensor elements with isotropic or custom radiation patterns. You can specify the number of elements and element spacing.Uniform rectangular array —

`phased.URA`

enables you to model a uniform rectangular array of sensor elements with isotropic or custom radiation patterns. You can specify the number of elements, element spacing along two orthogonal axes, and lattice geometry.Conformal array —

`phased.ConformalArray`

enables you to model a conformal array of sensor elements with isotropic or custom radiation patterns. To do so, specify the antenna element positions and normal directions.

**Radiator**— You can model waveform radiation through an antenna element, microphone, or array with the`phased.Radiator`

object.**Environment**— You can model the propagation of an electromagnetic (EM) wave in free space with`phased.FreeSpace`

. You can simulate one-way or two-way propagation of a narrowband EM signal by applying range-dependent attenuation and time delays, or phase shifts.**Target**— You can simulate a target with a specified radar cross section (RCS) using`phased.RadarTarget`

.`phased.RadarTarget`

supports both nonfluctuating and fluctuating (random) models of the RCS. The toolbox supports a family of random models based on the chi-square distribution known as*Swerling target models*.**Interference**— You can simulate wideband interference with a user-specified radiated power, using`phased.BarrageJammer`

.**Clutter**— You can simulate surface clutter using`phased.ConstantGammaClutter`

.**Signal collection**— You can simulate far-field or near-field narrowband and wideband signal reception from specified directions using`phased.Collector`

and`phased.WidebandCollector`

.**Receiver**—`phased.ReceiverPreamp`

enables you to simulate the gain, loss factor, and internal noise characteristics of your receiver.

For the processing of received data, Phased Array System Toolbox software supports a wide-range of array signal processing algorithms. The following figure presents a more detailed view of the general concepts discussed in Phased Array System Overview.

The preceding figure only presents an overview of the array signal processing operations supported by the software rather than predetermined orders of operation. For example, direction of arrival (DOA) estimation, beamforming, and space-time adaptive processing (STAP) often follow operations that improve the signal-to-noise ratio such as matched filtering. You can implement the supported algorithms in the manner best-suited to your application.

**Matched Filtering**— You can perform matched filtering on your data with`phased.MatchedFilter`

. See Matched Filtering for examples.**Time-varying gain**— You can equalize the power level of the incident waveform across samples from different ranges using`phased.TimeVaryingGain`

. This object compensates for signal power loss due to range.**Beamforming and direction-of-arrival (DOA) estimation**— The Phased Array System Toolbox provides a number of algorithms for beamforming and direction of arrival estimation.**Detection**— A number of utility functions implement and evaluate Neyman-Pearson detectors using both coherent and noncoherent pulse integration.The toolbox also provides routines for evaluating detector performance through the construction of receiver operating characteristic curves.

To model fluctuating noise characteristics,

`phased.CFARDetector`

object adaptively estimates the noise characteristics from the data to maintain a constant false-alarm rate.**Pulse Doppler**— The Phased Array System Toolbox has utility functions for estimating Doppler shift based on speed (`speed2dop`

) and to estimate speed based on the Doppler shift (`dop2speed`

. You can implement pulse-Doppler processing by using the spectrum estimation algorithms in the Signal Processing Toolbox™ product on the slow-time data. See Radar Data Cube for an explanation of the slow-time data.See Doppler Shift and Pulse-Doppler Processing for examples of Doppler processing.

To calculate the joint angle-Doppler response of the input data, use

`phased.AngleDopplerResponse`

.Example workflows for computing the angle-Doppler response can be found in Angle-Doppler Response.

**Space-time adaptive processing**— You can implement displaced phase center antenna techniques with`phased.DPCACanceller`

and`phased.ADPCACanceller`

.`phased.STAPSMIBeamformer`

implements an adaptive beamformer by calculating the beamformer weights using the estimated space-time interference covariance matrix.

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