phased.ArrayGain

Sensor array gain

Description

The ArrayGain object calculates the array gain for a sensor array. The array gain is defined as the signal to noise ratio (SNR) improvement between the array output and the individual channel input, assuming the noise is spatially white. It is related to the array response but is not the same.

To compute the SNR gain of the antenna for specified directions:

1. Define and set up your array gain calculator. See Construction.

2. Call step to estimate the gain according to the properties of phased.ArrayGain. The behavior of step is specific to each object in the toolbox.

Note

Starting in R2016b, instead of using the step method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

H = phased.ArrayGain creates an array gain System object, H. This object calculates the array gain of a 2-element uniform linear array for specified directions.

H = phased.ArrayGain(Name,Value) creates and array-gain object, H, with the specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

SensorArray	Sensor array Sensor array specified as an array System object belonging to the phased package. A sensor array can contain subarrays. Default: phased.ULA with default property values
PropagationSpeed	Signal propagation speed Specify the propagation speed of the signal, in meters per second, as a positive scalar. Default: Speed of light
WeightsInputPort	Add input to specify weights To specify weights, set this property to true and use the corresponding input argument when you invoke step. If you do not want to specify weights, set this property to false. Default: false

Methods

step	Calculate array gain of sensor array

Common to All System Objects
release	Allow System object property value changes

Examples

Array Gain of 4-Element ULA

Calculate the array gain for a 4-element uniform linear array (ULA) in the direction 30° azimuth and 20° elevation. The array operating frequency is 300 MHz.

fc = 300e6;
array = phased.ULA(4);
gain = phased.ArrayGain('SensorArray',array);
g = gain(fc,[30;20])

g = 
-17.1783

More About

Array Gain

The array gain is defined as the signal to noise ratio (SNR) improvement between the array output and the individual channel input, assuming the noise is spatially white. You can express the array gain as follows:

$$\frac{SN{R}_{\text{out}}}{SN{R}_{\text{in}}}=\frac{\left(\frac{w^{H}vs{v}^{H}w}{w^{H}Nw}\right)}{\left(\frac{s}{N}\right)}=\frac{w^{H}v{v}^{H}w}{w^{H}w}$$

In this equation:

• w is the vector of weights applied on the sensor array. When you use phased.ArrayGain, you can optionally specify weights by setting the WeightsInputPort property to true and specifying the W argument in the step method syntax.

• v is the steering vector representing the array response toward a given direction. When you call the step method, the ANG argument specifies the direction.

• s is the input signal power.

• N is the noise power.

• H denotes the complex conjugate transpose.

For example, if a rectangular taper is used in the array, the array gain is the square of the array response normalized by the number of elements in the array.

References

[1] Guerci, J. R. Space-Time Adaptive Processing for Radar. Boston: Artech House, 2003.

[2] Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Does not support arrays containing polarized antenna elements, that is, the phased.ShortDipoleAntennaElement or phased.CrossedDipoleAntennaElement antennas.

• See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2011a