G = step(H,FREQ,ANG)
G = step(H,FREQ,ANG,WEIGHTS)
G = step(H,FREQ,ANG,STEERANGLE)
G = step(H,FREQ,ANG,WEIGHTS,STEERANGLE)
returns
the array gain G
= step(H
,FREQ
,ANG
)G
of
the array for the operating frequencies specified in FREQ
and
directions specified in ANG
.
applies
weights G
= step(H
,FREQ
,ANG
,WEIGHTS
)WEIGHTS
on the sensor array. This syntax
is available when you set the WeightsInputPort
property
to true
.
uses G
= step(H
,FREQ
,ANG
,STEERANGLE
)STEERANGLE
as
the subarray steering angle. This syntax is available when you configure H
so
that H.Sensor
is an array that contains subarrays,
and H.Sensor.SubarraySteering
is either 'Phase'
or 'Time'
.
combines
all input arguments. This syntax is available when you configure G
= step(H
,FREQ
,ANG
,WEIGHTS
,STEERANGLE
)H
so
that H.WeightsInputPort
is true
, H.Sensor
is
an array that contains subarrays, and H.Sensor.SubarraySteering
is
either 'Phase'
or 'Time'
.
Note:
The object performs an initialization the first time the 

Array gain object. 

Operating frequencies of array in hertz. 

Directions in degrees. If If 

Weights on the sensor array. If If 

Subarray steering angle in degrees. If If 

Gain of sensor array, in decibels. 
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.
Construct a uniform linear array with six elements. The array operates at 1 GHz and the array elements are spaced at one half the operating frequency wavelength. Find the array gain in decibels for the direction 45 degrees azimuth and 10 degrees elevation.
% operating frequency 1 GHz fc = 1e9; % 1 GHz wavelength lambda = physconst('LightSpeed')/fc; % construct the ULA hULA = phased.ULA('NumElements',6,'ElementSpacing',lambda/2); % construct the array gain object with the ULA as the sensor array hgain = phased.ArrayGain('SensorArray',hULA); % use step method to determine array gain at the specified % operating frequency and angle arraygain = step(hgain,fc,[45;10]); % array gain is approximately 17.93 dB