step

System object: phased.ArrayGain
Namespace: phased

Calculate array gain of sensor array

Syntax

G = step(H,FREQ,ANG)
G = step(H,FREQ,ANG,WEIGHTS)
G = step(H,FREQ,ANG,STEERANGLE)
G = step(H,FREQ,ANG,WEIGHTS,STEERANGLE)
G = step(H,FREQ,ANG,WS)


Description

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.

G = step(H,FREQ,ANG) returns the array gain G of the array for the operating frequencies specified in FREQ and directions specified in ANG.

G = step(H,FREQ,ANG,WEIGHTS) applies weights WEIGHTS on the sensor array. This syntax is available when you set the WeightsInputPort property to true.

G = step(H,FREQ,ANG,STEERANGLE) uses 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'.

G = step(H,FREQ,ANG,WEIGHTS,STEERANGLE) combines all input arguments. This syntax is available when you configure H so that H.WeightsInputPort is true, H.Sensor is an array that contains subarrays, and H.Sensor.SubarraySteering is either 'Phase' or 'Time'.

G = step(H,FREQ,ANG,WS) uses WS as weights applied to each element within each subarray. To use this syntax, set the SensorArray property to an array that supports subarrays and set the SubarraySteering property of the array to 'Custom'.

Note

The object performs an initialization the first time the object is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first call the release method to unlock the object.

Input Arguments

H	Array gain object.
FREQ	Operating frequencies of array in hertz. FREQ is a row vector of length L. Typical values are within the range specified by a property of the sensor element. The element is H.SensorArray.Element, H.SensorArray.Array.Element, or H.SensorArray.Subarray.Element, depending on the type of array. The frequency range property is named FrequencyRange or FrequencyVector, depending on the type of element in the array. The element has zero response at frequencies outside that range.
ANG	Directions in degrees. ANG can be either a 2-by-M matrix or a row vector of length M. If ANG is a 2-by-M matrix, each column of the matrix specifies the direction in the form [azimuth; elevation]. The azimuth angle must be between –180 and 180 degrees, inclusive. The elevation angle must be between –90 and 90 degrees, inclusive. If ANG is a row vector of length M, each element specifies a direction’s azimuth angle. In this case, the corresponding elevation angle is assumed to be 0.
WEIGHTS	Weights on the sensor array. WEIGHTS can be either an N-by-L matrix or a column vector of length N. N is the number of subarrays if H.SensorArray contains subarrays, or the number of elements otherwise. L is the number of frequencies specified in FREQ. If WEIGHTS is a matrix, each column of the matrix represents the weights at the corresponding frequency in FREQ. If WEIGHTS is a vector, the weights apply at all frequencies in FREQ.
STEERANGLE	Subarray steering angle in degrees. STEERANGLE can be a length-2 column vector or a scalar. If STEERANGLE is a length-2 vector, it has the form [azimuth; elevation]. The azimuth angle must be between –180 and 180 degrees, and the elevation angle must be between –90 and 90 degrees. If STEERANGLE is a scalar, it represents the azimuth angle. In this case, the elevation angle is assumed to be 0.
WS	Subarray element weights Subarray element weights, specified as complex-valued NSE-by-N matrix or 1-by-N cell array where N is the number of subarrays. These weights are applied to the individual elements within a subarray. Subarray element weights Sensor Array Subarray weights phased.ReplicatedSubarray All subarrays have the same dimensions and sizes. Then, the subarray weights form an NSE-by-N matrix. NSE is the number of elements in each subarray and N is the number of subarrays. Each column of WS specifies the weights for the corresponding subarray. phased.PartitionedArray Subarrays may not have the same dimensions and sizes. In this case, you can specify subarray weights as an NSE-by-N matrix, where NSE is now the number of elements in the largest subarray. The first Q entries in each column are the element weights for the subarray where Q is the number of elements in the subarray. a 1-by-N cell array. Each cell contains a column vector of weights for the corresponding subarray. The column vectors have lengths equal to the number of elements in the corresponding subarray. Dependencies To enable this argument, set the SensorArray property to an array that contains subarrays and set the SubarraySteering property of the array to 'Custom'.

Output Arguments

G	Gain of sensor array, in decibels. G is an M-by-L matrix. G contains the gain at the M angles specified in ANG and the L frequencies specified in FREQ.

Examples

Array Gain of 6-Element ULA

Construct a uniform linear array (ULA) having six elements and operating at 1 GHz. The array elements are spaced at one-half the operating wavelength. Find the array gain in dB in the direction 45° azimuth and 10° elevation.

Create the phased.ArrayGain System object™.

fc = 1e9;
lambda = physconst('LightSpeed')/fc;
array = phased.ULA('NumElements',6,'ElementSpacing',lambda/2);
gain = phased.ArrayGain('SensorArray',array);

Determine array gain at the specified operating frequency and angle.

arraygain = gain(fc,[45;10])

arraygain = 
-17.9275

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.