System object: phased.SumDifferenceMonopulseTracker
Package: phased

Perform monopulse tracking using ULA




ESTANG = step(H,X,STANG) estimates the incoming direction ESTANG of the input signal, X, based on an initial guess of the direction.

    Note:   The object performs an initialization the first time the step method 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


Tracker object of type phased.SumDifferenceMonopulseTracker.


Input signal, specified as a row vector whose number of columns corresponds to number of channels.


Initial guess of the direction, specified as a scalar that represents the broadside angle in degrees. A typical initial guess is the current steering angle. The value of STANG is between –90 and 90. The angle is defined in the array's local coordinate system. For details regarding the local coordinate system of the ULA, type phased.ULA.coordinateSystemInfo.

Output Arguments


Estimate of incoming direction, returned as a scalar that represents the broadside angle in degrees. The value is between –90 and 90. The angle is defined in the array's local coordinate system.


Determine the direction of a target at around 60 degrees broadside angle of a ULA.

ha = phased.ULA('NumElements',4);
hstv = phased.SteeringVector('SensorArray',ha);
hmp = phased.SumDifferenceMonopulseTracker('SensorArray',ha);
x = step(hstv,hmp.OperatingFrequency,60.1).';
est_dir = step(hmp,x,60);


The sum-and-difference monopulse algorithm is used to the estimate the arrival direction of a narrowband signal impinging upon a uniform linear array (ULA). First, compute the conventional response of an array steered to an arrival direction φ0. For a ULA, the arrival direction is specified by the broadside angle. To specify that the maximum response axis (MRA) point towards the φ0 direction, set the weights to be


where d is the element spacing and k = 2π/λ is the wavenumber. An incoming plane wave, coming from any arbitrary direction φ, is represented by


The conventional response of the this array to any incoming plane wave is given by wsHv(φ) and is shown in the polar plot below as the Sum Pattern. The array is designed to steer towards φ0 = 30°.

The second pattern, called the Difference Pattern, is obtained by using phased-reversed weights. The weights are determined by phase-reversing the latter half of the conventional steering vector. For an array with an even number of elements, the phase-reversed weights are


(For an array with an odd number of elements, the middle weight is set to zero). The multiplicative factor –i is used for convenience. The response of the difference array to the incoming vector is


and is show in the polar plot below

The monopulse response curve is obtained by dividing the difference pattern by the sum pattern and taking the real part.


To use the monopulse response curve to obtain the arrival angle of a narrowband signal, x, compute


and invert the response curve, φ = R-1(z), to obtain φ.

The response curve is not single valued and can be inverted only when arrival angles lie within the mainlobe. The figure below shows the center portion of the monopulse response curve in the mainlobe for a 4-element ULA array.

There are two desirable properties of the monopulse response curve. The first is that it have a steep slope. A steep slope insures robustness against noise. The second property is that the mainlobe be as wide as possible. A steep slope is ensure by a larger array but leads to a smaller mainlobe. You will need to trade off one property with the other.

For further details, see [1].


[1] Seliktar, Y. Space-Time Adaptive Monopulse Processing. Ph.D. Thesis. Georgia Institute of Technology, Atlanta, 1998.

[2] Rhodes, D. Introduction to Monopulse. Dedham, MA: Artech House, 1980.

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