lcmvweights

Narrowband linearly constrained minimum variance (LCMV) beamformer weights

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Syntax

wt = lcmvweights(constr,resp,cov)

Description

wt = lcmvweights(constr,resp,cov) returns narrowband linearly-constrained minimum variance (LCMV) beamformer weights, wt, for a phased array. When applied to the elements of the array, these weights steer the response of the array toward a specific arrival direction or set of directions. LCMV beamforming requires that the beamformer response to signals from a direction of interest are passed with specified gain and phase delay. However, power from interfering signals and noise from all other directions is minimized. Additional constraints may be imposed to specifically nullify output power coming from known directions. The constraints are contained in the matrix, constr. Each column of constr represents a separate constraint vector. The desired response to each constraint is contained in the response vector, resp. The argument cov is the sensor spatial covariance matrix. All elements in the sensor array are assumed to be isotropic.

example

Examples

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Open Live Script

Construct a 10-element half-wavelength-spaced line array. Then, compute the LCMV weights for a desired arrival direction of 0 degrees azimuth. Impose three direction constraints: a null at -40 degrees, a unit desired response in the arrival direction 0 degrees, and another null at 20 degrees. The sensor spatial covariance matrix includes two signals arriving from -60 and 60 degrees and -10 dB isotropic white noise. 

N = 10;
d = 0.5;
elementPos = (0:N-1)*d;
sv = steervec(elementPos,[-40 0 20]);
resp = [0 1 0]';
Sn  = sensorcov(elementPos,[-60 60],db2pow(-10));

Compute the beamformer weights. 

w = lcmvweights(sv,resp,Sn);

Plot the array pattern for the computed weights. 

vv = steervec(elementPos,[-90:90]);
plot([-90:90],mag2db(abs(w'*vv)))
grid on
axis([-90,90,-50,10]);
xlabel('Azimuth Angle (degrees)');
ylabel('Normalized Power (dB)');
title('LCMV Array Pattern');

Figure contains an axes object. The axes object with title LCMV Array Pattern, xlabel Azimuth Angle (degrees), ylabel Normalized Power (dB) contains an object of type line.

The above figure shows that maximum gain is attained at 0 degrees as expected. In addition, the constraints impose nulls at -40 and 20 degrees and these can be seen in the plot. The nulls at -60 and 60 degrees arise from the fundamental property of the LCMV beamformer of suppressing the power contained in the two plane waves that contributed to the sensor spatial covariance matrix.

Input Arguments

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Constraint matrix specified as a complex-valued, N-by-K, complex-valued matrix. In this matrix N represents the number of elements in the sensor array while K represents the number of constraints. Each column of the matrix specifies a constraint on the beamformer weights. The number of K must be less than or equal to N.

Example: [0, 0, 0; .1, .2, .3; 0,0,0]

Data Types: double
Complex Number Support: Yes

Desired response specified as complex-valued, K-by-1 column vector where K is the number of constraints. The value of each element in the vector is the desired response to the constraint specified in the corresponding column of constr.

Example: [45;0]

Data Types: double
Complex Number Support: Yes

Sensor spatial covariance matrix specified as a complex-valued, N-by-N matrix. In this matrix, N represents the number of sensor elements. The covariance matrix consists of the variances of the element data and the covariance between sensor elements. It contains contributions from all incoming signals and noise.

Example: [45;0]

Data Types: double
Complex Number Support: Yes

Output Arguments

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Beamformer weights returned as an N-by-1, complex-valued vector. In this vector, N represents the number of elements in the array.

More About

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References

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

[2] Johnson, Don H. and D. Dudgeon. Array Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1993.

[3] Van Veen, B.D. and K. M. Buckley. “Beamforming: A versatile approach to spatial filtering”. IEEE ASSP Magazine, Vol. 5 No. 2 pp. 4–24.

Extended Capabilities

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Version History

Introduced in R2013a

See Also

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