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steervec

Steering vector

Description

example

sv= steervec(pos,ang)returns the steering vectorsvfor each incoming plane wave or set of plane waves impinging on a sensor array. The steering vector represents the set of phase-delays for an incoming wave at each sensor element. Theposargument specifies the positions of the sensor array elements. Theangargument specifies the incoming wave arrival directions in terms of azimuth and elevation angles. The steering vector,sv, is anN-by-Mcomplex-valued matrix. In this matrix,Nrepresents the number of element positions in the sensor array whileMrepresents the number of incoming waves. Each column ofsvcontains the steering vector for the corresponding direction specified inang. All elements in the sensor array are assumed to be isotropic.

example

sv= steervec(pos,ang,nqbits)返回量子化的窄带转向向量时the number of phase shifter bits is set tonqbits.

Examples

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Specify a uniform line array of five elements spaced 10 cm apart. Then, specify an incoming plane wave with a frequency of 1 GHz and an arrival direction of 45° azimuth and 0° elevation. Compute the steering vector of this wave.

elementPos = (0:.1:.4); c = physconst('LightSpeed'); fc = 1e9; lam = c/fc; ang = [45;0]; sv = steervec(elementPos/lam,ang)
sv =5×1 complex1.0000 + 0.0000i 0.0887 + 0.9961i -0.9843 + 0.1767i -0.2633 - 0.9647i 0.9376 - 0.3478i

Specify a uniform line array (ULA) containing five isotropic elements spaced 10 cm apart. Then, specify an incoming plane wave having a frequency of 1 GHz and an arrival direction of 45° azimuth and 0° elevation. Compute the steering vector of this wave. Quantize the steering vector to three bits.

elementPos = (0:.1:.4); c = physconst('LightSpeed'); fc = 1e9; lam = c/fc; ang = [45;0]; sv = steervec(elementPos/lam,ang,3)
sv =5×1 complex1.0000 + 0.0000i 0.0000 + 1.0000i -1.0000 + 0.0000i -0.0000 - 1.0000i 1.0000 + 0.0000i

Input Arguments

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Positions of the elements of a sensor array specified as a 1-by-Nvector, a 2-by-Nmatrix, or a 3-by-Nmatrix. In this vector or matrix,Nrepresents the number of elements of the array. Each column ofposrepresents the coordinates of an element. Ifposis a 1-by-Nvector, then it represents they-coordinate of the sensor elements of a line array. Thexandz-coordinates are assumed to be zero. Whenposis a 2-by-Nmatrix, it represents the(y,z)-coordinates of the sensor elements of a planar array. This array is assumed to lie in theyz-plane. Thex-coordinates are assumed to be zero. Whenposis a 3-by-Nmatrix, then the array can have an arbitrary shape. Sensor positions are in terms of signal wavelength.

Example:[0,0,0; 0.1,0.4,0.3; 1,1,1]

Data Types:double

Arrival directions of incoming signals specified as a 1-by-Mvector or a 2-by-Mmatrix, whereMis the number of incoming signals. Ifangis a 2-by-Mmatrix, each column specifies the direction in azimuth and elevation of the incoming signal[az;el]. The azimuth angle must lie between –180° and 180° and the elevation angle must lie between –90° and 90°. The azimuth angle is the angle between thex-axis and the projection of the arrival direction vector onto thexyplane. It is positive when measured from thex-axis toward they-axis. The elevation angle is the angle between the arrival direction vector andxy-plane. It is positive when measured towards thezaxis. Ifangis a 1-by-Mvector, then it represents a set of azimuth angles with the elevation angles assumed to be zero. Angle units are specified in degrees.

Example:[45;0]

Data Types:double

Number of bits used to quantize the phase shift in beamformer or steering vector weights, specified as a non-negative integer. A value of zero indicates that no quantization is performed.

Example:5

Output Arguments

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Steering vector returned as anN-by-Mcomplex-valued matrix. In this matrix,Nrepresents the number of sensor elements of the array andMrepresents the number of incoming plane waves. Each column ofsvcorresponds to the same column inang.

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]凡Veen,最初和k . M。Buckley. “Beamforming: A versatile approach to spatial filtering”.IEEE ASSP Magazine, Vol. 5 No. 2 pp. 4–24.

Extended Capabilities

Version History

Introduced in R2013a