steervec

Syntax

Function call

The steervec function can be called in the following ways:

sv = steervec(pos,ang) returns a steering vector sv for each incoming plane wave or set of plane waves incident on the antenna element. The control vector is a set of phase delays for the incoming wave at each antenna element. The pos argument defines the positions of the antenna elements. The ang argument defines the directions of incoming wave incidence in terms of azimuth and elevation angles. The control vector sv is a complex matrix to . In this matrix, represents the number of antenna elements, while represents the number of incoming waves. Each column of sv contains a control vector for the corresponding direction specified in ang. It is assumed that all antenna elements in the sensor matrix are isotropic.
sv = steervec(pos,ang,nqbits) returns the quantised narrowband control vector when the number of phase shifter bits is set in the nqbits argument.

Arguments

Entry

pos - antenna element positions
real vector 1 on N | real matrix 2 on N | real matrix 3 on N

Details

Antenna element positions given as vector 1 at , matrix 2 at or matrix 3 at . In this vector or matrix, represents the number of antenna elements. Each column of the pos argument represents the coordinates of an element.

If pos is vector 1 at , it represents -coordinates of the sensor elements of the linear array. It is assumed that and -coordinates are zero.
If pos is matrix 2 at , it represents the -coordinates of the antenna elements of the antenna array. It is assumed that this antenna array lies in the -plane. It is assumed that -coordinates are zero.
If pos is a 3-by- matrix, the antenna array can have an arbitrary shape. The position of the antenna elements is determined by the wavelength of the signal.

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

Data types: Float64

ang - directions of arrival of incoming signals
` real vector 1 on M` | ` real matrix 2 on M`

Details

Arrival directions of incoming signals given as vector 1 on or matrix 2 on , where is the number of incoming signals.

If ang is a matrix 2 on , each column defines a 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 the axis and the projection of the arrival direction vector onto the plane . It is positive when measured from the axis towards the axis . Elevation angle is the angle between the arrival direction vector and the -plane. It is positive when measured from the axis towards the axis.
If ang is vector 1 on , it is a set of azimuthal angles, with place angles assumed to be zero.

The units of angles are degrees.

Example: [45;0]

Data types: Float64

nqbits - number of phase shift quantisation bits
0 (by default) | non-negative integer

Details

The number of bits used for phase shift quantisation in the beamformer or control vector weighting coefficients is set as a non-negative integer.

A value of zero indicates that quantisation is not performed.

Example: 5

Output

sv — control vector
`complex matrix N on M

Details

The beam steering vector of the antenna DN beam, is returned as a complex matrix by . In this matrix, represents the number of antenna elements of the antenna array, and represents the number of incoming plane waves.

Each column of sv corresponds to the same column in the input argument ang.

Examples

Linear array of control vectors

Details

Define a homogeneous linear array of five elements spaced 10 cm apart. Then define an incoming plane wave with a frequency of 1 GHz and an arrival direction of 45° in azimuth and 0° in elevation. Calculate the direction vector of this wave.

elementPos = (0:.1:.4);
c = physconst("LightSpeed");
fc = 1e9;
lam = c/fc;
ang = [45;0];
sv = steervec(elementPos/lam,ang)

Quantised linear array of control vectors

Details

Define a uniform linear array (ULA) containing five isotropic elements spaced 10 cm apart. Then specify an incoming plane wave with a frequency of 1 GHz and an arrival direction of 45° in azimuth and 0° in elevation. Calculate the direction vector of this wave. Quantise the direction 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)

Syntax

Function call

Arguments

Entry

Output

Examples

Linear array of control vectors

Quantised linear array of control vectors

See also