Conventional Beamformer

Also refererd to as Delay and Sum Beamformer.

class ConventionalBeamformer(operator=None)

Bases: Serializable, TransmitBeamformer, ReceiveBeamformer

Conventional delay and sum beamforming.

The Bartlett1 beamformer, also known as conventional or delay and sum beamformer, maximizes the power transmitted or received towards a single direction of interest \((\theta, \phi)\), where \(\theta\) is the zenith and \(\phi\) is the azimuth angle of interest in spherical coordinates, respectively.

Let \(\mathbf{X} \in \mathbb{C}^{N \times T}\) be the the matrix of \(T\) time-discrete samples acquired by an antenna arrary featuring \(N\) antennas. The antenna array’s response towards a source within its far field emitting a signal of small relative bandwidth is \(\mathbf{a}(\theta, \phi) \in \mathbb{C}^{N}\). Then

\[\hat{P}_{\mathrm{Capon}}(\theta, \phi) = \mathbf{a}^\mathsf{H}(\theta, \phi) \mathbf{X} \mathbf{X}^\mathsf{H} \mathbf{a}(\theta, \phi)\]

is the Conventional beamformer’s power estimate with

\[\mathbf{w}(\theta, \phi) = \mathbf{a}(\theta, \phi)\]

being the beamforming weights to steer the sensor array’s receive characteristics towards direction \((\theta, \phi)\), so that

\[\mathcal{B}\lbrace \mathbf{X} \rbrace = \mathbf{w}^\mathsf{H}(\theta, \phi) \mathbf{X}\]

is the implemented beamforming equation.

yaml_tag: Optional[str] = 'ConventionalBeamformer'

YAML serialization tag.

property num_receive_focus_angles: int

Number of required receive focus angles.

Return type

int

Returns

Number of focus angles \(F\).

property num_receive_input_streams: int

Number of input streams required by this beamformer.

Dimension \(N\) of the input sample matrix \(\mathbf{X} \in \mathbb{C}^{N \times T}\).

Return type

int

Returns

Number of input streams \(N\).

property num_receive_output_streams: int

Number of output streams generated by this beamformer.

Dimension \(M\) of the output sample matrix \(\mathbf{Y} \in \mathbb{C}^{M \times T}\).

Return type

int

Returns

Number of output streams \(M\).

property num_transmit_focus_angles: int

Number of required transmit focus angles.

Return type

int

Returns

Number of focus angles.

property num_transmit_output_streams: int

Number of output streams generated by this beamformer.

Return type

int

Returns

Number of output streams.

property num_transmit_input_streams: int

Number of input streams required by this beamformer.

Return type

int

Returns

Number of input streams.

_encode(samples, carrier_frequency, focus_angles)

Encode signal streams for transmit beamforming.

Parameters
  • samples (np.ndarray) – Signal samples, first dimension being the number of transmit antennas, second the number of samples.

  • carrier_frequency (float) – The assumed carrier central frequency of the samples.

  • focus_angles (np.ndarray) – Focused angles of departure in radians. Two-dimensional numpy array with the first dimension representing the number of focus points and the second dimension of magnitude two being the azimuth and elevation angles, respectively.

  • azimuth (float) – Azimuth angle of departure in Radians.

  • zenith (float) – Zenith angle of departure in Radians.

Return type

ndarray

_decode(samples, carrier_frequency, angles)

Decode signal streams for receive beamforming.

This method is called as a subroutine during receive() and probe().

Parameters
  • samples (np.ndarray) – Signal samples, first dimension being the number of signal streams \(N\), second the number of samples \(T\).

  • carrier_frequency (float) – The assumed carrier central frequency of the samples \(f_\mathrm{c}\).

  • angles (ndarray) – (np.ndarray): Spherical coordinate system angles of arrival in radians. A three-dimensional numpy array with the first dimension representing the number of angles, the second dimension of magnitude number of focus points \(F\), and the third dimension containing the azimuth and zenith angle in radians, respectively.

Return type

ndarray

Returns

Stream samples of the focused signal towards all focus points. A three-dimensional numpy array with the first dimension representing the number of focus points, the second dimension the number of returned streams and the third dimension the amount of samples.

1

M. S. Bartlett. Periodogram analysis and continuous spectra. Biometrika, 37(1/2):1–16, 1950. URL: http://www.jstor.org/stable/2332141 (visited on 2022-06-28).