Phasor

The Phasor block computes the geometric delays and complex phasor weights that steer the Beamformer. From the ECEF antenna positions, the boresight pointing, and the coordinates of each beam, it derives one delay per beam and antenna and synthesizes one calibrated phasor per beam, antenna, channel, and polarization. All angles are in radians and all frequencies are in Hertz.

How it works

The block first converts the ECEF antenna positions into the array-centered XYZ frame defined by the array reference coordinates. Using the Julian date and DUT1 inputs it builds an astrometry context with radiointerferometryc99, converts the boresight and beam coordinates from right ascension and declination to hour angle and declination, and projects the antenna positions towards each direction to obtain per-antenna delays relative to the reference antenna. The boresight delay is subtracted from each beam delay, and the resulting relative delays are converted into complex exponentials per frequency channel, including the fringe rate at the band start frequency. Each phasor is finally multiplied by the per-antenna calibration before being emitted.

Configuration

Parameter	Type	Default	Description
observationFrequencyHz	float	1.4e9	Center frequency of the observation in hertz.
channelBandwidthHz	float	1e6	Bandwidth of a single frequency channel in hertz.
totalBandwidthHz	float	1e6	Total bandwidth of the observation in hertz.
frequencyStartIndex	integer	0	Zero-based index of the first frequency channel being processed.
referenceAntennaIndex	integer	0	Antenna used as the delay reference.
arrayReferenceLongitude	float	ATA	Longitude of the array reference position in radians.
arrayReferenceLatitude	float	ATA	Latitude of the array reference position in radians.
arrayReferenceAltitude	float	ATA	Altitude of the array reference position in meters.

Input

Name	Description
antennaPositions	F64 tensor shaped [antennas, 3] with the ECEF position of each antenna.
antennaCalibrations	CF64 tensor shaped [antennas, channels, polarizations] with the per-antenna bandpass calibration.
boresightCoordinates	F64 tensor with the boresight right ascension and declination.
beamCoordinates	F64 tensor shaped [beams, 2] with the right ascension and declination of each beam.
julianDate	Scalar F64 tensor with the Julian date of the observation.
dut1	Scalar F64 tensor with the UT1 minus UTC correction.

Output

Name	Description
delays	F64 tensor shaped [beams, antennas] with the relative geometric delay in seconds.
phasors	CF32 tensor shaped [beams, antennas, channels, polarizations] with the calibrated beamforming weights.