In previous posts, an aperture array was described where each receiver has its own free running clock and an external reference transmitter is used for time and frequency calibration. But does this really work? Can such a tiles do coherent reception?
As a first proof of concept, the signal from a GLONASS satellite (Kosmos 2459) was observed with three receivers as it passes over a tile. The satellite transmit at 1244.6875 MHz with a bandwidth of 500 kHz. The reference transmitter was set on 1244.5 MHz and the rtl-sdr dongles on 1244.75 MHz, sampling at 2.4 MHz. 20 seconds of data was captured at a time and the correlation between the signals was calculated with the Odroid C2.
Each dot in the figure below shows the ‘raw’ signal strength of each 20s block of data at (70 kHz bandwidth around) the satellite’s frequency.
Due to the receivers beam pattern, the signals drops quite fast as the satellite goes down, but it can be approximated by cos(zenith)^6.
Using this approximated signal strength, the known satellite position, the tile’s position and the receiver’s separation, the expected correlation coefficient can be calculated. PyEphem (and the satellite’s TLE data) was used to calculate the satellite’s direction rs in the sky. If ra is the distance vector between two antennas, the expected phase (in radians) is given by
(where the term in brackets is the dot product).
Show below is the expected and measured correlation coefficients between the three receivers.
The measurement matches the prediction quite good, which means that the tile can be used as a coherent receiver!