Lighthouse Cooperative Radar
In order to get an accurate altitude/position reading on the rocket, we are developing a cooperative radar system. We will uplink a signal from the ground, re-amplify and retransmit it using a repeater onboard the rocket. We will then use ranging and angle-of-arrival algorithms on the ground to determine the position of the rocket.
The signal will be a Pseudo-Random Noise (PRN) sequence. It will be generated by an FPGA, and modulated using Binary Phase Shift Keying (BPSK). The uplink signal will be on the 2.4 GHz HAM band, and the downlink signal will be on the 3.3GHz HAM band.
Ranging
The ranging algorithm will compute the 2-way time-of-flight (TOF) for the signal. It will estimate the TOF by correlating the recieved, demodulated stream with the PRN being transmitted. By timing the difference between correlation peaks, we can calculate the time of flight and get the distance the signal traveled using $ d = c*\frac{t}{2} $ where $c$ is the speed of light and $t$ is the 2 way TOF. The correlation algorithm will be written in Verilog for the Spartan 7 FPGA.
The bitrate of the PRN determines the ranging accuracy. Since we are using BPSK modulation, the bitrate is directly proportional to the signal bandwidth. At the HAM bands we have chosen, the largest bandwidth we can get is 20MHz, which means that we can get a 20 Mbps chip rate. This corresponds to an accuracy of 15 meters radially, which is good enough considering that the rocket will be more than 100km in the sky.
Angle of Arrival
Angle of arrival will consist of three phases.
- Initial Pointing
The repeater on the rocket will send out a pure tone beacon at 3.3GHz (only modulated using On-Off Keying (OOK) to comply with HAM laws). The groundstation horn antenna array will use either amplitude angle of arrival or phase interferometry (not sure yet). The gimbal control law will work to point the array towards the beacon source.
- Acquisition
Once the gimbal is pointing close enough to the rocket for it to recieve the uplinked PRN, the beacon tone will turn off and the repeater will automatically start retransmitting the PRN. The groundstation will continue to use the coarse angle of arrival algorithm.
- Tracking
Since the baseline of the antenna array is 1 meter in the azimuth and elevation axes, the $2\pi$ ambiguity angle will be ~2.5°. Once the coarse tracking gets within this threshold, it will switch to fine tracking, which will use phase interferometry with the 1m baseline to track with a higher accuracy. More details on the fine accuracy can be found in the PDR slideshow.
Antenna Design
Details can be found on the antenna design page.