Unsynchronized chirp results in two peaks in frequency domain. Assuming that the clock accuracy of the transmitter and the receiver is bad, sync position adjustment is required even after synchronization.
==> Simulation
Since I/Q modulation code did not fit into RAM of STM32, I am trying orthogonal chirp instead.
==> Simulation
Very weak orthogonal chirp tone was transmitted to the receiver:
The receiver could detect the signal and showed a strong peak of magnitude around zero Hz, as long as its time frame is in sync with the transmitter:
I spent a day to know that 4 times FFT does not fit into 20.5msec time frame (2048 samples/100000Hz) the day before. So I modified the sampling rate to 80MHz /32 divider /32 decimation = 78125Hz, so T of 2048 samples corresponds to 26.2msec.
Weak "Hello World!" tone was sent to the receiver, and it could decode the signal and showed the message!
==> Code