A coherent receiver for cdss

cdss is a CHIRP-DSSS-Polar digital modem. This was the receiver — where a real channel (drift, offset, noise) has to be undone before any bit is read.

Recovering timing. The receiver doesn't know where a symbol begins. It uses second-order timing recovery with linear interpolation between samples, which tracks not just a fixed sampling offset but a slowly changing one — the kind two free-running clocks, one on each end, inevitably produce.

Correcting carrier-frequency offset. Two radios never agree exactly on frequency; the residual offset rotates the signal and, left alone, destroys the symbols. The receiver estimates and corrects this offset during preamble synchronization, before the payload starts, then keeps phase and frequency tracking running through the frame so the correction doesn't drift back out.