Multiuser-MISO Precoding Under Channel Phase Uncertainty in Satellite Communication Systems

Linear and symbol-level precoding in satellite communications have received increasing research attention thanks to their ability to tackle inter-beam interference, allowing the use of spectral resources more efficiently. However, there are still challenges and open questions regarding the implementation of practical precoding systems taking the phase uncertainties in estimating the channel state information into account. This work assesses the impact of phase variations and uncertainties inherent to the satellite communication system operating a precoded forward link. Specifically, we address the inability to measure at the user terminal, the absolute phase rotation introduced by the channel, and the transponder local oscillator phase noise effects on the precoding operations considering the use of frequency division multiplexing in the forward-uplink transmission. We formally demonstrate that the system performance for linear and non-linear precoding operations is not affected by the uncertainty in the phase measurements at the user terminal. Additionally, we show that using a single frequency reference for all the local oscillators at the transponder does not avoid the phase variations related to the frequency division multiplexing in the forward-uplink. This work demonstrates that these phase variations would not affect the system performance for an ideal zero-delay precoding loop. However, this is not feasible in practical scenarios, where the phase noise of the frequency reference at the transponder and the loop delay determine the impact on the system performance. We validate our results by simulations considering three frequency references with different stability levels in a typical geosynchronous orbit (GEO) satellite system. Our results suggest that practical implementations of multiuser-MISO precoding systems must include a differential phase synchronization loop to compensate for this performance degradation.