Observation-augmented channel estimation for sparse-pilot free-space optical systems

To address insufficient channel observations caused by sparse pilots in turbulence-impaired free-space optical (FSO) systems, an observation-augmented iterative linear minimum mean square error (OA-I-LMMSE) channel estimation framework is proposed. The proposed method exploits pilot observations, channel temporal correlation, and channel information contained in detected data symbols to iteratively refine channel state information (CSI). Under the evaluated simulation conditions, the proposed method provides lower NMSE and BER than the considered LS and static LMMSE estimators. In the investigated moderate-to-high SNR region, the method achieves a 2-3-fold NMSE reduction (approximately 3-5 dB), under the specified turbulence, pilot-interval, and channel-correlation settings. The proposed method also exhibits a relatively small gap to the adopted Bayesian Cramér-Rao lower bound (BCRLB) reference while maintaining low pilot overhead. These results support OA-I-LMMSE as an effective channel estimation solution for sparse-pilot FSO systems within the evaluated parameter range.