A Kalman Smoothing Framework for Satellite NB-IoT Channel Estimation

In this paper we study channel estimation for Narrow-band Internet of things (NB-IoT) systems, a low-power radio access technology introduced by the Third Generation Partnership Project (3GPP) as a part of Long Term Evolution (LTE) in Release 13 and recently extended to support Non-Terrestrial Networks (NTN) in Release 17. To improve the quality of channel measurements from pilot signals, we propose a cross-slot smoothing algorithm based on a fixed-lag Kalman smoother (KS). The non-causal and recursive nature of the proposed smoother is suitable for NB-IoT systems, thanks to their delay-tolerant design (due the presence of sub-frame repetitions) and to unitary precoding (which ensures consistency of channel statistics across slots). We propose an efficient implementation of fixed-lag KS, which we call “reduced-redundancy” fixed-lag. Our algorithm eliminates computational redundancies by extending the state vector instead of augmenting it. We tailor our algorithm to practical scenarios, including geostationary (GEO) and low Earth orbit (LEO) satellites. Results show that the proposed algorithm outperforms causal Kalman filter and non-causal moving average or infinite impulse response filters, with comparable computational complexity.