Time-varying channel estimation through optimal piece-wise time-invariant approximation for high-speed train wireless communications

The practical time-varying channel between a high-speed train (HST) and infrastructure has a single Doppler shift on each resolvable multipath in most cases. As a result, the HST channel can be modelled by only 2L parameters: L Doppler shifts and L   complex channel gains. Based on this observation, we propose a novel channel estimation technique for orthogonal frequency-division multiplexing (OFDM) systems running on a HST, with the name PIece-wise Time-Invariant Approximation (PITIA). In PITIA, the HST channel is approximated by a bunch of time-invariant channels, whose channel impulse responses (CIRs) can be estimated through pilots. Variations of these CIR samples over time derive both Doppler shifts and complex channel gains, so the whole time-varying channel can be reconstructed. PITIA enjoys low computation complexity of O(NL)O(NL) for N subcarriers. The optimal duration of time-invariant channels used to approximate HST channel is derived from both analytical analysis and simulations. Compared to basis expansion model (BEM) methods, PITIA uses fewer channel parameters with comparable modelling error, shows better normalized mean squared error (NMSE) performance under high-mobility and high signal-to-noise ratio (SNR) environments, and achieves comparable NMSE in low SNR regime.