University of Oulu

P. De, M. Juntti and C. K. Thomas, "Multi Stage Kalman Filter (MSKF) Based Time-Varying Sparse Channel Estimation With Fast Convergence," in IEEE Open Journal of Signal Processing, vol. 3, pp. 21-35, 2022, doi: 10.1109/OJSP.2021.3132583

Multi Stage Kalman Filter (MSKF) based time-varying sparse channel estimation with fast convergence

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Author: De, Parthapratim1; Juntti, Markku2; Thomas, Christo Kurisummoottil3
Organizations: 1Wireless Department, Institute Infocomm Research, Singapore, Singapore, 119613
2Centre for Wireless Communications, University of Oulu, University of Oulu, Finland, FI-90014
3Institut Eurecom, 52887 Sophia Antipolis, France, 06904
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.4 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2021
Publish Date: 2021-12-13


The paper develops novel algorithms for time-varying (TV) sparse channel estimation in Massive multiple-input, multiple-output (MMIMO) systems. This is achieved by employing a novel reduced (non-uniformly spaced tap) delay-line equalizer, which can be related to low/reduced rank filters. This low rank filter is implemented by deriving an innovative TV (Krylov-space based) Multi-Stage Kalman Filter (MSKF), employing appropriate state estimation techniques. MSKF converges very quickly, within few stages/iterations (at each symbol). This is possible because MSKF uses those signal spaces, maximally correlated with the desired signal, rather than the standard principal component (PCA) signal spaces. MSKF is also able to reduce channel tracking errors, encountered by a standard Kalman filter in a high-mobility channel. In addition, MSKF is well suited for large-scale MMIMO systems. This is unlike most existing methods, including recent Bayesian-Belief Propagation, Krylov, fast iterative re-weighted compressed sensing (RCS) and minimum rank minimization methods, which requires more and more iterations to converge, as the scale of MMIMO system increases. A Bayesian Cramer Rao lower bound (BCRLB) for noisy CS (in sparse channel) is also derived, which provides a benchamrk for the performance for novel MSKF and other CS estimators.

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Series: IEEE open journal of signal processing
ISSN: 2644-1322
ISSN-E: 2644-1322
ISSN-L: 2644-1322
Volume: 3
Pages: 21 - 35
DOI: 10.1109/OJSP.2021.3132583
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Copyright information: This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see