Multi stage Kalman filter (MSKF) based time-varying sparse channel estimation with fast convergence

The paper develops novel algorithms for {it time-varying} (TV) {it sparse} channel estimation in {it Massive} multiple-input, multiple-output (MMIMO) systems. This is achieved by employing a novel {it 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 {it state estimation} techniques. MSKF converges very quickly, within few stages/iterations (at each symbol). This is possible because MSKF uses {it those} signal spaces, maximally correlated with the desired signal, {it 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 {it unlike} most existing methods, including recent Bayesian-Belief Propagation, Krylov, fast iterative re-weighted compressed sensing (RCS) and minimum rank minimization methods, which requires {it more and more} iterations to converge, as the scale of MMIMO system increases.