Compression-Aided Kalman Filter for recursive Bayesian estimation of sparse wideband channels in OFDM systems

Many wideband wireless propagation media, including millimeter-wave and underwater acoustic channels, exhibit sparse impulse responses. Exploiting the sparse character of such channels using compressed sensing techniques can potentially lead to substantial savings in pilot overhead. In this paper, we address sequential Bayesian estimation of sparse/compressible channels with a Kalman tracking filter termed the “Compression-Aided Kalman Filter (C-A KF)”. As opposed to much of the previous work on Bayesian compressed sensing, our approach is not built on a hierarchical or hypothesis-testing method for the modeling of a priori information. Rather, we acquire a priori information directly from the propagation environment by employing header symbols in order to derive the sparsity pattern, i.e., support locations, and the dynamic evolution of the discrete-time channel taps. Based on a priori information extracted by the header symbols, we develop a state-space pair for the CA KF. Our experimental results suggest that the proposed C-A KF algorithm leads to significant reductions in pilot overhead, regardless of how rapidly the underlying channel conditions may change.