Joint channel estimation and equalisation of fast time‐varying frequency‐selective channels

Abstract

This paper addresses joint channel and data estimation for transmission over frequency-selective and timevarying channels based on a Doppler-variant channel impulse response (CIR). A discrete spreading function (DSF), which corresponds to the Doppler Fourier series of the time-varying channel taps, is introduced. The spectral leakage associated with the Fourier series representation is reduced by oversampling in Dopplerdirection. This approach, however, requires joint channel estimation and equalisation (JCE). Therefore, a recursive least squares (RLS) algorithm for the DSF estimation is combined with the data detection in a reduced state diagram. Furthermore, an enhanced metric, previously introduced in De Broeck et al. published by Kluwer Academic Publishers: Dordrecht, 2000) for time-invariant channels, is applied here for path selection. The performance of this metric is investigated here for time-varying and frequency-selective (TV-FS) channels. The performance of the proposed approach is compared with the JCE algorithm which uses RLS estimation of a CIR by simulations.

Doppler-variant modeling of the vocal tract

“…As in [2], we address this problem by virtually lengthening the period N to N · ν with the oversampling factor ν ≥ 1, while retaining the optimization interval to the first N samples. By this Equation (7) becomes …”

“…This terminology originates from the field of wireless communications where spreading matrices are used to represent time-variant channels[2].…”

Discriminated Belief Propagation

“…The computation of w (h) for given w (l) is then simple as the independence assumptions ( 5) and (7) give that P Ci (x|m) = P Ci|R (x|r i + w…”

“…This problem is usually mitigated by a channel estimation prior to the decoding. However, an independent estimation needs -especially for time varying channels [7] -considerable excess redundancy. The optimal approach would be to perform decoding, estimation, and equalisation simultaneously.…”

“…Remark 33 (Miscellaneous) Note that without some known "training" sequence in the code word the iteration will by the symmetry usually stay at w (l) = 0. Note, moreover, that this approach is easily extended to time variant channels as considered in [7] or even to more complex, i.e., non linear channel maps. The complexity then remains dominated by the complexity of the computation of the means and correlations.…”