Equalization for multi-scale multi-lag OFDM channels

We consider an orthogonal frequency-division multiplexing (OFDM) transmission scheme over wideband underwater acoustic channels, where the propagation paths can experience distinct Doppler effects (manifested in signal scales) and time of arrivals (manifested in lags). We capture such an effect in this paper with a multi-scale multi-lag (MSML) model, and show that the resulting frequency-domain MSML-OFDM channel is subject to inter-carrier interference (ICI), whose amount differs per subcarrier. The corresponding channel matrix can still be approximated as highly sparse, but lacks a specific structure that can optimally be exploited by those low-complexity equalizers proposed for narrowband channels. In this paper, we propose to use the conjugate gradient (CG) algorithm to equalize the channel iteratively. The suitability of the preconditioning technique, that often accompanies the CG to accelerate the convergence, is discussed for the MSML-OFDM channel. We show that in order for the preconditioner to function properly, optimal resampling is indispensible.