Time-varying FIR equalization for MIMO transmission over doubly selective channels

We propose time-varying FIR equalization techniques for spatial multiplexing-based multiple-input multiple-output (MIMO) transmission over doubly selective channels. The doubly selective channel is approximated using the basis expansion model (BEM), and equalized by means of time-varying FIR filters designed according to the BEM. By doing so, the time-varying deconvolution problem is converted into a two-dimensional time-invariant deconvolution problem in the time-invariant coefficients of the channel BEM and the time-invariant coefficients of the equalizer BEM. The timevarying FIR equalizers are derived based on either the matched filtering criterion, or the linear minimum mean-square error (MMSE) or the zero-forcing (ZF) criteria. In addition to the linear equalizers, the decision feedback equalizer (DFE) is proposed. The DFE can be designed according to two different scenarios. In the first scenario, the DFE is based on feeding back previously estimated symbols from one particular antenna at a time. Whereas, in the second scenario, the previously estimated symbols from all transmit antennas are fed back together. The performance of the proposed equalizers in the context of MIMO transmission is analyzed in terms of numerical simulations.