Time-Frequency Selective MIMO Precoding for OFDM with Insufficient CP

A cyclic prefix (CP) for an orthogonal frequency division multiplexing (OFDM) transmission shorter than the maximum delay spread of the channel results into inter-symbol interference (ISI) and inter-carrier interference (ICI). This paper shows that an appropriate frequency-domain multi-antenna (MIMO) precoding for OFDM can asymptotically cancel out ISI/ICI as the number of antennas goes to infinity. The method is based on introducing time-delay selectivity over the channel taps from which a conventional frequency-domain precoding method can be based on. This time-selectivity enables to asymptotically remove undesired delayed signals, while the frequency-selectivity in the precoders is preserved to suit the conventional MIMO-OFDM air interface where precoding is applied on a subcarrier level. Analysis reveals an optimization trade-off in the precoding design between interference removal and multi-path diversity gain. The resulting optimized precoders are shown to provide subsequent gains in asymptotic achievable rate with infinite number of antennas, as well as in symbol-error-rate performance of a moderate finite-antenna system.