Synchronisation and equalisation of an FBMC/OQAM system by a polynomial matrix pseudo-inverse

Filter bank-based multicarrier using offset quadrature amplitude modulation (FMBC/OQAM) systems suffer from inter-symbol-interference (ISI) and co-channel interference (CCI) if the transmission channel is dispersive, or simply if the overall system is not synchronised. This paper considers the solution to an equaliser that can mitigate both ISI and CCI by describing the equivalent transmultiplexed channel including the filter banks as a polyphase matrix of transfer functions, and by using polynomial matrix algebra to equalise this system. We demonstrate that the reduced-rank nature of this channel matrix requires a polynomial matrix pseudo-inverse, and demonstrate how the overall FBMC/OQAM system is orthogonalised, thus removing ISI and ICI.