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

Abstract

Filter bank-based multicarrier using offset quadrature amplitude modulation (FMBC/OQAM) systems suffer from inter-symbol-interference (ISI) and cochannel 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 pseudoinverse, and demonstrate how the overall FBMC/OQAM system is orthogonalised, thus removing ISI and ICI.

Extending Narrowband Descriptions and Optimal Solutions to Broadband Sensor Arrays

“…addressed in (Nagy and Weiss, 2017;Nagy and Weiss, 2018). With this extended constraint equation, the Capon beamformer is given by (Alzin et al, 2016) This formulation is a direct polynomial extension of the narrowband formulation.…”

Channel Equalisation of a MIMO FBMC/OQAM System Using a Polynomial Matrix Pseudo-Inverse

“…An equaliser W[n] ∈ C MK×MNR , applied prior to the OQAM de-staggering in the receiver, has the aim of equalising and synchronising the overall system. This is similar to the equaliser and synchroniser and [13], but here also aims to cancel cancel spatial or interantenna-interference.…”

“…Different from OFDM, FBMC creates subcarriers that retain at least some frequencyselectivity. Even though recent practical measurements indicate that for a well-synchronised FBMC system, single tap equalisers may be sufficient [14], generally significant dispersion has to be considered [3], [12], if not through long channel impulse response then through insufficient timing synchronisation of the receiver [13]. As a result, significant inter-symbol interference (ISI) arises.…”

“…Thus equalisers cannot operate per-band but need to incorporate cross-terms with at least adjacent bands akin early subband filtering schemes such as [6]. Nevertheless, the high spectral efficiency of FBMC/OQAM has motivated numerous solutions that aim to solve this problem [13]- [15].…”

“…[11] for a SISO and [12] for a MIMO precoder and equaliser -but solutions to such problems have not been straightforward. We here rely in novel polynomial matrix formulations [21] and associated algorithms [4], [9], [16], [17] to calculate a polynomial matrix pseudo-inverse as equaliser as a MIMO extension of the work in [13]. The advantage of these polynomial matrix techniques lie in the coherent treatment of the problem, which avoids the challenge of association of bin-wise solution from DFT bin to DFT bin [12].…”