GFDM Pre-coding and Decoding in a Gabor Setting

The Gabor transform interpretation of the Generalized Frequency-Division Multiplexing (GFDM) leads to a modeling of the effect of the multipath channel as a Multiple-Input Multiple-Output (MIMO) system on each sub-carrier. In this paper, such a modeling is used to propose new pre-coding and decoding design approaches. Two different power allocation strategies based on a joint transmitter and receiver linear design are introduced. By exploiting the circularity of the resulting MIMO channel on each sub-carrier, an eigendecomposition can be implemented, once and for all, by computing the Discrete Fourier transform. The first proposed power allocation approach guarantees fairness among sub-carriers, while the second minimizes the error rate at the price of unfairness. The benefits achieved by the two approaches are demonstrated by numerical simulations and by comparison with other GFDM equalization and pre/de-coding schemes that, in contrast to the proposed one, work on a sub-symbol basis.