Design of DGT-based linear and non-linear equalizers for GFDM transmission

Abstract

This paper exploits the parallelism between Discrete Gabor Transform (DGT) and Generalized Frequency-Division Multiplexing (GFDM) that exists when the synthesis function, i.e. the pulse shaping filter, and the analysis function, i.e. the receiving filter, satisfy the Wexler–Raz identity. Choosing functions that satisfy the Wexler–Raz condition allows optimal symbol-by-symbol detection for a DGT-based GFDM receiver in case of transmission over an additive white Gaussian noise channel. However, multipath fading is the major problem of the wireless communication channel, hence, when transmission takes place over frequency selective channel, symbol-by-symbol detection is no longer optimal due to interference generated among the transmitted symbols. In this work, we deal with the design of linear and non-linear receivers for DGT-based GFDM transmission over a frequency selective channel that allows a good trade-off between complexity and performance. Different equalization schemes to mitigate distortions, such as Maximum Likelihood, Zero-Forcing and Minimum Mean-Squared Error, are developed and analyzed. Monte Carlo simulations are used to evaluate the error rate performance achieved with the considered design. A comparison is done with other works in the literature.