Generalized Frequency Division Multiplexing (GFDM) is one of the multi-carrier transmission techniques considered as an alternative to orthogonal frequency division multiplexing (OFDM) for 5G wireless communication systems. GFDM is a flexible multi-carrier scheme that spreads the data symbols in a time-frequency block. Compared to OFDM, in GFDM each subcarrier is additionally filtered with a circular pulse shaping filter. Tensor algebra efficiently describes multidimensional signals, preserves their structure and provides improved identifiability. Moreover, in the past communication systems have been modeled using tensor algebra and often showed a tensor gain compared to matrix based receivers. Therefore, we model the GFDM system using tensor algebra and tensor decompositions. In this paper, we present a tensor model for the GFDM transmit signal for single and multiple antennas based on the PARATUCK2 decomposition. Furthermore, based on this model we design an iterative receiver that simultaneously estimates the channel and the transmitted data. It significantly outperforms the Least Squares (LS) receiver. The proposed iterative receiver has a comparable performance with the state-of-the-art Linear Minimum Mean Square Error (LMMSE) receivers while having a significantly lower computational complexity.
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