On the Noise Enhancement of GFDM

Generalized frequency division multiplexing (GFDM) is a multicarrier system employing well-localized prototype filters to form the transmitted signal. However, because of the non-orthogonality of the waveform, the demodulation process of GFDM inherits a noise enhancement, which leads to the performance degradation. Eigenvalues of the GFDM matrix determine the level of noise enhancement. In this letter, by defining the condition number of the GFDM matrix as the noise enhancement factor (NEF), we derive a closed-form presentation of NEF criterion based on the prototype filter shape. We show that the value of NEF is independent of the number of subsymbols and subchannels, if they are even; contrarily, for odd numbers, a larger NEF is resulted as the number grows up.