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Generalized frequency division multiplexing (GFDM) is a block filtered multicarrier modulation scheme recently proposed for future wireless communication systems. It generalizes the concept of orthogonal frequency division multiplexing (OFDM), featuring multiple circularly pulse-shaped subsymbols per subcarrier. This paper presents an algorithm for GFDM synchronization and investigates the use of a preamble that consists of two identical parts combined with a windowing process in order to satisfy low out of band radiation requirements. The performance of time and frequency estimation, with and without windowing, is evaluated in terms of the statistical properties of residual offsets and the impact on symbol error rate over frequency-selective channels. A flexible metric that quantifies the penalty of misalignments is derived. The results show that this approach performs practically as state-of-the-art OFDM schemes known in the literature, while it additionally can reduce the sidelobes of the spectrum emission.

Future wireless communication systems are demanding a more flexible physical layer. GFDM is a block filtered multicarrier modulation scheme proposed to add multiple degrees of freedom and to cover other waveforms in a single framework. In this paper, GFDM modulation and demodulation is presented as a frequency-domain circular convolution, allowing for a reduction of the implementation complexity when MF, ZF and MMSE filters are employed as linear demodulators. The frequency-domain circular convolution shows that the DFT used in the GFDM signal generation can be seen as a precoding operation. This new point-of-view opens the possibility to use other unitary transforms, further increasing the GFDM flexibility and covering a wider set of applications. The following three precoding transforms are considered in this paper to illustrate the benefits of precoded GFDM: (i) Walsh Hadamard Transform; (ii) CAZAC transform and; (iii) Discrete Hartley Transform. The PAPR and symbol error rate of these three unitary transform combined with GFDM are analyzed as well.