  Due to its attractive properties, generalized frequency division multiplexing
(GFDM) is recently being discussed as a candidate waveform for the fifth
generation of wireless communication systems (5G). GFDM is introduced as a
generalized form of the widely used orthogonal frequency division multiplexing
(OFDM) modulation scheme and since it uses only one cyclic prefix (CP) for a
group of symbols rather than a CP per symbol, it is more bandwidth efficient
than OFDM. In this paper, we propose novel transceiver structures for GFDM by
taking advantage of the particular structure in the modulation matrix. Our
proposed transmitter is based on modulation matrix sparsification through
application of fast Fourier transform (FFT) to reduce the implementation
complexity. A unified receiver structure for matched filter (MF), zero forcing
(ZF) and minimum mean square error (MMSE) receivers is also derived. The
proposed receiver techniques harness the special block circulant property of
the matrices involved in the demodulation stage to reduce the computational
cost of the system implementation. We have derived the closed forms for the ZF
and MMSE receiver filters. Additionally, our algorithms do not incur any
performance loss as they maintain the optimal performance. The computational
costs of our proposed techniques are analyzed in detail and are compared with
the existing solutions that are known to have the lowest complexity. It is
shown that through application of our transceiver structure a substantial
amount of computational complexity reduction can be achieved.
