  The conventional receiver designs of generalized frequency division
multiplexing (GFDM) consider a large scale multiple-input multiple-output
(MIMO) system with a block circular matrix of combined channel and modulation.
Exploiting this structure, several approaches have been proposed for low
complexity joint linear minimum mean squared error (LMMSE) receiver. However,
the joint design is complicated and inappropriate for hardware implementation.
In this paper, we define the concept of GFDM-based linear receivers, which
first performs channel equalization (CEq) and afterwards the equalized signal
is processed with GFDM demodulator. We show that the optimal joint LMMSE
receiver is equivalent to a GFDM-based one, that applies LMMSE-CEq and
zero-forcing demodulation. For orthogonal modulation, the optimal LMMSE
receiver has an implementation-friendly structure. For the non-orthogonal case,
we propose two practical designs that approach the performance of the joint
LMMSE. Finally, we analytically prove that GFDM-based receivers achieve equal
signal-to-interference-plus-noise ratio per subsymbols within the same
subcarrier.
