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.