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Table 1 Precoding in time (T) and frequency (F) domains

From: Precoded GFDM transceiver with low complexity time domain processing

Domain Operation Number of multiplications
FT \({\vphantom {{\sum _{1}^{1}}}}\boldsymbol {\Delta } = \mathbf {W}_{K}^{\mathrm {H}} \mathbf {D} \mathbf {I}_{M}\) \(MK\log _{2}(K)\)
TT \({\vphantom {{\sum _{1}^{1}}}}\boldsymbol {\Delta } = \mathbf {I}_{K} \mathbf {D} \mathbf {I}_{M}\) 0
FF \({\vphantom {{\sum _{1}^{1}}}}\boldsymbol {\Delta } = \mathbf {W}_{K}^{\mathrm {H}} \mathbf {D} \mathbf {W}_{M}^{\mathrm {H}}\) \(MK\log _{2}(K)+KM\log _{2}(M)\)
TF \({\vphantom {{\sum _{1}^{1}}}}\boldsymbol {\Delta } = \mathbf {I}_{K} \mathbf {D} \mathbf {W}_{M}^{\mathrm {H}}\) \(KM\log _{2}(M)\)