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 | \({\vphantom {{\sum _{1}^{1}}}}\boldsymbol {\Delta } = \mathbf {I}_{K} \mathbf {D} \mathbf {W}_{M}^{\mathrm {H}}\) | \(KM\log _{2}(M)\) |