Table 1 Duality relations between STN and FTN multicarrier communication
From: FTN multicarrier transmission based on tight Gabor frames
System | STN | FTN |
|---|---|---|
Frequency spacing | \(\tilde {F}_{0} ~=~1/T_{0}\) | \(F_{0} = 1/\tilde {T_{0}}\) |
Time spacing | \(\tilde {T}_{0} ~=~1/F_{0}\) | \(T_{0}~=~1/\tilde {F_{0}}\) |
Density | \(\tilde {\rho } ~=~1/(\tilde {F}_{0} \tilde {T}_{0})~=~F_{0} T_{0}~<~1\) | \(\rho ~=~1/(F_{0} T_{0})~=~ \tilde {F}_{0} \tilde {T}_{0} ~>~1\) |
Interference mitigation | PR with biorthogonal frames | Dual frames |
Noise reduction | PR with orthogonal frames | Tight frames with A g = 1 |
Transmission generator | \(\tilde {g} ~=~ {g/\sqrt {\tilde {\rho }}} ~=~ \sqrt {\rho }\ g\) | \(g ~=~ {\tilde {{g}}/\sqrt {\rho }} ~=~ \sqrt {\tilde {\rho }}\ \tilde {{g}}\) |
Reception generator | \(\tilde {\check {g}} ~=~ {\check {g}/\sqrt {\tilde {\rho }}} ~=~ \sqrt {\rho }\ \check {g}\) | \(\check {g} ~=~ {\tilde {{\check {g}}}/\sqrt {\rho }} ~=~ \sqrt {\tilde {\rho }}\ \tilde {{\check {g}}}\) |