Non-orthogonal frequency-division multiplexing

The receiver picks up the signal ${\displaystyle \scriptstyle r(t)}$, which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on ${\displaystyle \scriptstyle 2f_{c}}$, so low-pass filters are used to reject these. The baseband signals are then sampled and digitised using analog-to-digital converters (ADCs), and a forward FFT is used to convert back to the frequency domain.

This returns ${\displaystyle \scriptstyle N}$ parallel streams, which use in appropriate symbol detector.

N-OFDM has become a technique for power line communications (PLC). In this area of research, a wavelet transform is introduced to replace the DFT as the method of creating non-orthogonal frequencies. This is due to the advantages wavelets offer, which are particularly useful on noisy power lines.[11]

To create the sender signal the wavelet N-OFDM uses a synthesis bank consisting of a ${\displaystyle \textstyle N}$-band transmultiplexer followed by the transform function

${\displaystyle F_{n}(z)=\sum _{k=0}^{L-1}f_{n}(k)z^{-k},\quad 0\leq n<N}$

On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform

${\displaystyle G_{n}(z)=\sum _{k=0}^{L-1}g_{n}(k)z^{-k},\quad 0\leq n<N}$

followed by another ${\displaystyle \textstyle N}$-band transmultiplexer.\ The relationship between both transform functions is

${\displaystyle f_{n}(k)=g_{n}(L-1-k)}$

${\displaystyle F_{n}(z)=z^{-(L-1)}G_{n}*(z-1)}$