# Non-orthogonal frequency-division multiplexing

(Redirected from N-OFDM)

Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals between frequency of sub-carriers. 

## Subcarriers system

The low-pass equivalent N-OFDM signal is expressed as:

$\ \nu (t)=\sum _{k=0}^{N-1}X_{k}e^{j2\pi \alpha kt/T},\quad 0\leq t where ${X_{k}}$ are the data symbols, $N$ is the number of sub-carriers, and $T$ is the N-OFDM symbol time. The sub-carrier spacing $\alpha /T$ for $\alpha <1$ makes them non-orthogonal over each symbol period.

## Idealized system model

This section describes a simple idealized N-OFDM system model suitable for a time-invariant AWGN channel.

## Transmitter N-OFDM signals

An N-OFDM carrier signal is the sum of a number of not-orthogonal subcarriers, with baseband data on each subcarrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phase-shift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier.

$s[n]$ is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into $N$ parallel streams, and each one mapped to a (possibly complex) symbol stream using some modulation constellation (QAM, PSK, etc.). Note that the constellations may be different, so some streams may carry a higher bit-rate than others.

A Digital Signal Processor (DSP) is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then quadrature-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digital-to-analogue converters (DACs); the analogue signals are then used to modulate cosine and sine waves at the carrier frequency, $f_{c}$ , respectively. These signals are then summed to give the transmission signal, $s(t)$ .

## Demodulation

The receiver picks up the signal $r(t)$ , which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on $2f_{c}$ , 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 $N$ parallel streams, which use in appropriate symbol detector.

## Demodulation after FFT

The 1st method of optimal processing for N-OFDM signals after FFT was proposed in 1992.

## N-OFDM+MIMO

The combination N-OFDM and MIMO technology is similar to OFDM.

## Fast-OFDM

Fast-OFDM method was proposed in 2002.

## FBMC

FBMC is Filter-Bank Multi-Carrier Modulation. As example of FBMC can consider Wavelet N-OFDM.

### Wavelet N-OFDM

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.

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

$F_{n}(z)=\sum _{k=0}^{L-1}f_{n}(k)z^{-k},\quad 0\leq n On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform

$G_{n}(z)=\sum _{k=0}^{L-1}g_{n}(k)z^{-k},\quad 0\leq n followed by another $\textstyle N$ -band transmultiplexer.\ The relationship between both transform functions is

$f_{n}(k)=g_{n}(L-1-k)$ $F_{n}(z)=z^{-(L-1)}G_{n}*(z-1)$ ## Spectrally efficient FDM (SEFDM)

N-OFDM is a spectrally efficient method. All SEFDM methods are similar to N-OFDM.

## GFDM

GFDM is generalized frequency division multiplexing.