Non-orthogonal frequency-division multiplexing

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Passband modulation
Analog modulation
AM FM PM QAM SM SSB
Digital modulation
ASK APSK CPM FSK MFSK MSK OOK PPM PSK QAM SC-FDE TCM WDM
Hierarchical modulation
QAM WDM
Spread spectrum
CSS DSSS FHSS THSS
See also
Capacity-approaching codes Demodulation Line coding Modem AnM PoM PAM PCM PDM PWM ΔΣM OFDM FDM Multiplexing
v t

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.^[1][2][3] N-OFDM signals can be used in communication and radar systems.

Subcarriers system

The low-pass equivalent N-OFDM signal is expressed as:^[3][2]

${\displaystyle \ \nu (t)=\sum _{k=0}^{N-1}X_{k}e^{j2\pi \alpha kt/T},\quad 0\leq t<T,}$

여기서 $X{\displaystyle {}_{}}$ ${\displaystyle k_{}}$ ${\$은(는) 데이터 기호, N ${\displaystyle N}$은(는) 서브캐리어 수, $T{\displaystyle }$ ${\displaystytle T}$은(는) N-OFDM 기호 시간이다. < ${\displaystyle \alpha <1}$에 대한 하위 캐리어 간격 $\alpha {\displaystyle }$/ ${\displaystyle T}$ ${\displaystyle \alpha /T}$을(를) 사용하면 각 기호 기간에 걸쳐 직교하지 않게 된다.

역사

N-OFDM 신호 이론의 역사는 1992년 러시아 연방 특허 제 2054684호에서 시작되었다.^[1] 이 특허에서 바디름 슬라이우사는 FFT(Fast Fourier Transform, FFT) 이후 N-OFDM 신호에 대한 최적의 처리 방법을 1차 제안했다.

그런 점에서 W. 코젝과 A.라고 말할 필요가 있다. F. Molisch는 에 < 1 $[\displaystyle \alpha <$1}을$($를) 가진 N-OFDM 신호에 대해 "이상적인 채널의 경우에도 수신된 신호로부터 정보를 복구할 수 없다"고 썼다.

2001년 V. Sliffusar는 통신 시스템용 OFDM의 대안으로 비직교 주파수 디지털 변조(N-OFDM)를 제안했다.^[5]

이 방법에 대한 다음 간행물은 I의 SEFDM에 관한 회의 논문 이전에 2002년^[2] 7월에 우선순위를 두고 있다. Darwazeh와 M.R.D. Rodrigues(2003년 9월).^[6]

N-OFDM의 장점

OFDM에 비해 N-OFDM 신호 강등 복잡성이 증가함에도 불구하고, 비직교 서브캐리어 주파수 배열로의 전환은 다음과 같은 몇 가지 이점을 제공한다.

1. 신호가 점유하는 주파수 대역을 줄이고 많은 단자의 전자기 호환성을 개선할 수 있는 높은 스펙트럼 효율성
2. 서브캐리어 공칭 주파수를 변경하여 주파수에 집중된 간섭으로부터 적응적 분리.^[7]
3. an ability to take into account Doppler frequency shifts of subcarriers when working with subscribers moving at high speeds;
4. reduction of the peak factor of the multi-frequency signal mixture.

Idealized system model

This section describes a simple idealized N-OFDM system model suitable for a time-invariant AWGN channel^[8]

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.

${\displaystyle \scriptstyle s[n]}$ is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into ${\displaystyle \scriptstyle N}$ 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, ${\displaystyle \scriptstyle f_{c}}$, respectively. These signals are then summed to give the transmission signal, ${\displaystyle \scriptstyle s(t)}$.

Demodulation

Receiver

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.

Demodulation after FFT

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

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Demodulation without FFT

Demodulation by using of ADC samples

The method of optimal processing for N-OFDM signals without FFT was proposed in October 2003.^[3][9] In this case can be used ADC samples.

Demodulation after Discrete Hartley transform

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N-OFDM+MIMO

The combination N-OFDM and MIMO technology is similar to OFDM. To the building of MIMO system can be used digital antenna array as transmitter and receiver of N-OFDM signals.

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Fast-OFDM

Fast-OFDM^[10][11][12] method was proposed in 2002.^[13]

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FBMC

FBMC is Filter-Bank Multi-Carrier Modulation.^[14][15][16] 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.^[17]

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

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

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

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Spectrally efficient FDM (SEFDM)

N-OFDM is a spectrally efficient method.^[6][18] All SEFDM methods are similar to N-OFDM.^{[6][19][20][21][22][23][24]}

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GFDM

GFDM is generalized frequency division multiplexing.

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See also

• OFDM
• COFDM

References