Method of encoding digital data on multiple carrier frequencies
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. N-OFDM signals can be used in communication and radar systems.
Subcarriers system.
The low-pass equivalent N-OFDM signal is expressed as:
formula_1
where formula_2 are the data symbols, formula_3 is the number of sub-carriers, and formula_4 is the N-OFDM symbol time. The sub-carrier spacing formula_5 for formula_6 makes them non-orthogonal over each symbol period.
History.
The history of N-OFDM signals theory was started in 1992 from the Patent of Russian Federation No. 2054684. In this patent, Vadym Slyusar proposed the 1st method of optimal processing for N-OFDM signals after Fast Fourier transform (FFT).
In this regard need to say that W. Kozek and A. F. Molisch wrote in 1998 about N-OFDM signals with formula_6 that "it is not possible to recover the information from the received signal, even in the case of an ideal channel."
In 2001, V. Slyusar proposed non-orthogonal frequency digital modulation (N-OFDM) as an alternative of OFDM for communications systems.
The next publication about this method has priority in July 2002 before the conference paper regarding SEFDM of I. Darwazeh and M.R.D. Rodrigues (September, 2003).
Advantages of N-OFDM.
Despite the increased complexity of demodulating N-OFDM signals compared to OFDM, the transition to non-orthogonal subcarrier frequency arrangement provides several advantages:
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.
formula_8 is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into formula_9 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, formula_10, respectively. These signals are then summed to give the transmission signal, formula_11.
Demodulation.
Receiver.
The receiver picks up the signal formula_12, which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on formula_13, 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 formula_3 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.
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. In this case can be used ADC samples.
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.
Fast-OFDM.
Fast-OFDM method was proposed in 2002.
Filter-bank multi-carrier modulation (FBMC).
Filter-bank multi-carrier modulation (FBMC) is. 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 formula_3-band transmultiplexer followed by the transform function
formula_16
On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform
formula_17
followed by another formula_3-band transmultiplexer. The relationship between both transform functions is
formula_19
Spectrally-efficient FDM (SEFDM).
N-OFDM is a spectrally efficient method. All SEFDM methods are similar to N-OFDM.
Generalized frequency division multiplexing (GFDM).
"Generalized frequency division multiplexing" ("GFDM") is.
References.
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