WO2018014969A1

WO2018014969A1 - Papr reduction through tone reservation for ofdm

Info

Publication number: WO2018014969A1
Application number: PCT/EP2016/067505
Authority: WO
Inventors: Renato Grosso
Original assignee: Telefonaktiebolaget Lm Ericsson (Publ)
Priority date: 2016-07-22
Filing date: 2016-07-22
Publication date: 2018-01-25

Abstract

Tone Reservation scheme for optical OFDM where the reserved tones are located outside the allocated transmit frequency band (out- of-band reserved tones). A plurality of peaks in the time-domain digital signal after IFFT are cancelled by adding amplitude and phase adjusted selected pre-calculated peak cancellation signals. Said cancellation signals are filtered out before transmission. Multiple peaks can be cancelled per symbol by using disjoint subsets of reserved tones.

Description

PAPR REDUCTION THROUGH TONE RESERVATION FOR OFDM

Technical Field

The invention relates to a method of OFDM transmission and to a transmitter. Background

Discrete Multitone/Orthogonal Frequency-Division Multiplexing, DMT/OFDM, are modulation techniques allowing optimization of the available frequency band utilization, and for this reason they have been adopted for many applications including wireline and optical links; DMT is the baseband version of OFDM. Among the many benefits, there are some drawbacks of using DMT/OFDM, a major one of which is a very high PAR (Peak to Average Ratio). The PAR effect within an OFDM symbol is generated by the subcarriers that form the OFDM symbol combining (summing and subtracting each other point by point) to form power peaks. The power peaks in DMT/OFDM symbols may have amplitudes that are very different from each other, with low amplitude peaks being extremely frequent, while the higher the peaks the rarer it is.

The tradeoff commonly adopted is using DMT/OFDM is to select a sub-optimal dynamic range for the transmitter that results in clipping of the transmitted signal so that the related Bit Error Rate, BER, is within a preselected limit. Existing system, for instance wireline copper xDSL systems and wireless systems, accept a compromise of a Power Amplifier supply voltage corresponding to PAR=12dB able to guarantee BER = 1x10^~7, an error rate low enough to be corrected by Forward Error Correction, FEC. The maximum acceptable PAR is a parameter representing a compromise between conversion accuracy (quantization noise) at the digital to analogue converter, DAC, and at the analogue to digital converter, ADC, of an OFDM transceiver and the clipping probability, as well as compromise between the power amplifier (when present) or the electro-optical conversion (in an optical transmission system) dynamics and the clipping probability.

Many methods have been proposed to try to get control over the PAR, but none of them has ever been adopted due to unacceptable drawbacks such as heavy performance degradation and high additional cost. One proposed method is tones reservation in which a subset of the N_sc carriers available in band are reserved, and "dummy" data is inserted on them that can be simply ignored at the receiver, but that at the transmitter can be controlled in terms of amplitude and phase, computed in such a way to reduce the PAR. This has been reported, for example, by Brian S. Krongold and Douglas L. Jones, "An active-set approach for OFDM PAR reductions via tone reservation", IEEE Transactions on Signal Processing, vol. 52, no.2, February 2004, pages 495-509.

Let's assume the set of reserved tones Ur and as Ut the set of tones left to the data transport, where Ur and Ut are disjoined groups of the available N_sc tones. In the discrete-time domain, a peak-cancelling c„ signal composed by the reserved tones can be written as:

designing a pulse relatively narrow and enough high, by acting on the coefficients C*. The transmitted signal can then be written, in the discrete-time domain, as:

where x'„ is the modified DMT/OFDM symbol having mitigated PAR, x„ is the original DMT/OFDM signal related to data transport and c„ is the peak-cancelling signal. To be effective, the peak-cancelling signal must be optimized for each DMT/OFDM symbol that requires PAR reduction, by means of a dedicated algorithm defining a clipping A_cu_P threshold, and then searching the coefficients, c_n, so that the resultant PAR of the signal x'„ is < A_cu_P. To avoid having to reiterate the inverse discrete Fourier transform, IDFT, the peak-cancelling signal is inserted after the IDFT operation. The main drawback of this method is that it suffers a constant bitrate reduction irrespective of the clipping probability, since the reserved tones can never be used for data transmission even for those DMT/OFDM symbols not requiring peak- cancelling, assuming we don't want to send to the receiver a symbol-by-symbol repartition of the available sub-carriers with all the risks related to such explicit communication.

Another method similar to tones reservation, is tones injection. The main difference with this method is that tones used to form the peak-cancelling signal share the same frequency as a subset of the OFDM subcarriers and are therefore overlapped. This is done in the attempt to minimize the data throughput losses, since all the tones available remain always active. Unfortunately the peak-cancelling signal in this method results in quite high noise negatively influencing performance. Moreover, the non-negligible power of the tones used to form the peak-cancelling signal add to the power of the subcarrier signals so they need to be reduced in order to comply with power spectral density, PSD constraints, further jeopardizing performance.

Summary

It is an object to provide an improved method of OFDM transmission. It is a further object to provide an improved transmitter.

An aspect of the invention provides a method of OFDM transmission. The method comprises providing an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band. Then, identifying a power peak in the OFDM symbol having a maximum peak-to-average-ratio and determining an amplitude of the power peak and a phase of the power peak. The method comprises providing a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak. The peak-cancelling signal is formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band. The method comprises summing the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol and then converting the modified OFDM symbol into an analogue signal.

The method may enable the PAR of an OFDM symbol to be reduced. The method may enable PAR reduction without causing an increase in one or more of BER, signal to noise ratio, SNR, and latency, and without reducing the number subcarrier frequencies available for data transmission. Reducing the PAR may avoid clipping of the carrier signal, so no BER is introduced allowing forward error correction, FEC, simplification or even avoidance, and may avoid any quantization noise increase due to suboptimal exploitation of component dynamics, such as DAC/ADC.

The term OFDM as used here encompasses both OFDM and DMT, the baseband version of OFDM.

In an embodiment, the peak-cancelling signal is provided by selecting one of a plurality of pre-calculated peak-cancelling signals. The selected peak-cancelling signal has a phase and has an opposite amplitude to the power peak. The phase of the selected pre-calculated peak- cancelling signal is then shifted to be substantially the same as the phase of the power peak. This may reduce the complexity of the method and thus the processing time and any associated latency.

In an embodiment, the amplitude of the selected pre-calculated peak-cancelling signal is scaled in proportion to the amplitude of the power peak. This may enable reduction of the PAR of an OFDM symbol without requiring iteration. The method may enable the PAR of an OFDM symbol to be reduced by at least 3dB, halving the maximum power peak amplitude.

In an embodiment, the pre-calculated peak-cancelling signals are sampled signals.

In an embodiment, anti-alias filtering is performed on the OFDM symbol and the power peak is identified after the anti-alias filtering. This may avoid peak regrowth due to oversampling within the anti-alias filtering.

In an embodiment, a plurality of the sub-signals have respective frequencies below the subcarrier frequency band and a plurality of the sub-signals have respective frequencies above the subcarrier frequency band.

In an embodiment, the subcarriers are orthogonal subcarriers and the sub-signals are orthogonal with respect to the subcarriers. This may minimize inter-carrier-interference, ICI, between the sub-signals and the subcarriers.

In an embodiment, the sub-signals are synchronous with the subcarriers, being based on the same reference clock.

In an embodiment, the OFDM symbol is only summed with the peak-cancelling signal if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold. This may avoid unnecessary application of the rest of the method when the power peak will not cause clipping. In an embodiment, the method additionally comprises identifying an additional power peak having an absolute amplitude value at least equal to the predetermined amplitude threshold and providing an additional peak-cancelling signal formed from an additional plurality of sub-signals having respective frequencies outside the subcarrier frequency band. The additional peak-cancelling signal comprises an impulse having an opposite amplitude to the additional power peak and has a phase substantially the same as the phase of the additional power peak. The OFDM symbol is additionally summed with the additional peak-cancelling signal to form the modified OFDM symbol. This may enable a more aggressive PAR reduction to be performed when there is some probability of having more than one peak above the threshold in the same OFDM symbol, by providing two, or even more, peak cancelling signals by means of two or more distinct sets of out-of-band sub-signals.

In an embodiment, the method additionally comprises identifying a power peak in the modified OFDM symbol having a maximum peak-to-average-ratio, determining an amplitude of the power peak and summing the modified OFDM symbol with the peak-cancelling signal if an absolute value of the amplitude of the power peak in the modified OFDM symbol is at least equal to a predetermined amplitude threshold.

In an embodiment, this is performed iteratively until the absolute amplitude of all identified power peaks are less than the predetermined amplitude threshold. This may enable a more aggressive PAR reduction to be performed when a particularly high number of power peaks exist within an OFDM symbol.

In an embodiment, the method additionally comprising filtering the analogue signal to remove frequencies corresponding to the sub-signals and transmitting the filtered analogue signal. The PAR of the OFDM symbol may therefore be reduced for the process of conversion into an analogue signal and the original OFMD symbol then recovered prior to transmission.

In an embodiment, the method additionally comprises transmitting the analogue signal, receiving the analogue signal following transmission and downconverting the received analogue signal to recover the modified OFDM symbol. The recovered modified OFDM symbol is then filtered to remove the sub-signals. The sub-signals may therefore be transmitted with the modified OFDM symbol enabling an analogue-to-digital converter, ADC, at a receiver configured to receive the carrier signal also to be optimized by means of the reduced PAR.

In an embodiment, the method additionally comprises transmitting the analogue signal, receiving the analogue signal following transmission and downconverting the received analogue signal to recover the modified OFDM symbol. Only the subcarriers are then selected from the received modified OFDM symbol. The sub-signals may therefore be transmitted with the modified OFDM symbol enabling an analogue-to-digital converter, ADC, at a receiver configured to receive the carrier signal also to be optimized by means of the reduced PAR.

In an embodiment, the method additionally comprises converting the analogue signal into an optical carrier signal modulated with the modified OFDM symbol; filtering the optical carrier signal to remove optical frequencies corresponding to the sub-signals and transmitting the filtered optical carrier signal. The original OFDM symbol is therefore recovered prior to transmission, and has its original power peaks, but it is downstream of components that are adversely affected by high PAR, such as a DAC and laser used to generate the optical carrier signal. Since the OFDM symbol is fully recovered no additional operation dedicated to PAR control will be required when the OFDM symbol is received following transmission of the carrier signal.

In an embodiment, the method additionally comprises: converting the analogue signal into an optical carrier signal modulated with the modified OFDM symbol; transmitting the optical carrier signal; receiving the transmitted optical carrier signal and downconverting the received optical carrier signal to recover the modified OFDM symbol. The method then comprises one of filtering the recovered modified OFDM symbol to remove the sub-signals or selecting only the subcarriers from the modified OFDM symbol. The sub-signals may therefore be transmitted with the modified OFDM symbol enabling an analogue-to-digital converter, ADC, at a receiver configured to receive the carrier signal also to be optimized by means of the reduced PAR. Transmitting the modified OFDM symbol with reduced PAR benefits optical fibre behaviour during transmission, since a high PAR stimulates fibre non-linear effects. Reducing the PAR of the OFDM symbol may therefore reduce noise added during transmission.

In an embodiment, there is a respective frequency guard band on either side of the subcarrier frequency band and the sub-signals do not have frequencies within the guard bands. This may allow simple passive filtering to be performed straight after the electrical-to-optical conversion to remove optical frequencies corresponding to the sub-signals and therefore to recover the original OFDM symbol and sure that Power Spectral Density, PSD, eventual constraints on the OFDM symbol are met.

In an embodiment, the frequencies of the sub-signals are selected to have enough distance from the subcarrier band to allow a simple passive optical filter to completely eliminate optical frequencies corresponding to the sub-signals but to be not too far from subcarrier band so they can be handled by a digital-to-analogue converter, DAC, used to generate the analogue signal.

Another aspect of the invention provides a transmitter comprising OFDM symbol generation apparatus, OFDM symbol checking apparatus, peak-cancelling signal apparatus, summing apparatus and conversion apparatus. The OFDM symbol generation apparatus is configured to generate an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band. The OFDM symbol checking apparatus is configured to identify a power peak in the OFDM symbol having a maximum peak-to-average- ratio and to determine an amplitude of the power peak and a phase of the power peak. The peak-cancelling signal apparatus is configured to provide a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak. The peak-cancelling signal is formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band. The summing apparatus is configured to sum the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol. The conversion apparatus is configured to convert the modified OFDM symbol into an analogue signal.

The transmitter may enable the PAR of an OFDM symbol to be reduced. The transmitter may enable PAR reduction of an OFDM symbol without causing an increase in one or more of BER, signal to noise ratio, SNR, and latency, and without reducing the number subcarrier frequencies available for data transmission. Reducing the PAR may avoid clipping of the carrier signal, so no BER is introduced allowing forward error correction, FEC, simplification or even avoidance, and avoid any quantization noise increase due to suboptimal exploitation of component dynamics, such as DAC/ADC.

In an embodiment, the peak-cancelling signal apparatus is configured to provide the peak-cancelling signal by selecting one of a plurality of pre-calculated peak-cancelling signals. The selected pre-calculated peak-cancelling signal has a phase and has an opposite amplitude to the power peak. The peak-cancelling signal apparatus is configured to shift the phase of the selected pre-calculated peak-cancelling signal to be substantially the same as the phase of the power peak. This may reduce the complexity of the method and thus the processing time and any associated latency.

In an embodiment, the peak-cancelling signal apparatus is configured to scale the amplitude of the selected pre-calculated peak-cancelling signal in proportion to the amplitude of the power peak. This may enable the PAR of an OFDM symbol to be reduced without requiring iteration. The method may enable the PAR of an OFDM symbol to be reduced by at least 3dB, halving the maximum power peak amplitude.

In an embodiment, the pre-calculated peak-cancelling signals are sampled signals. The transmitter comprises a memory in which samples of the pre-calculated peak-cancelling signals are stored and the peak-cancelling signal apparatus is configured to obtain the samples of the selected pre-calculated peak-cancelling signal from the memory.

In an embodiment, the transmitter additionally comprises an anti-aliasing filter configured to perform anti-aliasing filtering on the OFDM symbol. The OFDM symbol checking apparatus is configured to identify a power peak in the OFDM symbol after the anti-aliasing filter. This may avoid peak regrowth due to oversampling within the anti-alias filtering.

In an embodiment, the sub-signals are synchronous with the subcarriers, being based on the same reference clock. In an embodiment, the summing apparatus is configured to sum the OFDM symbol with the peak-cancelling signal only if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold. This may avoid unnecessary operations when the power peak will not cause clipping

In an embodiment, the OFDM symbol checking apparatus is configured to identify a plurality of power peaks having respective absolute amplitude values at least equal to the predetermined amplitude threshold. The peak-cancelling signal apparatus is configured to provide a plurality of peak-cancelling signals formed from respective pluralities of sub-signals having respective frequencies outside the subcarrier frequency band. The peak-cancelling signals comprises respective impulses having an opposite amplitude to the respective power peak and having phases substantially the same as the phase of the respective power peak. The summing apparatus is configured to sum the OFDM symbol with the plurality of peak- cancelling signals to form a modified OFDM symbol. This may enable a more aggressive PAR reduction to be performed when there is some probability of having more than one peak above the threshold in the same OFDM symbol, by providing two, or even more, peak cancelling signals by means of two or more distinct sets of out-of-band sub-signals.

In an embodiment, the OFDM symbol checking apparatus is additionally configured to identify a power peak in the modified OFDM symbol having a maximum peak-to-average-ratio and determine an amplitude of the power peak. The summing apparatus is additionally configured to sum the modified OFDM symbol with the peak-cancelling signal if an absolute value of the amplitude of the power peak in the modified OFDM symbol is at least equal to a predetermined amplitude threshold.

In an embodiment, the OFDM symbol checking apparatus is configured to operate iteratively until the absolute amplitude of all identified power peaks are less than the predetermined amplitude threshold. This may enable a more aggressive PAR reduction to be performed when particularly high power peaks exist within an OFDM symbol.

In an embodiment, the transmitter additionally comprises a filter configured to filter the analogue signal to remove frequencies corresponding to the sub-signals. The original OFDM symbol may therefore be recovered prior to transmission and has its original power peaks, but it is downstream of the electro-optical conversion apparatus that is adversely affected by high PAR. Since the OFDM symbol is fully recovered no additional operation dedicated to PAR control will be required when the OFDM symbol is received following transmission of the carrier signal.

In an embodiment, the transmitter additionally comprises a power amplifier configured to amplify the analogue signal.

In an embodiment, the conversion apparatus comprises electro-optical conversion apparatus configured to convert the analogue signal into an optical carrier signal modulated with the modified OFDM symbol. The transmitter additionally comprises an optical filter configured to filter the optical carrier signal to remove optical frequencies corresponding to the sub-signals. The original OFDM symbol is therefore recovered prior to transmission and has its original power peaks, but it is downstream of the electro-optical conversion apparatus that is adversely affected by high PAR. Since the OFDM symbol is fully recovered no additional operation dedicated to PAR control will be required when the OFDM symbol is received following transmission of the carrier signal.

In an embodiment, the conversion apparatus comprises a digital-to-analogue, D/A, converter and a laser driven with an output from the D/A converter. The laser may be a direct modulation laser, DML, or an electro-absorption modulated laser, EML. The original OFDM symbol may therefore recovered, having its original power peaks, but it is downstream of components the D/A converter and the laser which are adversely affected by high PAR.

In an embodiment, there is a respective frequency guard band on either side of the subcarrier frequency band and the sub-signals do not have frequencies within the guard bands. This may allow a simple passive filter to be used straight after the optical transmitter to remove optical frequencies corresponding to the sub-signals and therefore to recover the original OFDM symbol and sure that Power Spectral Density, PSD, eventual constraints on the OFDM symbol are met.

In an embodiment, the frequencies of the sub-signals are selected to have enough distance from the subcarrier band to allow a simple passive optical filter to completely eliminate optical frequencies corresponding to the sub-signals but to be not too far from subcarrier band so they can be handled by a digital-to-analogue converter, DAC, used to generate the optical carrier signal modulated with the modified OFDM symbol.

In an embodiment, each guard band has a bandwidth of approximately 10% of a bandwidth of the subcarrier band. This may enable an optical filter configured to reduce the PAR of an OFDM symbol by at least 40dB to be used.

In an embodiment, at least one of the OFDM symbol generation apparatus, the OFDM symbol checking apparatus, the peak-cancelling signal apparatus and the summing apparatus are implemented in a processor.

In an embodiment, the OFDM symbol generation apparatus comprises an inverse discrete Fourier transform, IDFT, module configured to receive a plurality of data symbols and configured to perform an inverse fast Fourier transform, IFFT, on the data symbols to form the OFDM symbol. The peak-cancelling signal is therefore inserted after the IDFT, which may reduce the complexity of the method and thus the processing time and any associated latency.

References to a processor can encompass any kind of logic or analogue circuitry, integrated to any degree, and not limited to general purpose processors, digital signal processors, ASICs, FPGAs, discrete components or logic and so on. References to a processor are intended to encompass implementations using multiple processors which may be integrated together, or co-located in the same node or distributed at different locations for example.

A further aspect of the invention provides a transceiver comprising a transmitter and a receiver. The transmitter comprises OFDM symbol generation apparatus, OFDM symbol checking apparatus, peak-cancelling signal apparatus, summing apparatus and conversion apparatus. The OFDM symbol generation apparatus is configured to generate an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band. The OFDM symbol checking apparatus is configured to identify a power peak in the OFDM symbol having a maximum peak-to-average-ratio and to determine an amplitude of the power peak and a phase of the power peak. The peak-cancelling signal apparatus is configured to provide a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak. The peak-cancelling signal is formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band. The summing apparatus is configured to sum the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol. The conversion apparatus is configured to convert the modified OFDM symbol into an analogue signal. The conversion apparatus comprises electro-optical conversion apparatus configured to convert the analogue signal into an optical carrier signal modulated with the modified OFDM symbol. The receiver is configured to receive a said carrier signal modulated with a said modified OFDM symbol and to downconvert the received carrier signal to recover the modified OFDM symbol. The receiver apparatus is configured to filter the recovered modified OFDM symbol to remove the sub-signals.

The transceiver may enable the PAR of an OFDM symbol to be reduced. The transmitter may enable PAR reduction of an OFDM symbol without causing an increase in one or more of BER, signal to noise ratio, SNR, and latency, and without reducing the number subcarrier frequencies available for data transmission. Reducing the PAR may avoid clipping of the carrier signal, so no BER is introduced allowing forward error correction, FEC, simplification or even avoidance, and avoid any quantization noise increase due to suboptimal exploitation of component dynamics, such as DAC/ADC. The sub-signals may therefore be transmitted with the modified OFDM symbol enabling an analogue-to-digital converter, ADC, within the receiver to be optimized by means of the reduced PAR. Transmitting the modified OFDM symbol with reduced PAR benefits optical fibre behaviour during transmission, since a high PAR stimulates fibre non-linear effects. Reducing the PAR of the OFDM symbol may therefore reduce noise added during transmission.

In an embodiment, the receiver comprises an electrical filter configured to filter the recovered modified OFDM symbol to remove the sub-signals.

In an embodiment, the receiver is configured receive a said carrier signal modulated with a said modified OFDM symbol, downconvert the received carrier signal to recover the modified OFDM and select only the subcarriers from the modified OFDM symbol.

A further aspect of the invention provides a computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out any of the above steps of the method of OFDM transmission. Another aspect of the invention provides a data carrier having computer readable instructions embodied therein. The said computer readable instructions are for providing access to resources available on a processor. The computer readable instructions comprise instructions to cause the processor to perform any of the above steps of the method of OFDM transmission.

In an embodiment, the data carrier is a non-transitory data carrier.

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings.

Brief Description of the drawings

Figure 1 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 2 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 3 illustrates pre-calculated peak-cancelling signals which may be selected from in the method of Figure 2;

Figure 4 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 5 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 6 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 7 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 8 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 9 illustrates a method of OFDM transmission according to an embodiment of the invention;

Figure 10 is a frequency-domain representation of OFDM subcarriers and the peak- cancelling signal sub-signals used in a method of OFDM transmission according to an embodiment of the invention;

Figure 1 1 illustrates the orthogonality of the peak-cancelling signal sub-signals with respect to the OFDM subcarriers in a method of OFDM transmission according to an embodiment of the invention;

Figure 12 illustrates how the pre-calculated peak cancelling signals of Figure 3 may be generated;

Figure 13 illustrates a transmitter according to an embodiment of the invention;

Figure 14 illustrates a transmitter according to an embodiment of the invention;

Figure 15 illustrates a transmitter according to an embodiment of the invention; Figure 16 illustrates a transmitter according to an embodiment of the invention;

Figure 17 illustrates a transmitter according to an embodiment of the invention;

Figure 18 is a frequency-domain view of the OFDM symbol and the peak-cancelling signal in the transmitter of Figure 15;

Figure 19 is a time-domain view of the OFDM symbol and the peak-cancelling signal in the transmitter of Figure 15;

Figure 20 illustrates an optical channel implemented using a transmitter according to an embodiment of the invention;

Figure 21 illustrates an optical channel implemented using a transceiver according to an embodiment of the invention;

Figure 22 illustrates the OFDM subcarrier frequency band and the peak-cancelling signals frequencies used in a simulation of the method of Figure 1 ;

Figure 23 illustrates the OFDM symbol used in the simulation of the method of Figure

1 ;

Figure 24 illustrates the peak-cancelling signal used in the simulation of the method of Figure 1 ; and

Figure 25 illustrates the modified OFDM signal obtained by summing the OFDM symbol of Figure 23 with the peak-cancelling signal of Figure 24.

Detailed description

The same reference numbers will used for corresponding features in different embodiments.

An embodiment of the invention provides a method 10 of OFDM transmission as illustrated in Figure 1. The method 10 comprises providing 12 an OFDM symbol, which comprises a plurality of subcarriers having respective frequencies within a subcarrier frequency band, and identifying 14 a power peak in the OFDM symbol having a maximum peak-to- average-ratio, PAR. The amplitude of the power peak and the phase of the power peak are then determined.

PAR, also referred to as the Peak to Average Power Ratio, PAPR, is the peak power to average, root-mean-squared, RMS, power ratio expressed in dB; it is sometimes also represented as Crest Factor, is the amplitude ratio expressed as simple number:

PAR = lOxLog

Q =

Of course this is not the only peak but just the maximum of many. The maximum PAR, in dB, for an OFDM symbol with n uncorrected sub-carriers is PARMAX = 10 log n + PARc, where PARc is the PAR for each sub-carrier i.e. 3.01dB since the sub-carriers are sine waves. As an example, an OFDM symbol formed from 1000 sub-carriers has a PARMAX of 33.01dB, i.e. it includes extremely rare peaks 2000 times higher than the RMS value. In the method 10, a peak-cancelling signal, formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band, is provided 16. The peak- cancelling signal comprises an impulse having an opposite amplitude to the power peak and a phase substantially the same as the phase of the power peak.

The peak-cancelling signal may be written as:

where K_c is the number of sub-carrier signals and T is the symbol duration.

The OFDM symbol, f, is summed 18 with the peak-cancelling signal to form a modified OFDM symbol, xt , which may be written as:

N_Se -l I -l

*t' = ∑ X_k ^^{(Nsc +k ) ft} + y_{k e}32*{K_e+l!)Aft k

The modified OFDM symbol is then converted 20 into an analogue signal.

The method 10 therefore provides a peak-cancelling signal, formed of Out-of-band' signals, that comprises an impulse with appropriate phase so that, when summed with the OFDM symbol violating the PAR constraints, it is able to consistently reduce the PAR of the OFDM symbol.

The term OFDM as used here encompasses both OFDM and DMT, the baseband version of OFDM. It will be understood that both the OFDM symbol and the peak-cancelling signal are in the continuous time-domain.

An embodiment of the invention provides a method 30 of OFDM transmission illustrated in Figure 2. In this embodiment the peak-cancelling signal is provided by selecting 32 one of a plurality of pre-calculated peak-cancelling signals, for example the peak-cancelling signals 38 illustrated in Figure 3. One of the pre-calculated peak-cancelling signals having an opposite amplitude to the power peak is selected. For example, if the power peak has a power peak with a positive amplitude, the peak-cancelling signal 38a having a negative impulse is selected, and vice versa. The phase of the selected pre-calculated peak-cancelling signal is then shifted 34 to be substantially the same as the phase of the identified power peak and the OFDM symbol is summed 36 with the phase-shifted pre-calculated peak-cancelling signal.

From the basis of the pre-calculated peak-cancelling signals, stored in memory, we only need to select the most suitable for the symbol PAR under analysis and apply a simple phase shift and amplitude scale to adjust to the given symbol. This is a single operation.

The method 30 therefore provides a peak-cancelling signal, formed of Out-of-band' signals, that is an impulse appropriately large, high and with appropriate phase so that, when summed with the OFDM symbol violating the PAR constraints, it is able to consistently reduce the PAR.

An embodiment of the invention provides a method 40 of OFDM transmission illustrated in Figure 4. The method 40 of this embodiment additionally comprises performing 42 anti-alias filtering on the OFDM symbol and the power peak is identified 14 after the anti-alias filtering. Since the peak-cancelling signal is formed from sub-signals outside the subcarrier band, referred to as Out-of-band' signals, it is possible to add the peak-cancelling signal after antialiasing filtering. In this way the PAR of an OFDM symbol can be reduced as soon as it in the continuous-time domain, without running into peak-regrowth problems. Anti-alias filtering is digital filtering required to guarantee out-of-band Power Spectral Density compliance.

To understand peak-regrowth, let's assume we have a PAR just below a preselected amplitude threshold for a certain OFDM symbol, as soon as the PAR is checked in the discrete- time domain, i.e. measured after OFDM symbol generation but before the anti-aliasing filtering. There is a possibility that, as soon as the OFDM symbol is translated into the continuous-time domain, i.e. after anti-aliasing filtering, the PAR of the OFDM symbol doesn't look as good as it was in the discrete-time. This Peak Regrowth effect is caused by the fact that oversampling and filtering performed during anti-aliasing filtering recombine the discrete-time samples and after such recombination one or more peaks larger than the preselected PAR threshold may occur.

An embodiment of the invention provides a method 50 of OFDM transmission, illustrated in Figure 5, in which the OFDM symbol is only summed with the peak-cancelling signal if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold 52.

A further embodiment of the invention provides a method 60 of OFDM transmission, illustrated in Figure 6, in which two or more power peaks are identified 62 and an amplitude and phase is determined for each of the identified power peaks. The absolute amplitude of each of the identified power peaks is compared to a predetermined amplitude threshold.

For each of the identified power peaks having an absolute amplitude that is at least equal to the threshold, a peak-cancelling signal is provided 66 formed from a respective plurality of sub-signals having respective frequencies outside the subcarrier frequency band.

The following mathematical formulation describes two peak-canceling signals yt e y't summed with the OFDM symbol:

Each peak-cancelling signal comprises an impulse having an opposite amplitude to the respective power peak and has a phase substantially the same as the phase of the respective power peak. The OFDM symbol is summed 68 with the peak-cancelling signals relating to the identified power peaks, to form the modified OFDM symbol.

The method 60 of this embodiment may be used to implement a more aggressive PAR reduction, where there is some probability that the OFDM symbol will have more than one peak above the preselected threshold.

A further embodiment of the invention provides a method 70 of OFDM transmission, illustrated in Figure 7. The method of this embodiment additionally comprises filtering 72 the analogue signal to remove frequencies corresponding to the sub-signals before transmitting 74 the analogue signal.

In a method 80 of OFDM transmission according to another embodiment, illustrated in Figure 8, the method additionally comprises converting 82 the analogue signal into an optical carrier signal modulated with the modified OFDM symbol. The optical carrier signal is then filtered 84 to remove optical frequencies corresponding to the sub-signals. The filtered optical carrier signal is transmitted 86. The original OFDM symbol is therefore recovered prior to transmission, and has its original power peaks, but it is downstream of the electro-optical conversion from analogue signal to optical signal, so any part of the electro-optical conversion that would be adversely affected by high PAR, is not exposed to high PAR. Since the OFDM symbol is fully recovered no additional operation dedicated to PAR control will be required when the OFDM symbol is received following transmission of the optical carrier signal.

Another embodiment of the invention provides a method 90 of OFDM transmission, illustrated in Figure 9, which is similar to the method 80 of the previous embodiment, with the following modifications. In this embodiment, the analogue signal is similarly converted 82 into an optical carrier signal modulated with the modified OFDM symbol. But instead of filtering the optical carrier signal before transmitting it the optical carrier signal is transmitted 92 unfiltered across a communications link and received 94 at an end of the communications link. The received carrier signal is then downconverted 96 to recover the modified OFDM symbol.

The recovered modified OFDM symbol is then filtered 98, in the electrical domain, to remove the sub-signals.

Alternatively, the downconversion includes selecting 98 only the subcarriers from the modified OFDM symbol.

The sub-signals may therefore be transmitted with the modified OFDM symbol enabling an analogue-to-digital converter, ADC, at a receiver configured to receive the carrier signal also to be optimized by means of the reduced PAR.

In an embodiment, the method of OFDM transmission may be implemented as an algorithm, as follows:

1. PAR is evaluated after anti-aliasing i.e. at continuous- time domain signal so that any eventual peak regrowth due to the anti-aliasing oversampling is taken into account; 2. if | f| < Aciip, no actions are performed, otherwise peak clipping position (phase) and amplitude are stored; | f| is the absolute amplitude of the identified peak and A_cu_P is the preselected amplitude threshold;

3. with the OFDM symbol is summed with the peak-cancelling yt signal opportunely scaled in amplitude and shifted in phase so to be centered on the identified peak;

4. if |x'f| < Aciip, no further actions are performed, otherwise re-iterate the operation.

Figures 10 to 12 illustrate features of the peak-cancelling signals used in the above embodiments.

As shown in Figure 10, the sub-signals may be arranged in two sets 102, 104, on either side of the subcarriers 100; one set 102 comprises sub-signals having frequencies below the subcarrier frequency band and the other set 104 comprises sub-signals having frequencies above the subcarrier frequency band. In the example illustrated in Figure 10, the sub-signals are equally spaced in frequency and have equal powers but many possible combinations of frequency spacing and power are possible, to design an optimal peak-cancelling signal.

To comply with PSD constraints, the sub-signal frequencies are selected to be sufficiently separated from the in-band subcarrier signals to allow simple passive filtering after the electrical-to-optical conversion to completely eliminate the sub-carrier frequency components and recover the original OFDM symbol. While on the other hand the sub-signals should not be too far separated in frequency from the subcarriers in order to be effective in designing the peak-cancelling signal and to be handled by a DAC during generation of the analogue signal.

The OFDM symbol if formed from a plurality of orthogonal subcarriers. As illustrated in Figure 1 1 , the sub-signals 1 12 of the peak-cancelling signal are spaced in frequency so they are orthogonal to the subcarriers 1 10. The sub-signals are also synchronous with subcarriers, being generated using same reference clock signal.

As noted above, the peak-cancelling signal can be provided by selecting one of a plurality of pre-calculated peak-cancelling signals and then phase shifted and, optionally, amplitude scaled according to the phase and amplitude of the identified power peak.

A continuous time peak-cancelling signal, yt, can pre-calculated as illustrated in Figure 12. The sub-signal frequencies are selected, one set either side of the subcarrier band, as described above, and the amplitudes and frequency spacing of the sub-signals are pre-selected to form a peak-cancelling signal comprising an impulse having a preselected amplitude and phase. An inverse discrete Fourier transform, IDFT, 120 is applied to the sub-signals and then anti-alias filtering 122 is applied, to obtain the continuous time pre-calculated peak-cancelling signal, yt. Samples of the pre-calculated peak-cancelling signal are calculated and stored; the stored samples are used, in some of the above embodiments, to provide a peak cancelling signal that is synchronous with the OFDM subcarriers. Figure 13 illustrates a transmitter 200 according to an embodiment of the invention. The transmitter comprises OFDM symbol generation apparatus 202, OFDM symbol checking apparatus 204, peak-cancelling signal apparatus 206, summing apparatus 208 and conversion apparatus 210. The OFDM symbol generation apparatus is configured to generate an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band. The OFDM symbol checking apparatus is configured to identify a power peak in the OFDM symbol having a maximum peak-to-average-ratio and to determine an amplitude of the power peak and a phase of the power peak. The peak-cancelling signal apparatus is configured to provide a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak. The peak-cancelling signal is formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band. The summing apparatus is configured to sum the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol. The conversion apparatus is configured to convert the modified OFDM symbol into an analogue signal 212.

The transmitter 200 may be configured to implement the method of OFDM transmission described above with reference to any of Figures 1 to 12, in particular the transmitter may be configured as follows.

In an embodiment, the peak-cancelling signal apparatus 206 is configured to provide the peak-cancelling signal by selecting one of a plurality of pre-calculated peak-cancelling signals 38 and shifting the phase of the selected pre-calculated peak-cancelling signal to be substantially the same as the phase of the power peak, as described above with reference to Figures 3, 4 and 12.

Another embodiment provides a transmitter 220 as illustrated in Figure 14. The transmitter 220 additionally comprises an anti-aliasing filter 222 configured to perform antialiasing filtering on the OFDM symbol. The OFDM symbol checking apparatus is provided after the anti-aliasing filter and is configured to identify a power peak in the OFDM symbol after antialiasing filtering has been performed.

In an embodiment, the OFDM symbol checking apparatus 204 is configured to identify a plurality of power peaks having respective absolute amplitude values at least equal to the predetermined amplitude threshold. The peak-cancelling signal apparatus 206 is configured to provide a plurality of peak-cancelling signals formed from respective pluralities of sub-signals having respective frequencies outside the subcarrier frequency band. The peak-cancelling signals comprise respective impulses having opposite amplitudes to the respective power peaks and having phases substantially the same as the phase of the respective power peak. The summing apparatus 208 is configured to sum the OFDM symbol with the plurality of peak- cancelling signals to form a modified OFDM symbol.

Another embodiment provides a transmitter 230 as illustrated in Figure 15, in which the transmitter additionally comprises a filter 234 configured to filter the analogue signal to remove frequencies corresponding to the sub-signals. The original OFDM symbol is fully recovered by leveraging simple filtering.

Another embodiment provides a transmitter 240 as illustrated in Figure 16. In this embodiment, the OFDM symbol generation apparatus is an IDFT module 242 and the transmitter comprises an anti-aliasing filter 244 provided after the IDFT module; the anti-aliasing filter is a digital filter required to guarantee out-of-band Power Spectral Density, PSD, compliance. The peak cancelling signal apparatus comprises a processor 248 configured to perform the PAR optimization algorithm described below, including performing a PAR check on the OFDM symbol to identify a power peak in the OFDM symbol having a maximum peak-to- average-ratio and to determine an amplitude of the power peak and a phase of the power peak.

The peak-cancelling signal is inserted after the anti-aliasing filter. In this way we are able to reduce the PAR of the OFDM symbol as soon as it is in the continuous-time domain, i.e. before it is input to D/A converter, without running into peak-regrowth problems, as described above.

The transmitter comprises a digital-to-analogue, D/A, converter 252 and a laser 254, such as a direct modulation laser, DML, or an electro-absorption modulated laser, EML, driven with the output from the D/A converter, i.e. with an analogue electrical signal comprising an indication of the modified OFDM symbol. A passive optical filter 256 configured to filter the optical carrier signal to remove optical frequencies corresponding to the sub-signals is provided directly after the laser 254.

The PAR optimization algorithm comprises:

1. PAR is evaluated after the anti-aliasing filter i.e. on the continuous- time domain signal f, so that any peak regrowth due to oversampling by the anti-aliasing filter is taken into account.

2. if | f| < Aciip, no actions are performed, otherwise the peak clipping phase and amplitude are stored.

3. the identified peak is summed with the peak-canceling signal yt opportunely scaled in amplitude and shifted in phase so to be centered at the peak.

The PAR optimization algorithm results in OFDM symbols input to the D/A converter

252 and then to the laser 254 having amplitude A < A_Cii_P allowing dynamic-range exploitation optimization at both, but including the out-of-band sub-signal frequency components. In this example, the sub-signals are provided as two distinct sets, one below and one above the subcarrier band, as illustrated in Figure 10, and the sub-signals are equi-spaced in frequency and are equi-powered. To comply with PSD constraints, the sub-signals of the peak- cancelling signal are selected so to have enough distance from the subcarrier band, to allow to a simple passive filter positioned just after the electrical-to-optical conversion to completely eliminate the corresponding frequency components and therefore to recover the original symbol. While on the other hand the sub-signals cannot be too far from the subcarrier band in order to be effective in designing the peak-canceling signal and to be handled by the D/A converter. As soon as the peak-canceling signal components have been eliminated, the symbol is recovered as it was before summing with the peak-cancelling signal, i.e. the OFDM symbol will have original PAR (and content) but the signal is now downstream of the critical components that may be affected by high PAR.

Since it is fully recovered, at the receiver the OFDM symbol doesn't need any specific operation dedicated to PAR control, or any other additional operation. Furthermore, the method eliminates any clipping at the laser 254 and D/A converter 252, and therefore avoids an increase in noise, avoiding SNR being made worse. In other words, the method eliminates any compromise between PAR reduction and performance such as reduced number of subcarriers (such as in tone reservation), increased noise, increased latency, etc.

The summing apparatus 250 is configured to sum the OFDM symbol with the peak- cancelling signal only if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold.

Another embodiment provides a transmitter 260 as illustrated in Figure 17. In this embodiment, the peak cancelling signal apparatus comprises a processor 262 configured to perform the PAR optimization algorithm but using samples of a pre-calculated peak-cancelling signal to provide the peak-cancelling signal, as described above.

Figure 18 illustrates a frequency-domain view of the signals in the transmitter 240 of Figure 16. Figure 18 illustrates the OFDM symbol 280 and the peak-cancelling signal 282, the summed signals 284 after the summing apparatus 250, the optical signal modulated with the modified OFDM symbol 286 and the optical signal modulated with the recovered original OFDM symbol 288 after the optical filter 256 (after the sub-carrier signals have been removed).

Figure 19 illustrates a time-domain view of the signals in the transmitter 240 of Figure

16.

Figure 20 illustrates an optical channel implemented using the transmitter 240 of Figure 16 at one end of an optical link 258, with a receiver, Rx, at the other end of the optical link. The receiver is configured to downconvert the received optical carrier signal to recover the OFDM symbol. In this example, the receiver comprises a photodetector 260 in the form of a PIN diode and a transimpedance amplifier, TIA, and an analogue to digital converter, ADC, 262.

By means of the PAR reduction performed at the transmitter, we are able to improve the performance of just the DAC or the laser. Then, the optical filter re-establishes the OFDM symbol as originally received, as if no PAR reduction actions have been performed. The optical filter recovers the original OFDM symbol having its original power peaks but the OFDM symbol is now downstream of the components, i.e. the DAC and the laser, which are adversely affected by high PAR. The advantage of this approach is that extra carriers (the sub-signals), i.e. extra- frequencies and extra-power, are not transmitted across the optical link, which might be useful for instance when several systems share in frequency the same medium.

The components of a transceiver 300 according to a further embodiment of the invention are illustrated in Figure 21. The transceiver 300 comprises a transmitter, Tx, 302 and a receiver, RX, 304.

The transmitter is as illustrated in any of Figures 16 to 20, but without an optical filter. In this embodiment, the modified OFDM symbol is converted into an analogue signal, and the analogue signal is converted into an optical carrier signal by the DAC 252, driver 253 and laser 254, which may be a DML or EML. The optical carrier signal is then transmitted across the optical link 258.

The receiver, Rx, comprises a photodetector 260, an ADC 262 and an electrical filter 272. The photodetector 260 comprises a PIN diode and a transimpedance amplifier, TIA. The electrical filter 272 is configured to filter the received modified OFDM symbol, following detection and analogue to digital conversion, to remove the sub-signals.

At the electrical filter output, the symbol is recovered to its original PAR, and may then be sent to further decoding operations, such as Cyclic-Prefix removal, serial to parallel conversion, Discrete Fourier Transformation, DFT, etc.

In another embodiment, the rather than including an electrical filter, the receiver 304 is configured to ignore received components corresponding to the sub-signals.

As a further possibility, due to the fact that the Cyclic-Prefix does not alter the PAR, it is possible to act after the Cyclic-Prefix removal and after the DFT, i.e. in the frequency domain, by simply ignoring the out-of-band sub-signals.

The OFDM symbol may therefore be transmitted with the sub-signals of the peak- cancelling signal, which may be used to resolve PAR issues at the ADC dynamic on the receiver and PAR related non-linearities in the fibre. Since the sub-signals are outside the subcarrier band, there is no need to exchange information dedicated to PAR control between the two ends of the optical link.

Referring to Figures 22 to 25, a simulation was run to reduce the PAR of a DMT/OFDM signal composed of 1000 subcarriers. The scope of the simulation was to demonstrate that it is possible to realize a good peak-cancelling signal by making use of out-of-band sub-signals. The simulation did not attempt to minimize the number of out-of-band sub-signals used to form the peak-cancelling signal, but simply tested a few combinations of equi-spaced and equi-powered sub-signals; it will be understood that many other combinations are possible. The simulation used 70 out-of-band sub-signals having frequencies below the subcarrier band, positioned at a frequency range -10% below the lower bandwidth limit, and 70 out-of-band sub-signals having frequencies above the subcarrier band, positioned at a frequency range -10% above the upper bandwidth limit. A guard band of +/-10% was selected to get an ideal attenuation of >40dB of the out-of-band sub-signals, and the simulation of a commercial filter resulted in a 42dB attenuation. Figure 21 illustrates the subcarrier band 400 and the frequency range allocations of the out-of-band sub-signals 402, 404 used to build the peak-cancelling signal.

Figure 23 shows the DMT/OFDM symbol signal and its huge peak. Figure 24 shows the peak-cancelling signal formed using the out-of-band sub-signals 402, 404 shown in Figure 21. Figure 25 shows the modified DMT/OFDM symbol signal, with reduced PAR i.e. the peak amplitude reduction achieved by means of the peak-cancelling signal.

The peak-cancelling signal of Figure 24 was able to reduce the PAR of the OFDM symbol by 3.34dBm. This means the peak-cancelling operation has halved the PAR of the DMT/OFDM symbol.

A further embodiment of the invention provides a computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out any of the above steps of the method of OFDM transmission.

Another embodiment of the invention provides a data carrier having computer readable instructions embodied therein. The said computer readable instructions are for providing access to resources available on a processor. The computer readable instructions comprise instructions to cause the processor to perform any of the above steps of the method of OFDM transmission.

In an embodiment, the data carrier is a non-transitory data carrier.

Claims

A method of OFDM transmission, the method comprising:

providing an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band;

identifying a power peak in the OFDM symbol having a maximum peak-to-average- ratio and determining an amplitude of the power peak and a phase of the power peak; providing a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak, the peak-cancelling signal being formed from a plurality of sub- signals having respective frequencies outside the subcarrier frequency band;

summing the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol; and

converting the modified OFDM symbol into an analogue signal.

A method as claimed in claim 1 , wherein the peak-cancelling signal is provided by selecting one of a plurality of pre-calculated peak-cancelling signals, the selected peak-cancelling signal having a phase and having an opposite amplitude to the power peak, and wherein the phase of the selected pre-calculated peak-cancelling signal is shifted to be substantially the same as the phase of the power peak.

A method as claimed in any preceding claim, additionally comprising performing anti- alias filtering on the OFDM symbol and wherein the power peak is identified after the anti-alias filtering.

A method as claimed in any preceding claim, wherein a plurality of the sub-signals have respective frequencies below the subcarrier frequency band and a plurality of the sub-signals have respective frequencies above the subcarrier frequency band. A method as claimed in any preceding claim, wherein the OFDM symbol is only summed with the peak-cancelling signal if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold.

A method as claimed in claim 5, additionally comprising:

identifying an additional power peak having an absolute amplitude value at least equal to the predetermined amplitude threshold; and

providing an additional peak-cancelling signal formed from an additional plurality of sub-signals having respective frequencies outside the subcarrier frequency band, the additional peak-cancelling signal comprising an impulse having an opposite amplitude to the additional power peak and having a phase substantially the same as the phase of the additional power peak, and

wherein the OFDM symbol is additionally summed with the additional peak-cancelling signal to form the modified OFDM symbol.

7. A method as claimed in any preceding claim, additionally comprising filtering the analogue signal to remove frequencies corresponding to the sub-signals and transmitting the filtered analogue signal.

8. A method as claimed in any of claims 1 to 6, additionally comprising converting the analogue signal into an optical carrier signal modulated with the modified OFDM symbol, filtering the optical carrier signal to remove optical frequencies corresponding to the sub-signals and transmitting the filtered optical carrier signal.

9. A method as claimed in any of claims 1 to 6, additionally comprising: converting the analogue signal into an optical carrier signal modulated with the modified OFDM symbol; transmitting the optical carrier signal; receiving the transmitted optical carrier signal and downconverting the received optical carrier signal to recover the modified OFDM symbol; and one of filtering the recovered modified OFDM symbol to remove the sub-signals or selecting only the subcarriers from the modified OFDM symbol.

10. A transmitter comprising:

OFDM symbol generation apparatus configured to generate an OFDM symbol comprising a plurality of subcarriers having respective frequencies within a subcarrier frequency band;

OFDM symbol checking apparatus configured to identify a power peak in the OFDM symbol having a maximum peak-to-average-ratio and configured to determine an amplitude of the power peak and a phase of the power peak;

peak-cancelling signal apparatus configured to provide a peak-cancelling signal comprising an impulse having an opposite amplitude to the power peak and having a phase substantially the same as the phase of the power peak, the peak-cancelling signal being formed from a plurality of sub-signals having respective frequencies outside the subcarrier frequency band;

summing apparatus configured to sum the OFDM symbol with the peak-cancelling signal to form a modified OFDM symbol; and

conversion apparatus configured to convert the modified OFDM symbol into an analogue signal.

11. A transmitter as claimed in claim 10, wherein the peak-cancelling signal apparatus is configured to provide the peak-cancelling signal by selecting one of a plurality of pre- calculated peak-cancelling signals, the selected pre-calculated peak-cancelling signal having a phase and having an opposite amplitude to the power peak, and wherein the peak-cancelling signal apparatus is configured to shift the phase of the selected pre- calculated peak-cancelling signal to be substantially the same as the phase of the power peak.

12. A transmitter as claimed in claim 10 or claim 11 , additionally comprising an antialiasing filter configured to perform anti-aliasing filtering on the OFDM symbol, wherein the OFDM symbol checking apparatus is configured to identify a power peak in the OFDM symbol after the anti-aliasing filter.

13. A transmitter as claimed in any of claims 10 to 12, wherein a plurality of the sub- signals have respective frequencies below the subcarrier frequency band and a plurality of the sub-signals have respective frequencies above the subcarrier frequency band.

14. A transmitter as claimed in any of claims 10 to 13, wherein the summing apparatus is configured to sum the OFDM symbol with the peak-cancelling signal only if an absolute value of the amplitude of the power peak is at least equal to a predetermined amplitude threshold.

15. A transmitter as claimed in claim 14, wherein the OFDM symbol checking apparatus is configured to identify a plurality of power peaks having respective absolute amplitude values at least equal to the predetermined amplitude threshold, the peak- cancelling signal apparatus is configured to provide a plurality of peak-cancelling signals formed from respective pluralities of sub-signals having respective frequencies outside the subcarrier frequency band, the peak-cancelling signals comprising respective impulses having an opposite amplitude to the respective power peak and having phases substantially the same as the phase of the respective power peak, and the summing apparatus is configured to sum the OFDM symbol with the plurality of peak-cancelling signals to form a modified OFDM symbol.

16. A transmitter as claimed in any of claims 10 to 15, wherein the transmitter additionally comprises a filter configured to filter the analogue signal to remove frequencies corresponding to the sub-signals.

17. A transmitter as claimed in any of claims 10 to 15, wherein the conversion apparatus comprises electro-optical conversion apparatus configured to generate an optical carrier signal modulated with the modified OFDM symbol and the transmitter additionally comprises an optical filter configured to filter the optical carrier signal to remove optical frequencies corresponding to the sub-signals.

18. A transceiver comprising:

a transmitter as claimed in any of claims 10 to 15, wherein the conversion apparatus comprises electro-optical conversion apparatus configured to convert the analogue signal into an optical carrier signal modulated with the modified OFDM symbol; and a receiver configured to: receive a said optical carrier signal modulated with a said modified OFDM symbol; downconvert the received optical carrier signal to recover the modified OFDM symbol; and one of filter the recovered modified OFDM symbol to remove the sub-signals and select only the subcarriers from the modified OFDM symbol. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out the method according to any one of claims 1 to 9.