Method and apparatus for reducing probability of clipping

Claims

We claim:

1. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output

sequence;

if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation to the IFFT output sequence, thereby to define a transmitted sequence, the transformation-applying step comprising:

decomposing the IFFT output sequence into a first component sequence and a second component sequence;

rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

combining said third and fourth component sequences into a final output sequence.

2. A method according to claim 1 wherein said step of rearranging comprises translating one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is translated with respect to one of the first and second component sequences.

3. A method according to claim 2 wherein said step of rearranging also comprises reversing one of the new component sequences relative to the other.

4. A method according to claim 1 wherein said step of rearranging comprises reversing one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is reversed with respect to one of the first and second component sequences.

5. A method according to claim 3 wherein said step of rearranging also comprises translating one of the new component sequences relative to the other.

6. A method according to claim 1 wherein said first component comprises first initial and first subsequent subsequences of samples of equal length and wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, and

wherein said second component comprises second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

7. A method according to claim 6 wherein only one of the first subsequences is stored in memory and only one of the second subsequences is stored in memory.

8. A method according to claim 1 wherein said at least one transformation comprises at least one power preserving transformation.

9. A method according to claim 8 wherein said first component comprises first initial and first subsequent subsequences of samples of equal length and wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, and

wherein said second component comprises second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

10. A method according to claim 9 wherein said final sequence for transmission comprises a first sequence of samples and said comparison sequence comprises a second sequence of samples and wherein the first sequence of samples comprises a permutation of the second sequence of samples in which signs of none or all of the samples have been inverted.

11. A system according to claim 10 wherein said transformation comprises a plurality of transformations performed respectively on a plurality of subsequences of said preliminary digital output sequence, wherein said plurality of subsequences together forms a partition of said preliminary digital output sequence.

12. A method according to claim 1 wherein said transmitted sequence is characterized in that the original sequence is recovered by first applying an FFT to said transmitted sequence as received, thereby to generate an FFT output, and subsequently applying the inverse transformation, to the FFT output.

13. A method according to claim 12 wherein said first component comprises first initial and first subsequent subsequences of samples of equal length and wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, and

wherein said second component comprises second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

14. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define a final sequence for transmission characterized in that the original sequence is recovered by first applying an FFT to said final sequence as received, thereby to generate an FFT output and subsequently applying the inverse transformation, to the FFT output.

15. A method according to claim 14 wherein said at least one transformation comprises at least one power preserving transformation.

16. A method according to claim 14 wherein said if-applying step comprises applying first and second transformations to the IFFT output sequence without re-computing the IFFT between application of the first transformation and application of the second transformation.

17. A method according to claim 14 wherein said final sequence for transmission comprises a version of a comparison sequence generated by operating one of the following transformations: t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, t.sub.6, t.sub.7 on said IFFT output sequence.

18. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

at a transmitting end,

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define a final sequence for transmission; and

at a receiving end,

recovering the original sequence by first applying an FFT to said final sequence as received, thereby to generate an FFT output and subsequently applying the inverse transformation, to the FFT output.

19. A method according to claim 18 wherein said clipping profile comprises an IFFT output sequence having at least one value exceeding a predetermined clipping threshold.

20. A method according to claim 18 wherein said at least one transformation comprises at least one power preserving transformation.

21. Receiver apparatus comprising:

an FFT unit operative to perform an FFT operation on an incoming sequence, thereby to generate an FFT interim sequence; and

a recovering transformation unit operative to perform a recovering transformation on said FFT interim sequence, wherein performance of said recovering transformation comprises:

computation of additive inverses of at least a portion of the samples within said FFT interim sequence, thereby to define a new interim sequence in which at least a portion of the samples are replaced by their additive inverses respectively.

22. Apparatus according to claim 21 wherein said recovering transformation also comprises a computation of complex conjugates of at least a portion of the samples in the new interim sequence.

23. Apparatus according to claim 21 wherein said portion of samples comprises a subsequence of samples within said FFT interim sequence wherein the intervals between the indices of samples within the subsequence are equal.

24. Receiver apparatus comprising:

an FFT unit operative to perform an FFT operation on an incoming sequence, thereby to generate an FFT interim sequence; and

a recovering transformation unit operative to perform a recovering transformation on said FFT interim sequence, wherein performance of said recovering transformation comprises:

computation of complex conjugates of at least a portion of the samples within said FFT interim sequence.

25. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one power preserving transformation to the IFFT output sequence, thereby to define a transmitted sequence for transmission to a remote terminal.

26. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one power preserving transformation to the IFFT output sequence, thereby to define a transmitted sequence for transmission to a remote terminal,

wherein said transmitted sequence is characterized in that said original sequence is derived from said transmitted sequence by applying an FFT which is an inverse of said IFFT, thereby to define an FFT output sequence, and subsequently performing an inverse of said at least one power preserving transformation on said FFT output sequence.

27. A method according to claim 26 wherein said inverse of said at least one power preserving transformation does not include multiplication operations.

28. A method according to claim 26 wherein said inverse of said at least one power preserving transformation includes no addition/subtraction operations other than computation of additive inverses.

29. A method according to claim 26 wherein said FFT output sequence comprises a plurality of FFT output components and wherein said inverse of said at least one power preserving transformation includes computation of an additive inverse pertaining to at least one of said plurality of FFT output components.

30. A method according to claim 29 wherein said plurality of FFT output components comprises at least one complex FFT output component having an imaginary part and a real part and wherein said computation of an additive inverse comprises compu- tation of an additive inverse of at least one of said imaginary and real parts.

31. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one power preserving transformation to the IFFT output sequence, thereby to define a transmitted sequence for transmission to a remote terminal,

wherein the transmitted sequence comprises a combination of a first permutation of a first component sequence and a second permutation of a second component sequence wherein said first and second component sequences, when combined, yield said IFFT output sequence.

32. A method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence; and

if the IFFT output sequence fits a predetermined clipping profile, applying at least one power preserving transformation to the IFFT output sequence, thereby to define a transmitted sequence for transmission to a remote terminal,

wherein the transformation-applying step comprises:

decomposing the IFFT output sequence into a first component sequence and a second component sequence;

rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

combining said third and fourth component sequences.

33. A system for reducing probability of clipping in a multitone communication transmitter, the system comprising:

a multichannel modulator operative to generate a preliminary digital output sequence;

a transformation unit operative, if the preliminary digital output sequence fits a predetermined clipping profile, to apply at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define a transmitted sequence, the transformation unit comprising:

a decomposer operative to decompose the preliminary digital sequence into a first component sequence and a second component sequence;

a sequence rearranging unit operative to rearrange at least one of the

first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

a final output sequence generator operative to combine said third and fourth component sequences into a final output sequence.

34. A system according to claim 33 wherein all of the plurality of transformations are linear and wherein at least one transformation from among said plurality of transformations is different from at least one other transformation from among said plurality of transformations.

35. A method for reducing probability of clipping in a multitone communication transmitter, the method comprising:

generating a preliminary digital output sequence;

if the preliminary digital output sequence fits a predetermined clipping profile, applying at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define a transmitted sequence, the if-applying step comprising:

decomposing the preliminary digital sequence into a first component sequence and a second component sequence;

rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

combining said third and fourth component sequences into a final output sequence.

36. Receiver apparatus comprising:

an FFT unit operative to perform an FFT operation on an incoming sequence, thereby to generate an FFT interim sequence; and

a recovering transformation unit operative to perform a recovering transformation on said FFT interim sequence, wherein performance of said recovering transformation comprises:

computation of complex conjugates of at least a portion of the samples within said FFT interim sequence,

wherein said portion of the samples comprises a subsequence of samples within said FFT interim sequence wherein the intervals between the indices of samples within the subsequence are equal.

37. A method for controlling the output power of an IFFT-based multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence;

applying at least one transformation to the IFFT output sequence, thereby to define one or more transformed sequences, the transformation-applying step comprising:

decomposing the IFFT output sequence into a first component sequence and a second component sequence;

rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

combining said third and fourth component sequences into a final output sequence; and

responsive to a predetermined criterion, selecting for transmission either the IFFT output sequence or one of the transformed sequences.

38. A method according to claim 37, wherein said step of rearranging comprises translating one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is translated with respect to one of the first and second component sequences.

39. A method according to claim 37, wherein said step of rearranging comprises reversing one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is reversed with respect to one of the first and second component sequences.

40. A method according to claim 37, wherein said at least one transformation comprises at least one power preserving transformation.

41. A method according to claim 40, wherein said first component comprises first initial and first subsequent subsequences of samples of equal length and wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequences of samples, and

wherein said second component comprises second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

42. A method according to claim 37, wherein said transformed sequence is characterized in that the original sequence is recovered by first applying an FFT to said transformed sequence as received, thereby to generate an FFT output, and subsequently applying the inverse transformation to the FFT output.

43. A method for controlling the output power of an IFFT-based multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence;

applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define one or more transformed sequences characterized in that the original sequence is recovered by first applying an FFT to said transformed sequence as received, thereby to generate an FFT output, and subsequently applying the inverse transformation to the FFT output; and

responsive to a predetermined criterion, selecting for transmission either the IFFT output sequence or one of the transformed sequences.

44. A method according to claim 43, wherein said at least one transformation comprises at least one power preserving transformation.

45. A method for controlling the output power of an IFFT-based multitone communication transmitter, the method comprising:

at a transmitting end,

applying an IFFT to an original sequence, thereby to generate an IFFT output sequence;

applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define one or more transformed sequences; and

responsive to a predetermined criterion, selecting for transmission either the IFFT output sequence or one of the transformed sequences; and at a receiving end,

recovering the original sequence by first applying an FFT to said transmitted sequence as received, thereby to generate an FFT output and subsequently, if one of the transformed sequences was selected for transmission, applying the inverse transformation to the FFT output.

46. A method according to claim 45, wherein said at least one transformation comprises at least one power preserving transformation.

47. A method for controlling the output power of an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method comprising:

applying an IFFT to an original sequence thereby to generate an IFFT output sequence;

applying at least one power preserving transformation to the IFFT output sequence, thereby to define one or more transformed sequences; and

responsive to a predetermined criterion, selecting for transmission to a remote terminal either the IFFT output sequence or one of the transformed sequences,

wherein said transformed sequences are characterized in that said original sequence is derived from said transformed sequences by applying an FFT which is an inverse of said IFFT, thereby to define an FFT output sequence, and subsequently performing an inverse of said at least one power preserving transformation on said FFT output sequence.

48. A system for controlling the output power of a multitone communication transmitter, the system comprising:

a multichannel modulator operative to generate a preliminary digital output sequence;

a transformation unit operative to apply at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define one or more transformed sequences, the transformation unit comprising:

a decomposer operative to decompose the preliminary digital sequence into a first component sequence and a second component sequence;

a sequence rearranging unit operative to rearrange at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

a final sequence generator operative to combine said third and fourth component sequences into a final transformed sequence; and

a multiplexer, which is operative to select for transmission either the IFFT output sequence or one of the transformed sequences responsive to a predetermined criterion.

49. A method for controlling the output power of a multitone communication transmitter, the method comprising:

generating a preliminary digital output sequence;

applying at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define one or more transformed sequences, said transformation comprising:

decomposing the preliminary digital sequence into a first component sequence and a second component sequence;

rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences; and

combining said third and fourth component sequences into a final transformed sequence; and

responsive to a predetermined criterion, selecting for transmission either the preliminary digital output sequence or one of the transformed sequences.

50. Transmitter apparatus, comprising:

an IFFT unit, adapted to apply an IFFT to an original multitone sequence for transmission, thereby to generate an IFFT output sequence;

a comparator, adapted to compare a characteristic of the IFFT output sequence to a predetermined criterion;

a transformation generator, adapted to apply at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define one or more transformed sequences characterized in that the original sequence is recovered by first applying an FFT to said final sequence as received, thereby to generate an FFT output and subsequently applying the inverse transformation to the FFT output; and

a multiplexer, adapted to select for transmission either the IFFT output sequence or one of the transformed sequences responsive to the comparison performed by the comparator.

51. Apparatus according to claim 50, wherein the characteristic comprises a magnitude of the IFFT output sequence.

FIELD OF THE INVENTION

The present invention relates to apparatus and methods for reducing the need for clipping in multi-carrier based transmission systems.

BACKGROUND OF THE INVENTION

Discrete Multitone Modulation (DMT), also known as multicarrier modulation or Orthogonal Frequency-Division Multiplexing (OFDM) has been proposed in recent years for applications of transmission of data over severely distorted channels. For instance, this transmission technique has been adopted by ANSI T1E1.4 as the standard technique for the ADSL application.

A multicarrier transceiver divides the available channel bandwidth into a plurality of relatively narrow-band subchannels. These channels are equally spaced across the system bandwidth. Data are transmitted over each subchannel independently of the others. When the transmitter obeys some suitable orthogonal conditions and thus avoids interference between adjacent channels, and the subchannels are sufficiently narrow, then Inter Symbol Interference (ISI) across the subchannel bandwidth is significantly reduced. These conditions date back to R. W. Chang, "Synthesis of band-limited orthogonal signals for multi-channel data transmission," Bell Syst. Tech. Journal, pp. 1775-1796, December 1966. The DMT transmitter can tune the data rate and the transmission power over the individual subchannels according to their transmission characteristics and hence to optimize the system performance.

The transmitted data in a multi-carrier system is grouped in so-called symbols. Each symbol represents a defined time-period and a total number of bits. The bits within a symbol are allocated to the different subchannels. The bits being conveyed over each subchannel are modulated generating a so-called frequency domain vector. This vector includes coordinate sequences representing the constellation point that corresponds to each channel. The coordinates may be drawn for example from a QAM constellation.

The DMT signal is generated by means of a vector frequency-to-time transformation on the plurality of independent frequency-domain coordinates. The common transformation used is the Inverse Fast Fourier Transform (IFFT). Each entry of the IFFT sequence is a sum with a constant phasor shift of all the frequency-domain coordinates. Consequently, the resulting time-domain signal exhibits a high peak-to-average ratio.

This fact in turn has a major impact on the design requirements of the analog circuitry of the DMT transmitter. Statistically, the large amplitude spikes are very rare and in a practical transceiver, when the signal amplitude exceeds the maximum input value of a D/A converter, the output signal is clipped to this threshold level. This operation results in a distorted transmitted signal and it degrades the system performance. Several methods are now described which are regarded as reducing the probability of clipping events in DMT-based systems.

One possible technique to reduce the peak-to-average ratio is to employ pre-coding of the input data. This method requires an appreciable increase of the transmitted line rate and consequently it reduces the energy per data bit and deteriorates performance.

Another method to reduce the peak-to-average ratio is to decrease the amplitude of the entire sequence of samples corresponding to a symbol by a predetermined factor when at least one sample in this sequence is clipped. This technique requires only a few additional bits per symbol to convey the information regarding the "reduction factor" used. Evidently this increase is insignificant. However, the reduction of the transmit power increases the vulnerability of the system to noise and thus it degrades the system performance.

A third method which was proposed very recently employs a properly chosen phasor transformations of the QAM modulated carriers and a plurality of IFFT operations. This method does not degrade the system performance but it entails a significant additional complexity of the DMT transceiver since it accommodates several IFFT computations per symbol period.

The three methods mentioned above are described in detail in references 1 and 2, 3, and 4, respectively:

1. "Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes", A. E. Jones et al., Electronics letters, Vol. 30, No. 25, pp. 2098-2099, Dec. 8th 1994.

2. "Simple coding scheme to reduce peak factor in QPSK multicarrier modulation", S. J. Shepherd et al, Electronics Letters, Vol. 31, No. 14, pp. 1131-1132, Jul. 6th, 1995.

3. U.S. Pat. No. 5,623,513 to Chow et al, and

4. "A method to reduce the probability of clipping in DMT-based transceivers", D. J. G. Mestdagh and P. M. P. Spruyt, IEEE Transactions on Communications, Vol. 44, No. 10, pp. 1234-1238, October 1996.

The disclosures of all publications mentioned in the specification and of

the publications cited therein are hereby incorporated by reference.

SUMMARY OF THE INVENTION

The present invention relates to generally lossless apparatus and methods for reducing the need for clipping in multi-carrier based transmission systems.

In the present application, the term "lossless" is used to denote a transformation that does not increase the susceptibility of a communication system to noise.

The present invention seeks to provide improved apparatus and methods to reduce the probability of clipping occurrence in a multi-carrier based system. Several IFFT computations are preferably avoided by using several transformations of the sample sequence available at the output of the IFFT machine. These transformations may be realized with a reduced complexity in comparison with the methods which perform the transformations on the time-domain vector.

Similarly to some prior art methods of reducing clipping, the methods and apparatus shown and described herein hardly increase the actual transmission rate. Another advantage of a preferred embodiment of the present invention is that the inverse process in the receiver is very simple. The inverse transformations in the receiver are preferably carried out on the frequency-domain vector generated by the FFT.

According to a preferred embodiment of the present invention, the samples are decomposed into two distinct sequences. One sequence carries the information identified with the even-numbered frequency carriers and the second stream corresponds to the information transported over the odd-numbered frequency carriers.

There is thus provided, in accordance with a preferred embodiment of the present invention, a method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method including applying an IFFT to an original sequence thereby to generate an IFFT output sequence, if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation to the IFFT output sequence, thereby to define a transmitted sequence, the transformation-applying step including decomposing the IFFT output sequence into a first component sequence and a second component sequence, rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences, and combining the third and fourth component sequences into a final output sequence.

Further in accordance with a preferred embodiment of the present invention, the step of rearranging includes translating one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is translated with respect to one of the first and second component sequences.

Still further in accordance with a preferred embodiment of the present invention, the step of rearranging includes reversing one of the first and second component sequences with respect to the other along a time axis, thereby to define new component sequences, one of which is reversed with respect to one of the first and second component sequences.

Further in accordance with a preferred embodiment of the present invention, the step of rearranging also includes reversing one of the new component sequences relative to the other.

Still further in accordance with a preferred embodiment of the present invention, the step of rearranging also includes translating one of the new component sequences relative to the other.

Additionally in accordance with a preferred embodiment of the present invention, the first component includes first initial and first subsequent subsequences of samples of equal length and the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, wherein the second component includes second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

Also provided, in accordance with another preferred embodiment of the present invention, is a method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method including applying an IFFT to an original sequence thereby to generate an IFFT output sequence, and, if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define a final sequence for transmission characterized in that the original sequence is recovered by first applying an FFT to the final sequence as received, thereby to generate an FFT output and subsequently applying the inverse transformation, to the FFT output.

Also in accordance with a preferred embodiment of the present invention is a method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method including: at a transmitting end, applying an IFFT to an original sequence thereby to generate an IFFT output sequence, and if the IFFT output sequence fits a predetermined clipping profile, applying at least one transformation, having an inverse transformation, to the IFFT output sequence, thereby to define a final sequence for transmission, and at a receiving end, recovering the original sequence by first applying an FFT to the final sequence as received, thereby to generate an FFT output and subsequently applying the inverse transformation, to the FFT output.

Further in accordance with a preferred embodiment of the present invention, the clipping profile includes an IFFT output sequence having at least one value exceeding a predetermined clipping threshold.

Also provided, in accordance with another preferred embodiment of the present invention, is receiver apparatus including an FFT unit operative to perform an FFT operation on an incoming sequence, thereby to generate an FFT interim sequence, and a recovering transformation unit operative to perform a recovering transformation on the FFT interim sequence, wherein performance of the recovering transformation includes computation of additive inverses of at least a portion of the samples within the FFT interim sequence, thereby to define a new interim sequence in which at least a portion of the samples are replaced by their additive inverses respectively.

Additionally provided, in accordance with another preferred embodiment of the present invention, is receiver apparatus including an FFT unit operative to perform an FFT operation on an incoming sequence, thereby to generate an FFT interim sequence, and a recovering transformation unit operative to perform a recovering transformation on the FFT interim sequence, wherein performance of the recovering transformation includes computation of complex conjugates of at least a portion of the samples within the FFT interim sequence.

Further in accordance with a preferred embodiment of the present invention, the recovering transformation also includes a computation of complex conjugates of at least a portion of the samples in the new interim sequence.

Still further in accordance with a preferred embodiment of the present invention, the portion of samples includes a subsequence of samples within the FFT interim sequence wherein the intervals between the indices of samples within the subsequence are equal.

Further in accordance with a preferred embodiment of the present invention, at least one transformation includes at least one power preserving transformation.

Also provided, in accordance with another preferred embodiment of the present invention, is a method for reducing probability of clipping in an IFFT-based (inverse fast Fourier transform based) multitone communication transmitter, the method including applying an IFFT to an original sequence thereby to generate an IFFT output sequence, and, if the IFFT output sequence fits a predetermined clipping profile, applying at least one power preserving transformation to the IFFT output sequence, thereby to define a transmitted sequence for transmission to a remote terminal.

Further in accordance with a preferred embodiment of the present invention, the transmitted sequence is characterized in that the original sequence is derived from the transmitted sequence by applying an FFT which is an inverse of the IFFT, thereby to define an FFT output sequence, and subsequently performing an inverse of the at least one power preserving transformation on the FFT output sequence.

Still further in accordance with a preferred embodiment of the present invention, the inverse of the at least one power preserving transformation does not include multiplication operations.

Additionally in accordance with a preferred embodiment of the present invention, the inverse of the at least one power preserving transformation includes no addition/subtraction operations other than computation of additive inverses.

Further in accordance with a preferred embodiment of the present invention, the FFT output sequence includes a plurality of FFT output components wherein the inverse of the at least one power preserving transformation includes computation of an additive inverse pertaining to at least one of the plurality of FFT output components.

Additionally in accordance with a preferred embodiment of the present invention, the plurality of FFT output components includes at least one complex FFT output component having an imaginary part and a real part wherein the computation of an additive inverse includes computation of an additive inverse of at least one of the imaginary and real parts.

Further in accordance with a preferred embodiment of the present invention, the transmitted sequence includes a combination of a first permutation of a first component sequence and a second permutation of a second component sequence wherein the first and second component sequences, when combined, yield the IFFT output sequence.

It is appreciated that one of the first and second permutations may be the identity permutation.

Further in accordance with a preferred embodiment of the present invention, the transformation-applying step includes decomposing the IFFT output sequence into a first component sequence and a second component sequence, rearranging at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences, and combining the third and fourth component sequences.

Still further in accordance with a preferred embodiment of the present invention, only one of the first subsequences is stored in memory and only one of the second subsequences is stored in memory.

Further in accordance with a preferred embodiment of the present invention, the if-applying step includes applying first and second transformations to the IFFT output sequence without re-computing the IFFT between application of the first transformation and application of the second transformation.

Still further in accordance with a preferred embodiment of the present invention, the transmitted sequence is characterized in that the original sequence is recovered by first applying an FFT to the transmitted sequence as received, thereby to generate an FFT output, and subsequently applying the inverse transformation, to the FFT output.

Additionally in accordance with a preferred embodiment of the present invention, the first component includes first initial and first subsequent subsequences of samples of equal length wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, and wherein the second component includes second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

Still further in accordance with a preferred embodiment of the present invention, the first component includes first initial and first subsequent subsequences of samples of equal length wherein the values of the first initial subsequence of samples are respectively equal to the values of the first subsequent subsequence of samples, wherein the second component includes second initial and second subsequent subsequences of samples of equal length and wherein the values of the second initial subsequence of samples are respectively additive inverses of the values of the second subsequent subsequence of samples.

Still further in accordance with a preferred embodiment of the present invention, the final sequence for transmission includes a version of a comparison sequence generated by operating one of the following transformations: t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, t.sub.6, t.sub.7 on the IFFT output sequence.

Additionally in accordance with a preferred embodiment of the present invention, the final sequence for transmission includes a first sequence of samples and the comparison sequence comprises a second sequence of samples and the first sequence of samples includes a permutation of the second sequence of samples in which signs of none or all of the samples have been inverted.

Also provided, in accordance with another preferred embodiment of the present invention, is a system for reducing probability of clipping in a multitone communication transmitter, the system including a multichannel modulator operative to generate a preliminary digital output sequence, a transformation unit operative, if the preliminary digital output sequence fits a predetermined clipping profile, to apply at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define a transmitted sequence, the transformation unit including a decomposer operative to decompose the preliminary digital sequence into a first component sequence and a second component sequence, a sequence rearranging unit operative to rearrange at least one of the first and second component sequences with respect to the other, thereby to define third and fourth component sequences, and a final output sequence generator operative to combine the third and fourth component sequences into a final output sequence.

Further in accordance with a preferred embodiment of the present invention, the transformation includes a plurality of transformations performed respectively on a plurality of subsequences of the preliminary digital output sequence, wherein the plurality of subsequences together forms a partition of the preliminary digital output sequence. One or some of the plurality of transformations may be the identity transformation.

Further in accordance with a preferred embodiment of the present invention, all of the plurality of transformations are linear and at least one transformation from among the plurality of transformations is different from at least one other transformation from among the plurality of transformations.

Also provided, in accordance with another preferred embodiment of the present invention, is a system for reducing probability of clipping in a multitone communication transmitter, the system including a multichannel modulator operative to generate a preliminary digital output sequence, a transformation unit operative, if the preliminary digital output sequence fits a predetermined clipping profile, to apply at least one invertible non-linear transformation to the preliminary digital output sequence, thereby to define a transmitted sequence, the transformation unit including a decomposer operative to decompose the preliminary digital sequence into a first compone