Spectral optimization for communication under a peak frequency-domain power constraint

• US 6,839,429 B1
• Filed: 03/10/1999
• Issued: 01/04/2005
• Est. Priority Date: 12/19/1997
• Status: Expired due to Fees

• Current Assignee: Rice University
• Original Assignee: Rice University
• Inventors: Baraniuk, Richard G., Gaikwad, Rohit V.
• Primary Examiner(s): Isen, F. W.
• Assistant Examiner(s): SINGH, RAMNANDAN P
• Application Number:
  US09/266,413
• Time in Patent Office: 2,127 Days
• Field of Search: 379/417, 375/295, 375/296, 375/297, 455/63.1, 455/63.3, 455/67.13, 455/114.2, 455/115.3, 455/452.2, 455/455, 455/509, 455/513
• US Class Current: 379/417
• CPC Class Codes: H04L 27/00 Modulated-carrier systems
• CPC Class Codes: H04L 27/2614 Peak power aspects
• CPC Class Codes: H04L 27/2646 using feedback from receiver for adjusting OFDM transmission parameters, e.g. transmission timing or guard interval length
• CPC Class Codes: H04L 5/14 Two-way operation using the same type of signal, i.e. duplex
• CPC Class Codes: H04W 52/346 distributing total power among users or channels

Abstract

System and methods for determining an optimized transmit spectra (spectral distributions of transmission power) for a set of communications channels that experience cross-talk among themselves and for transmitting data on the channels. The transmit spectra are preferably constructed so that largely contiguous frequency bands are allocated to each signaling direction (upstream/downstream) on each communications channel and/or to each channel in the set of channels. In one embodiment, each communications channel is restricted to a maximum time-averaged power. The method preferably includes steps of determining the channel transfer functions of the communications channel, determining interference characteristics of the channels, calculating substantially optimal transmit spectra for the communications channels, and redistributing the frequency bins so that they are contiguously grouped in each transmit spectra. The contiguous groupings allow wider frequency bands for signaling in the channel. In one embodiment, the channel is limited by a “peak-power constraint.”

Claims

1. A method for communicating data on a set of communications channels limited by predetermined peak power constraints in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels;

determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraints in frequency, wherein said determining the transmit spectra comprises using a peak-constrained water-filling technique to determine power spectral density functions for the set of communications channels; and

transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra.

2. The method of claim 1, wherein one or more of the communications channels are further limited to a predetermined average power, and wherein one or more of the transmit spectra are determined in response to the predetermined average power.

3. The method of claim 1, wherein said transmitting data on the set of communications channels comprises transmitting data using one type of service on all communications channels in the set of communications channels.

4. The method claim 1, wherein the communications channels in the set of communications channels carry one type of service from the group consisting of:

xDSL, ISDN, T1, T2, Tn, cable modem, and wireless modem.

5. The method claim 1, wherein the set of communications channels is a subset of a set of communications channels carrying one type of service.

6. The method of claim 1, wherein at least one communications channel in the set of communications channels is a twisted-pair line.

7. The method of claim 1, wherein said transmitting data on the set of communications channels comprises transmitting the data in discrete multi-tone signals.

8. The method of claim 1, wherein the predetermined peak power constraint in frequency is a constraining static PSD mask.

9. The method of claim 1, wherein said determining the transmit spectra comprises determining one upstream transmit spectrum for the set of communications channels and one downstream transmit spectrum for the set of communications channels.

10. The method of claim 1, wherein said determining the transmit spectra comprises determining one transmit spectrum for each one of the communications channels in the set of communications channels.

11. The method of claim 1, wherein said determining the transmit spectra comprises determining one upstream transmit spectrum for each one of the communications channels in the set of communications channels and determining one downstream transmit spectrum for each one of the communications channels in the set of communications channels.

12. The method of claim 1,

wherein said determining interference characteristics comprises:

determining an amount of uncorrelated interference into the set of communications channels; and

determining an amount of cross-talk coupling among communications channels in the set of communications channels;

wherein the transmit spectra are determined in response to the uncorrelated interference and the amount of cross-talk coupling.

13. The method of claim 1, wherein said determining the transmit spectra comprises determining one or more upstream transmit spectra in response to an upstream portion of the predetermined peak power constraints in frequency and determining one or more downstream transmit spectra in response to a downstream portion of the predetermined peak power constraints in frequency.

14. The method of claim 1, wherein said determining the transmit spectra comprises determining one or more upstream transmit spectra in response to a predetermined average upstream power and determining one or more downstream transmit spectra in response to a predetermined average downstream power.

15. The method of claim 1, wherein the interference includes additive Gaussian noise (AGN);

wherein the transmit spectra are determined in response to the amount of AGN.

16. The method of claim 1, wherein the interference includes different service interference (DSIN);

wherein the transmit spectra are determined in response to the amount of DSIN.

17. The method of claim 1, wherein said determining the channel transfer functions comprises receiving the channel transfer functions.

18. The method of claim 1, wherein said determining the channel transfer functions comprises measuring the channel transfer functions.

19. The method of claim 1, wherein said determining the channel transfer functions is performed in response to a power-up, or at regular intervals in time, or in response to temperature changes.

20. The method of claim 1, wherein said determining interference characteristics and said determining the transmit spectra are dynamically performed each time a data transfer is initiated.

21. The method of claim 1, wherein the transmit spectra are determined so that the communications channels have equal upstream and downstream capacities.

22. The method of claim 1, wherein the transmit spectra are determined so that the communications channels have equal upstream and downstream performance margins.

23. The method of claim 1, wherein the transmit spectra for the set of communications channels are spectrally compatible.

24. The method of claim 1, wherein the transmit spectra for the set of communications channels are spectrally compatible and are configured to substantially maximize a data transmission rate for the communications channels.

25. A method for communicating data on a set of communications channels limited by predetermined peak power constraints in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels;

determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraints in frequency; and

transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra,

wherein said determining the transmit spectra comprises determining one transmit spectrum for each one communications channel in the set of communications channels, wherein said determining one transmit spectrum for one communications channel comprises;

(a) determining a preliminary transmit spectrum S(f) in response to the interference characteristics and the channel transfer function for the one communications channel;

(b) comparing the preliminary transmit spectrum S(f) to the predetermined peak power constraint Q(f); and

(c) in spectral regions where S(f)>

Q(f), modifying the preliminary transmit spectrum S(f) so that S(f)=Q(f) to generate the transmit spectrum for the one communications channel.

26. The method of claim 25, wherein said determining the preliminary transmit spectrum S(f) comprises determining a substantially optimized transmit spectrum.

27. A method for communicating data on a set of communications channels limited by predetermined peak power constraints in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels;

determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraints in frequency; and

transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra,

wherein said determining the transmit spectra comprises determining two transmit spectra for each one communications channel in the set of communications channels, wherein for each communications channel the two transmit spectra are used for signaling in opposite directions along the communications channel, and wherein said determining two transmit spectra for one communications channel comprises;

determining a substantially optimized transmit spectrum S^u(f) for signaling in a first direction in response to the channel transfer function of the one communications channel and in response to the interference characteristics;

determining a first transmit spectrum S_opt^u(f) in the two transmit spectra from the substantially optimized transmit spectrum S^u(f) and from the predetermined peak power constraint in frequency Q(f), wherein S_opt^u(f)=S^u(f) in spectral regions where S^u(f)<

=Q(f) and wherein S_opt^u(f)=Q(f) in spectral regions where S^u(f)>

Q(f), and wherein the first transmit spectrum S_opt^u(f) is useable for transmitting data on the one communications channel in the first direction; and

determining a second transmit spectrum S_opt^d(f) in the two transmit spectra from the first transmit spectrum S_opt^u(f), wherein the second transmit spectrum S_opt^u(f) is complementary to the first transmit spectrum S_opt^u(f), and wherein the second transmit spectrum S_opt^d(f) is useable for transmitting data on the one communications channel in a second direction.

28. The method of claim 27,

wherein said determining the substantially optimized transmit spectrum comprises using a water-filling technique.

29. The method of claim 27,

wherein said determining interference characteristics includes determining an amount of near-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the substantially optimized transmit spectrum S^u(f) comprises determining a transmit spectrum with at least one spectral region of FDS signaling in response to the near-end cross-talk interference.

30. The method of claim 27,

wherein said determining interference characteristics includes determining an amount of near-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the first transmit spectrum and said determining the second transmit spectrum comprise determining the first and second transmit spectra such that the first and second transmit spectra are orthogonally separated in at least one spectral region in response to the near-end cross-talk interference.

31. The method of claim 27,

wherein said determining interference characteristics includes determining an amount of far-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the substantially optimized transmit spectrum S^u(f) comprises determining a transmit spectrum with at least one spectral region of multi-line FDS signaling in response to the far-end cross-talk interference.

32. The method of claim 27,

wherein said determining interference characteristics includes determining an amount of far-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the transmit spectra comprises determining the transmit spectra such that the communications channels in the set of communications channels are orthogonally separated in at least one spectral region in response to the far-end cross-talk interference.

33. A method for communicating data on a set of communications channels limited by predetermined peak power constraints in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels;

determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraints in frequency; and

transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra,

wherein the predetermined peak power constraint in frequency includes a first peak power constraint in frequency Q^u(f) for signaling in a first direction and a second peak power constraint in frequency Q^d(f) for signaling in a second direction, and wherein the communications channels are further limited by a predetermined total power constraint,

wherein said determining the transmit spectra comprises determining two transmit spectra for each one communications channel in the set of communications channels, wherein for each communications channel the two transmit spectra are used for signaling in opposite directions along the communications channel, and wherein said determining the two transmit spectra for one communications channel comprises;

determining a substantially optimized transmit spectrum S^u(f) for signaling in a first direction in response to a channel transfer function of the one communications channel and in response to the interference characteristics;

determining a first constrained transmit spectrum S_opt^u(f) in response to the substantially optimized transmit spectrum S^u(f) and in response to a combined peak power constraint Q(f)=max(Q^u(f), Q^d(f)), wherein S_opt^u(f)=S^u(f) in spectral regions where S^u(f)<

=Q(f) and wherein S_opt^u(f)=Q(f) in spectral regions where S^u(f)>

Q(f);

determining a second constrained transmit spectrum S_opt^d(f) in response to the first constrained transmit spectrum S_opt^u(f), wherein the second constrained transmit spectrum S_opt^d(f) is complementary to the first constrained transmit spectrum S_opt^u(f);

merging the first and second constrained transmit spectra to form a combined constrained transmit spectrum S_opt(f);

determining a first transmit spectrum S₁^u(f) in the two transmit spectra from the combined constrained transmit spectrum S_opt(f) in response to Q^u(f) and Q^d(f);

determining a second transmit spectrum S₁^d(f) in the two transmit spectra from the combined constrained transmit spectrum S_opt(f) in response to Q(f) and Q^d(f);

if a total power of the first transmit spectrum violates the predetermined total power constraint, modifying the first transmit spectrum S₁^u(f) to reduce the total power of the first transmit spectrum; and

if a total power of the second transmit spectrum violates the predetermined total power constraint, modifying the second transmit spectrum S₁^d(f) to reduce the total power of the second transmit spectrum.

34. The method of claim 33,

wherein said determining the substantially optimized transmit spectrum comprises using a water-filling technique to calculate the substantially optimized transmit spectrum.

35. The method of claim 33,

wherein said determining interference characteristics includes determining an amount of near-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the substantially optimized transmit spectrum S^u(f) comprises determining a transmit spectrum with at least one spectral region of FDS signaling in response to the near-end cross-talk interference.

36. The method of claim 33,

wherein said determining interference characteristics includes determining an amount of near-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the first constrained transmit spectrum and said determining the second constrained transmit spectrum comprise determining the first and second constrained transmit spectra such that the first and second constrained transmit spectra are orthogonally separated in at least one spectral region in response to the near-end cross-talk interference.

37. The method of claim 33,

wherein said determining interference characteristics includes determining an amount of far-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the substantially optimized transmit spectrum S^u(f) comprises determining a transmit spectrum with at least one spectral region of multi-line FDS signaling.

38. The method of claim 33,

wherein said determining interference characteristics includes determining an amount of far-end cross-talk interference among channels in the set of communications channels;

and

wherein said determining the transmit spectra comprises determining the transmit spectra such that each communications channel in the set of communications channels is orthogonally separated from other communications channels in the set of communications channels in at least one spectral region in response to the far-end cross-talk interference.

39. The method of claim 33,

wherein the second constrained transmit spectrum is equal to the first constrained transmit spectrum in spectral regions of EQPSD signaling in the first constrained transmit spectrum.

40. The method of claim 33,

wherein the second constrained transmit spectrum is orthogonally separated from the first constrained transmit spectrum in spectral regions of FDS signaling in the first constrained transmit spectrum.

41. The method of claim 33,

wherein the second constrained transmit spectrum is equal to the first constrained transmit spectrum in spectral regions of multi-line FDS signaling in the first constrained transmit spectrum, and wherein each communications channel in the set of communications channels is orthogonally separated from other communications channels in the set of communications channels in spectral regions of multi-line FDS signaling in the first constrained transmit spectrum.

42. The method of claim 33,

wherein said merging the first and second constrained transmit spectra comprises constructing the combined constrained transmit spectrum S_opt(f) such that, in spectral regions of EQPSD signaling in the first constrained transmit spectrum, the combined constrained transmit spectrum S_opt(f) is equal to the first constrained transmit spectrum.

43. The method of claim 33,

wherein said merging the first and second constrained transmit spectra comprises constructing the combined constrained transmit spectrum S_opt(f) such that, in spectral regions of FDS signaling in the first constrained transmit spectrum, the combined constrained transmit spectrum S_opt(f) is equal to the maximum of the first and second constrained transmit spectra.

44. The method of claim 33,

wherein said merging the first and second constrained transmit spectra comprises constructing the combined constrained transmit spectrum S_opt(f) such that, in spectral regions of multi-line FDS signaling in the first constrained transmit spectrum, the combined constrained transmit spectrum S_opt(f) is equal to the maximum of constrained transmit spectra for the communications channels in the set of communications channels.

45. The method of claim 33, wherein said modifying the first transmit spectrum S₁^u(f) to reduce the total power of the first transmit spectrum comprises modifying the first transmit spectrum S₁^u(f) and the second transmit spectrum S₁^d(f) so that the total power of the first transmit spectrum is decreased by an amount of power and so that the total power of the second transmit spectrum is increased by the amount of power.

46. The method of claim 33, wherein said modifying the second transmit spectrum S₁^d(f) to reduce the total power of the second transmit spectrum comprises modifying the second transmit spectrum S₁^d(f) and the first transmit spectrum S₁^u(f) so that the total power of the second transmit spectrum is decreased by an amount of power and so that the total power of the first transmit spectrum is increased by the amount of power.

47. A method for communicating data on a set of communications channels limited by predetermined peak power constraints in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels;

determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraints in frequency; and

transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra,

wherein said determining the interference characteristics comprises determining a noise power spectral density (PSD) for each one of the communications channels in the set of communications channels;

wherein said determining the transmit spectra comprises;

determining a first transmit spectrum S₁(f) for each one of the communications channels in the set of communications channels, wherein the first transmit spectrum for one communications channel has the form given by the following equation;

$S_1<br><br>\left(f\right)=\mathrm{\lambda <br><br>}-\frac{I<br><br>\left(f\right)}{{<br><br>H_C<br><br>\left(f\right)<br><br>}^2},$

wherein I(f) is the noise PSD for the one communications channel, wherein H_C(f) is a channel transfer function for the one communications channel, and wherein λ

is determined in response to a predetermined average power for the one communications channel.

48. A method for communicating data on a communications channel, wherein the communications channel is limited by a predetermined peak power constraint in frequency, and wherein the communications channel is subject to interference, the method comprising:

determining a channel transfer function of the communications channel;

determining interference characteristics of the communications channel;

determining a transmit spectrum in response to the channel transfer function, the interference characteristics, and the predetermined peak power constraint in frequency, wherein said determining the transmit spectrum comprises using a peak-constrained water-filling technique to determine a power spectral density function; and

transmitting data on the communications channel with a spectral power distribution given by the transmit spectrum.

49. The method of claim 48, wherein the communications channel is further limited to a predetermined average power, and wherein the transmit spectrum is determined in response to the predetermined average power.

50. The method of claim 48, wherein the predetermined peak power constraint in frequency is a constraining static PSD mask.

51. The method of claim 48, wherein said determining the transmit spectrum comprises determining an upstream transmit spectrum in response to an upstream portion of the predetermined peak power constraint in frequency and determining a downstream transmit spectrum in response to a downstream portion of the predetermined peak power constraint in frequency.

52. The method of claim 48, wherein said determining the transmit spectrum comprises determining an upstream transmit spectrum in response to a predetermined average upstream power and determining a downstream transmit spectrum in response to a predetermined average downstream power.

53. The method of claim 48, wherein the interference includes additive Gaussian noise (AGN);

wherein the transmit spectrum is determined in response to the amount of AGN.

54. The method of claim 48, wherein the interference includes different service interference (DSIN);

wherein the transmit spectrum is determined in response to the amount of DSIN.

55. The method of claim 48, wherein said determining the channel transfer function comprises receiving the channel transfer function.

56. The method of claim 48, wherein said determining the channel transfer function comprises measuring the channel transfer function.

57. The method of claim 48, wherein said determining the channel transfer function is performed in response to a power-up, or at regular intervals in time, or in response to temperature changes.

58. The method of claim 48, wherein said determining interference characteristics and said determining the transmit spectrum are dynamically performed each time a data transfer is initiated.

59. The method of claim 48, wherein the transmit spectrum is determined so that the communications channel has equal upstream and downstream capacities.

60. The method of claim 48, wherein the transmit spectrum is determined so that the communications channel has equal upstream and downstream performance margins.

61. The method of claim 48, wherein the transmit spectrum is spectrally compatible with the one or more other communications channels.

62. The method of claim 48, wherein the transmit spectrum is configured to substantially maximize a data transmission rate for the communications channel and is spectrally compatible with the one or more other communications channels.

63. The method of claim 48, wherein said determining interference characteristics and said transferring the data are performed a plurality of times;

wherein said determining interference characteristics and said determining the transmit spectrum are performed each time a data transfer is initiated.

64. The method of claim 48, further comprising:

repeating said determining interference characteristics and said determining the transmit spectrum during the data transfer to produce a new transmit spectrum;

wherein the new transmit spectrum is used during a remainder of the data transfer.

65. The method of claim 48, wherein said transmitting data on the communications channel comprises transmitting data on a twisted-pair line.

66. The method of claim 48, wherein said transmitting data on the communications channel comprises transmitting the data on the communications channel in a discrete multi-tone signal.

67. A method for communicating data on a communications channel, wherein the communications channel is limited by a predetermined peak power constraint in frequency, and wherein the communications channel is subject to interference, the method comprising:

determining a channel transfer function of the communications channel;

determining interference characteristics of the communications channel;

determining a transmit spectrum in response to the channel transfer function, the interference characteristics, and the predetermined peak power constraint in frequency; and

transmitting data on the communications channel with a spectral power distribution given by the transmit spectrum,

wherein said determining the transmit spectrum comprises;

(a) determining a preliminary transmit spectrum S(f) in response to the channel transfer function and the interference characteristics;

(b) comparing the preliminary transmit spectrum S(f) to the predetermined peak power constraint Q(f); and

(c) in spectral regions where S(f)>

Q(f), modifying the preliminary transmit spectrum S(f) so that S(f)=Q(f).

68. The method of claim 67, wherein said determining preliminary transmit spectrum S(f) comprises determining a substantially optimized transmit spectrum.

69. A method for communicating data on a communications channel, wherein the communications channel is limited by a predetermined peak power constraint in frequency, and wherein the communications channel is subject to interference, the method comprising:

determining a channel transfer function of the communications channel;

determining interference characteristics of the communications channel;

determining a transmit spectrum in response to the channel transfer function, the interference characteristics, and the predetermined peak power constraint in frequency; and

transmitting data on the communications channel with a spectral power distribution given by the transmit spectrum,

wherein the communications channel is further limited to a predetermined average power, and wherein said determining the transmit spectrum comprises;

(a) determining a first transmit spectrum S₁(f) in response to the channel transfer function and the interference characteristics;

(b) comparing the first transmit spectrum S₁(f) to the predetermined peak power constraint Q(f);

(c) determining a second transmit spectrum S₂(f), wherein S₂(f)=S₁(f) in spectral regions where S₁(f)<

=Q(f) and wherein S₂(f)=Q(f) in spectral regions where S₁(f)>

Q(f);

(d) determining an average power of the second transmit spectrum S₂(f); and

(e) if the average power of the second transmit spectrum S₂(f) is not substantially equal to the predetermined average power, modifying the first transmit spectrum S₁(f) and repeating said steps (b)-(e).

70. The method of claim 69, wherein said determining the first transmit spectrum S₁(f) comprises determining a substantially optimized transmit spectrum.

71. The method of claim 69,

wherein said determining the first transmit spectrum S₁(f) comprises determining a substantially optimized transmit spectrum;

wherein said determining the first transmit spectrum S₁(f) is performed in response to a set of one or more adjustable parameters, and

wherein said modifying the first transmit spectrum S₁(f) comprises changing one or more of the adjustable parameters and redetermining the first transmit spectrum S₁(f) in response to the adjustable parameters.

72. The method of claim 69,

wherein said determining the first transmit spectrum S₁(f) comprises determining a substantially optimized transmit spectrum;

and

wherein said modifying the first transmit spectrum S₁(f) comprises adding or subtracting an offset to the first transmit spectrum S₁(f).

73. The method of claim 69,

wherein said determining the interference characteristics of the communications channel comprises determining a noise power spectral density (PSD) I(f) for the communications channel;

wherein said determining the first transmit spectrum S₁(f) comprises determining a transmit spectrum with the form given by the following equation;

$S_1<br><br>\left(f\right)=\mathrm{\lambda <br><br>}-\frac{I<br><br>\left(f\right)}{{<br><br>H_C<br><br>\left(f\right)<br><br>}^2},$

wherein H_C(f) is the channel transfer function and wherein λ

is a constant;

wherein said modifying the first transmit spectrum S₁(f) comprises changing the constant λ

to minimize a difference between the average power of the second transmit spectrum S₂(f) and the predetermined average power.

74. The method of claim 69,

wherein said determining the interference characteristics of the communications channel comprises determining an amount of channel noise N_o(f) into the communications channel, an amount of near-end cross-talk interference from a communications channel carrying a different type of service DS_N(f) into the communications channel, and an amount of far-end cross-talk interference from a communications channel carrying a different type of service DS_F(f) into the communications channel;

wherein said determining the first transmit spectrum S₁(f) comprises determining a transmit spectrum with the form given by the following equation;

$S_1<br><br>\left(f\right)=\mathrm{\lambda <br><br>}-\frac{N_o<br><br>\left(f\right)+{\mathrm{DS}}_N<br><br>\left(f\right)+{\mathrm{DS}}_F<br><br>\left(f\right)}{{<br><br>H_C<br><br>\left(f\right)<br><br>}^2},$

wherein H_C(f) is the channel transfer function and wherein λ

is a constant;

wherein said modifying the first transmit spectrum S₁(f) comprises changing the constant λ

to minimize a difference between the average power of the second transmit spectrum S₂(f) and the predetermined average power.

75. A method for determining a transmit spectrum for a communications channel, wherein the transmit spectrum is limited by a predetermined peak power constraint in frequency, and wherein the communications channel is subject to interference, the method comprising:

determining a channel transfer function of the communications channel;

determining interference characteristics of the communications channel;

determining the transmit spectrum in response to the channel transfer function, the interference characteristics, and the predetermined peak power constraint in frequency, wherein said determining the transmit spectrum comprises using a peak-constrained water-filling technique to determine a power spectral density function;

wherein the transmit spectrum is useable in communicating data on the communications channel.

76. The method of claim 75, further comprising:

transmitting data on the communications channel using the transmit spectrum.

77. The method of claim 76, wherein said transmitting data on the communications channel comprises transmitting data on a twisted-pair line.

78. The method of claim 76, wherein said transmitting data on the communications channel comprises transmitting the data on the communications channel in a discrete multi-tone signal.

79. The method of claim 75, wherein the transmit spectrum is further limited to a predetermined average power on the communications channel, and wherein the transmit spectrum is determined in response to the predetermined average power on the communications channel.

80. A method for determining transmit spectra for use in communicating data on a set of communications channels, wherein each communications channel in the set of communications channels is limited by a predetermined peak power constraint in frequency, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:

determining channel transfer functions of the set of communications channels;

determining interference characteristics of the set of communications channels; and

determining the transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined peak power constraint in frequency, wherein said determining the transmit spectra comprises using a peak-constrained water-filling technique to determine power spectral density functions for the set of communications channels;

wherein the transmit spectra are useable in communicating data on the communications channels.

81. The method of claim 80, further comprising:

transmitting data on the communications channels using the transmit spectra.

82. The method of claim 81, wherein said transmitting data on the communications channels comprises transmitting the data on the communications channels in a discrete multi-tone signal.

83. The method of claim 80, wherein each communications channel in the set of communications channels is further limited to a predetermined average power, and wherein the transmit spectra are determined in response to the predetermined average power.

84. The method of claim 80, wherein at least one communications channel in the set of communications channels is a twisted-pair line.