Method, apparatus and system for pilotless frequency offset compensation in multipoint-to-point wireless systems with OFDM

• US 20050085249A1
• Filed: 10/16/2003
• Published: 04/21/2005
• Est. Priority Date: 10/16/2003
• Status: Abandoned Application

• Current Assignee: PCTEL, Inc. (Amphenol Corporation)
• Original Assignee: PCTEL, Inc. (Amphenol Corporation)
• Inventors: Okunev, Yuri, Goldstein, Yuri
• Application Number:
  US10/685,615
• Publication Number:
  US 20050085249A1
• Time in Patent Office: Days
• US Class Current: 455/502
• CPC Class Codes: H04L 27/2657 Carrier synchronisation
• CPC Class Codes: H04L 27/2679 Decision-aided

Abstract

Apparatus, methods and systems for frequency offset compensation in multipoint-to-point orthogonal frequency division multiplexing (OFDM) systems are provided. In the hub, frequency offset estimates are made in the frequency domain for each group of carriers of the OFDM system. The hub then transmits indications (parameters) of the frequency offset for each group of carriers to the nodes. Frequency offset compensation is then accomplished in each node, preferably in the time domain.

Claims

1. An orthogonal frequency division multiplexing (OFDM) multipoint-to-point multicarrier wireless telecommunications system, comprising:

a hub including a hub receiver and a hub transmitter; and

a plurality of nodes each having a node receiver and a node transmitter, each said node transmitter for transmitting data over a unique group of carriers at the same time, wherein

said hub receiver is adapted to receive said data from each of said node transmitters and said hub is adapted to use said data to derive a frequency offset estimation for each node transmitter and to send an indication of each said frequency offset estimation to said nodes, and

said node receivers are adapted to receive said indication, and said node is adapted to modify data for transmission based at least partially on said indication.

2. A system according to claim 1, wherein:

said hub includes a fast Fourier transform (FFT) which converts data transmitted by said node transmitters over said carriers and received by said hub receiver into a frequency domain, and

said frequency offset estimation is conducted in said frequency domain.

3. A system according to claim 2, wherein:

said hub includes decision means coupled to said FFT for determining quadrature components X_dkn and Y_dkn of a decision vector from received vector outputs X_kn, Y_kn of said FFT, where n is an index of OFDM symbols and k is an index of said carriers.

4. A system according to claim 3, wherein:

said hub includes means for calculating differential quadrature components dX_kn, dY_kn where dX_kn=(X_kn−

X_dkn) and dY_kn=(Y_kn−

Y_dkn).

5. A system according to claim 4, wherein:

said hub includes means for reducing said differential quadrature components to obtain reduced differential components dX_rkn and dY_rkn according to

dX_rkn=(A₀/A_kn) (dX_kn cos Δ

_kn−

dY_kn sin Δ

_kn), and
dY_rkn=(A₀/A_kn) (dY_kn cos Δ

_kn−

dX_kn sin Δ

_kn),

where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, A_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

6. A system according to claim 5, wherein:

said hub includes means for averaging reduced differential components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{\mathrm{dX}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dX}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dX}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-{\mathrm{dY}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{\mathrm{dY}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dY}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

7. A system according to claim 6, wherein:

N is chosen such that KN is a desired value.

8. A system according to claim 7, wherein:

KN is chosen to be at least 50.

9. A system according to claim 6, wherein:

said hub includes means for generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

10. A system according to claim 9, wherein:

said means for generating an indication includes means for estimating phase shift for each carrier group according to

Sin φ

=[dX_rY₀−

dY_rX₀]/A, and Cos φ

=[(A₀)²+dX_rX₀+dY_rY₀]/A

where φ

is said phase shift, and A=A₀*[(X₀+dX_r)²+(Y₀+dY_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

11. A system according to claim 10, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

12. A system according to claim 10, wherein:

said indication is a function of Sin φ and

Cos φ

.

13. A system according to claim 12, wherein:

said indication is one of φ and

Δ

f where Δ

f=φ

/2π

T.

14. A system according to claim 3, wherein:

said hub includes means for reducing said quadrature components to obtain reduced quadrature components dX_rkn and dY_rkn according to

X_rkn=(A₀/A_kn) (X_kn cos Δ

_kn−

Y_kn sin Δ

_kn),
Y_rkn=(A₀/A_kn) (Y_kn cos Δ

_kn−

X_kn sin Δ

_kn)

where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, A_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

15. A system according to claim 14, wherein:

said hub includes means for averaging reduced quadrature components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{X}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>X_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(X_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-Y_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{Y}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>Y_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(Y_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+X_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

16. A system according to claim 15, wherein:

N is chosen such that KN is a desired value.

17. A system according to claim 16, wherein:

KN is chosen to be at least 50.

18. A system according to claim 15, wherein:

said hub includes means for generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

19. A system according to claim 18, wherein:

said means for generating an indication includes means for estimating phase shift for each carrier group according to

Sin φ

=[X_rY₀−

Y_rX₀]/A, and Cos φ

=[X_rX₀+Y_rY₀]/A

where φ

is said phase shift, and A=A₀*[(X_r)²+(Y_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

20. A system according to claim 19, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

21. A system according to claim 4, wherein:

said hub includes means for reducing said differential quadrature components to obtain reduced differential components dY_rkn according to dY_rkn=(dY_kn cos Δ

_kn+dX_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

22. A system according to claim 21, wherein:

said hub includes means for accumulating signs of the reduced components for each said carrier group.

23. A system according to claim 22, wherein:

said means for accumulating signs accumulates said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right),$

Sign (dY_kn cos Δ

_kn+dX_kn sin Δ

_kn), where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

24. A system according to claim 23, wherein:

N is chosen such that KN is a desired value.

25. A system according to claim 24, wherein:

KN is chosen to be at least 50.

26. A system according to claim 23, wherein:

said hub further includes means for comparing said D₊₋

to a predetermined threshold value T_d.

27. A system according to claim 26, wherein:

said hub includes means for determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

28. A system according to claim 26, wherein:

said hub includes means for determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right)\right].$

Sign (dY_kn cos Δ

_kn+dX_kn sin Δ

_kn)].

29. A system according to claim 3, wherein:

said hub includes means for reducing said quadrature components to obtain reduced quadrature components Y_rkn according to Y_rkn=(Y_kn cos Δ

_kn+X_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

30. A system according to claim 29, wherein:

said hub includes means for accumulating signs of the reduced components for each said carrier group.

31. A system according to claim 30, wherein:

said means for accumulating signs accumulates said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left(Y_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+X_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right),$

Sign (Y_kn cos Δ

_kn+X_kn sin Δ

_kn) , where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

32. A system according to claim 31, wherein:

N is chosen such that KN is a desired value.

33. A system according to claim 32, wherein:

KN is chosen to be at least 50.

34. A system according to claim 29, wherein:

said hub further includes means for comparing said D₊₋

to a predetermined threshold value T_d.

35. A system according to claim 34, wherein:

said hub includes means for determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

36. A system according to claim 34, wherein:

said hub includes means for determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right)\right].$

37. A system according to claim 1, wherein:

a first of said plurality of nodes utilizes a group of carriers including a first plurality of carriers and a second of said plurality of nodes utilizes a group of carrier including a second plurality of carriers different than said first plurality of carriers.

38. A system according to claim 1, wherein:

a first of said plurality of nodes utilizes a group of carriers including a single carrier and a second of said plurality of nodes utilizes a group of carrier including a plurality of carriers different than said single carrier.

39. A system according to claim 1, wherein:

each said node includes an inverse fast Fourier transformer (IFFT) and a signal correction means coupled to said IFFT for frequency offset compensation of data signals applied to and processed by said IFFT.

40. A system according to claim 39, wherein:

said signal correction means corrects a data signal according to X_mc=X_m cos(mφ

)+Y_m sin(mφ

), Y_mc=Y_m cos(mφ

)−

X_m sin(mφ

), where X_m and Y_m are respectively real and imaginary parts of an m-th complex sample of said signal at an output of said IFFT after processing by said IFFT, where m is an integer changing from 1 to M, and M is the number of carriers in said multicarrier system, X_mc and Y_mc are respectively real and imaginary parts of the m-th corrected sample, and φ

is a function of said indication of said frequency offset estimation sent by said hub to said node.

41. A system according to claim 40, wherein:

each said node includes means for calculating a product mφ and

a table which provides cos(mφ

) and sin(mφ

) values to said signal correction means in response to said means for calculating a product mφ

.

42. A system according to claim 40, wherein:

said indication of said frequency offset estimation sent by said hub to said node is one of phase φ and

a function of a change in frequency Δ

f where φ

=2π

Δ

fT and where T is an FFT interval.

43. A system according to claim 1, wherein:

said OFDM system is a time division multiplexed system where at least two of said plurality of nodes transmit on at least one same carrier for transmission but at different times.

56. A hub according to claim 5, wherein:

said indication is one of φ and

Δ

f where Δ

f=φ

/2π

T.

44. A hub for an orthogonal frequency division multiplexing (OFDM) multipoint-to-point multicarrier wireless telecommunications system, comprising:

a hub receiver for receiving data from a plurality of nodes with each node sending said data over a unique group of carriers at the same time, and

a hub transmitter for sending a separate frequency offset estimation for each node, wherein

said hub includes means for utilizing said data to derive each said separate frequency offset estimation.

45. A hub according to claim 44, wherein:

said hub includes a fast Fourier transform (FFT) which converts said data into a frequency domain, and

said means for utilizing said data conducts a frequency offset estimation in said frequency domain.

46. A hub according to claim 45, wherein:

said means for utilizing said data includes decision means coupled to said FFT for determining quadrature components X_dkn and Y_dkn of a decision vector from received vector outputs X_kn, Y_kn of said FFT, where n is an index of OFDM symbols and k is an index of said carriers.

47. A hub according to claim 46, wherein:

said means for utilizing said data includes means for calculating differential quadrature components dX_kn, dY_kn where dX_kn=(X_kn−

Xd_kn) and dY_kn=(Y_kn−

Y_dkn).

48. A hub according to claim 47, wherein:

said means for utilizing said data includes means for reducing said differential quadrature components to obtain reduced differential components dX_rkn and dY_rkn according to

dX_rkn=(A₀/A_kn) (dX_kn cos Δ

_kn−

dY_kn sin Δ

_kn), and
dY_rkn=(A₀/A_kn) (dY_kn cos Δ

_kn−

dX_kn sin Δ

_kn),

where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, Δ

_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

49. A hub according to claim 48, wherein:

said means for utilizing said data includes means for averaging reduced differential components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{\mathrm{dX}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dX}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dX}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-{\mathrm{dY}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{\mathrm{dY}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dY}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

50. A hub according to claim 49, wherein:

N is chosen such that KN is a desired value.

51. A hub according to claim 50, wherein:

KN is chosen to be at least 50.

52. A hub according to claim 49, wherein:

said means for utilizing said data includes means for generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

53. A hub according to claim 52, wherein:

said means for generating an indication includes means for estimating phase shift for each carrier group according to

Sin φ

=[dX_rY₀−

dY_rX₀]/A, and Cos φ

=[(A₀)²+dX_rX₀+dY_rY₀]/A

where φ

is said phase shift, and A=A₀*[(X₀+dX_r)²+(Y₀+dY_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

54. A hub according to claim 53, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

55. A hub according to claim 54, wherein:

said indication is a function of Sin φ and

Cos φ

.

57. A hub according to claim 46, wherein:

said means for utilizing said data includes means for reducing said quadrature components to obtain reduced quadrature components dX_rkn and dY_rkn according to X_rkn=(A₀/A_kn) (X_kn cos A_kn−

Y_kn sin Δ

_kn), Y_rkn=(A₀/A_kn) (Y_kn cos Δ

_kn+X_kn sin A_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, A_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

58. A hub according to claim 57, wherein:

said means for utilizing said data includes means for averaging reduced quadrature components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{X}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>X_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(X_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-Y_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{Y}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>Y_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(Y_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+X_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

59. A hub according to claim 58, wherein:

N is chosen such that KN is a desired value.

60. A hub according to claim 59, wherein:

KN is chosen to be at least 50.

61. A hub according to claim 58, wherein:

said means for utilizing said data includes means for generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

62. A hub according to claim 61, wherein:

said means for generating an indication includes means for estimating phase shift for each carrier group according to

Sin φ

=[X_rY₀−

Y_rX₀]/A, and Cos φ

[X_rX₀+Y_rY₀]/A

where φ

is said phase shift, and A=A₀*[(X_r)²+(Y_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

63. A hub according to claim 62, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

64. A hub according to claim 47, wherein:

said means for utilizing said data includes means for reducing said differential quadrature components to obtain reduced differential components dY_rkn according to dY_rkn=(dY_kn cos Δ

_kn+dX_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

65. A hub according to claim 64, wherein:

said means for utilizing said data includes means for accumulating signs of the reduced components for each said carrier group.

66. A hub according to claim 65, wherein:

said means for accumulating signs accumulates said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right),$

where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

67. A hub according to claim 66, wherein:

N is chosen such that KN is a desired value.

72. A hub according to claim 46, wherein:

said means for utilizing said data includes means for reducing said quadrature components to obtain reduced quadrature components Y_rkn according to Y_rkn=(Y_kn cos Δ

_kn+X_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

73. A hub according to claim 72, wherein:

said means for utilizing said data includes means for accumulating signs of the reduced components for each said carrier group.

74. A hub according to claim 73, wherein:

said means for accumulating signs accumulates said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left(Y_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+X_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right),$

where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

75. A hub according to claim 74, wherein:

N is chosen such that KN is a desired value.

76. A hub according to claim 75, wherein:

KN is chosen to be at least 50.

77. A hub according to claim 72, wherein:

said means for utilizing said data further includes means for comparing said D₊₋

to a predetermined threshold value T_d.

78. A hub according to claim 77, wherein:

said means for utilizing said data includes means for determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

79. A hub according to claim 77, wherein:

said means for utilizing said data includes means for determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right)\right].$

80. A hub according to claim 44, wherein:

said hub receiver receives data from at least two nodes which utilize at least one same carrier at different times, wherein said means for utilizing said data derives a separate frequency offset estimation for each of said at least two nodes which utilize at least one same carrier at different times, and

said hub transmitter sends separate frequency offset estimation for said at least two nodes which utilize at least one same carrier at different times.

69. A hub according to claim 67, wherein:

KN is chosen to be at least 50.

70. A hub according to claim 69, wherein:

said means for utilizing said data includes means for determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

71. A hub according to claim 69, wherein:

said means for utilizing said data includes means for determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right)\right].$

69-1. A hub according to claim 68, wherein:

said means for utilizing said data further includes means for comparing said D₊₋

to a predetermined threshold value T_d.

81. A node for an orthogonal frequency division multiplexing (OFDM) multipoint-to-point multicarrier wireless telecommunications system having a hub and a plurality of other nodes, the node comprising:

a node receiver which receives a function of an indication of a frequency offset estimation from the hub, the hub having generated the indication of a frequency offset estimation for said node receiver as a function of data receiver from said node and from the plurality of other nodes; and

a node transmitter for transmitting modulated corrected signals over at least one carrier, said node transmitter having an inverse fast Fourier transformer (IFFT), a signal correction means coupled to said IFFT for frequency offset compensation of data signals applied to and processed by said IFFT, and a modulator coupled to said signal correction means for modulating signals corrected by said signal correction means.

82. A node according to claim 81, wherein:

said signal correction means corrects a data signal according to X_mc=X_m cos(mφ

)+Y_m sin(mφ

), Y_mc=Y_m cos(mφ

)−

X_m sin(mφ

), where X_m and Y_m are respectively real and imaginary parts of an m-th complex sample of said signal at an output of said IFFT after processing by said IFFT, where m is an integer changing from 1 to M, and M is the number of carriers in the multicarrier system, X_mc and Y_mc are respectively real and imaginary parts of the m-th corrected sample, and φ

is said function of said indication of said frequency offset estimation sent by the hub to said node.

83. A node according to claim 82, wherein:

said node transmitter includes means for calculating a product mφ and

a table which provides cos(mφ

) and sin(mφ

) values to said signal correction means in response to said means for calculating a product mφ

.

84. A node according to claim 81, wherein:

said indication of said frequency offset estimation sent by the hub to said node is one of phase φ and

a function of a change in frequency Δ

f where φ

=2π

Δ

fT and where T is a time interval.

85. A method for implementing frequency offset compensation in an orthogonal frequency division multiplexing (OFDM) multipoint-to-point multicarrier wireless telecommunications system having a hub and a plurality of nodes, where each respective node transmits data over a unique group of carriers at the same time as the other nodes, said method comprising:

a) in the hub, estimating frequency offset in the frequency domain for each group of carriers;

b) transmitting frequency offset parameters for each group of carriers from the hub to the nodes; and

c) in each node transmitter using said frequency offset parameters to implement frequency offset compensation in the time domain.

86. A method according to claim 85, wherein:

said estimating frequency offset comprises utilizing a fast Fourier transform (FFT) to convert data transmitted by the node transmitters over the carriers and received by the hub into a frequency domain, and conducting said estimating in the frequency domain.

87. A method according to claim 86, wherein:

said estimating comprises determining quadrature components X_dkn and Y_dkn of a decision vector from received vector outputs X_kn, Y_kn of the FFT, where n is an index of OFDM symbols and k is an index of the carriers.

88. A method according to claim 87, wherein:

said estimating further comprises calculating differential quadrature components dX_kn, dY_kn where dX_kn=(X_kn−

X_dkn) and dY_kn=(Y_kn−

Y_dkn).

89. A method according to claim 88, wherein:

said estimating further comprises reducing said differential quadrature components to obtain reduced differential components dX_rkn and dY_rkn according to

dX_rkn=(A₀/A_kn) (dX_kn cos Δ

_kn−

dY_kn sin Δ

_kn), and
dY_rkn=(A₀/A_kn) (dY_kn cos Δ

_kn−

dX_kn sin Δ

_kn),

where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, A_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

90. A method according to claim 89, wherein:

said estimating further comprises averaging reduced differential components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{\mathrm{dX}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dX}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dX}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-{\mathrm{dY}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{\mathrm{dY}}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>{\mathrm{dY}}_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

91. A method according to claim 90, wherein:

N is chosen such that KN is a desired value.

92. A method according to claim 91, wherein:

KN is chosen to be at least 50.

93. A method according to claim 90, wherein:

said estimation includes generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

94. A method according to claim 93, wherein:

said generating an indication includes means for estimating phase shift for each carrier group according to

Sin φ

=[dX_rY₀−

dY_rX₀]/A, and Cos φ

=[(A₀)²+dX_rX₀+dY_rY₀]/A

where φ

is said phase shift, and A=A₀*[(X₀+dX_r)²+(Y₀+dY_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

95. A method according to claim 94, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

96. A method according to claim 94, wherein:

said indication is a function of Sin φ and

Cos φ

.

97. A method according to claim 86, wherein:

said indication is one of φ and

Δ

f where Δ

f=φ

/2π

T.

98. A method according to claim 87, wherein:

said estimating further comprises reducing said quadrature components to obtain reduced quadrature components dX_rkn and dY_rkn according to X_rkn=(A₀/A_kn) (X_kn cos Δ

_kn−

Y_kn sin Δ

_kn),

Y_rkn=(A₀/A_kn) (Y_kn cos Δ

_kn+X_kn sin Δ

_kn)

where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector, A_kn is an amplitude of said decision vector for the n-th symbol of the k-th carrier, and A₀ is an amplitude of said reference vector.

99. A method according to claim 98, wherein:

said estimating further comprises averaging reduced quadrature components by carrier group according to obtain group averages dX_r and dY_r according to

$\begin{array}{c}{X}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>X_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(X_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}-Y_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_k\end{array}$$\begin{array}{c}{Y}_r=<br><br>\left(1/\mathrm{KN}\right)<br><br>\sum <br><br>Y_{\mathrm{rkn}}\\ =<br><br>\left(A_0/\mathrm{KN}\right)<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\left(Y_{\mathrm{kn}<br><br>\text{\hspace{1em}<br><br>}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+X_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)/A_{\mathrm{kn}}\end{array}$

where K is the number of carriers in a respective carrier group, and N is the number of symbols over which averaging is done.

100. A method according to claim 99, wherein:

N is chosen such that KN is a desired value.

101. A method according to claim 100, wherein:

KN is chosen to be at least 50.

102. A method according to claim 99, wherein:

said estimating further comprises generating an indication of frequency offset for each carrier group based on said group average for said respective carrier group.

103. A method according to claim 102, wherein:

said generating an indication includes estimating phase shift for each carrier group according to Sin φ

=[X_rY₀−

Y_rX₀]/A, and Cos φ

=[X_rX₀+Y_rY₀]/A where φ

is said phase shift, and A=A₀*[(X_r)²+(Y_r)²]^0.5 where X₀ and Y₀ are coordinates of said reference vector.

104. A method according to claim 103, wherein:

said reference vector is chosen such that X₀=1 and Y₀=0.

105. A method according to claim 88, wherein:

said estimating further comprises reducing said differential quadrature components to obtain reduced differential components dY_rkn according to dY_rkn=(dY_kn cos Δ

_kn+dX_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

106. A method according to claim 105, wherein:

said estimating further comprises accumulating signs of the reduced components for each said carrier group.

107. A method according to claim 106, wherein:

said accumulating signs comprises accumulating said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}}_{\mathrm{kn}}\right),$

where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

108. A method according to claim 107, wherein:

N is chosen such that KN is a desired value.

109. A method according to claim 108, wherein:

KN is chosen to be at least 50.

110. A method according to claim 107, wherein:

said estimating further includes comparing said D₊₋

to a predetermined threshold value T_d.

111. A method according to claim 110, wherein:

said estimating includes determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

112. A method according to claim 110, wherein:

said estimating includes determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)\right].$

113. A method according to claim 86, wherein:

said estimating further comprises reducing said quadrature components to obtain reduced quadrature components Y_rkn according to Y_rkn=(Y_kn cos Δ

_kn+X_kn sin Δ

_kn), where Δ

_kn is a phase difference between said decision vector for the n-th symbol of the k-th carrier and a reference vector.

114. A method according to claim 113, wherein:

said estimating includes accumulating signs of the reduced components for each said carrier group.

115. A method according to claim 114, wherein:

said accumulating signs comprises accumulating said signs according to

$D_{+-}=\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}$

Sign (Y_kn cos Δ

_kn+X_kn sin Δ

_kn), where K is the number of carriers in a respective carrier group, N is the number of symbols over which averaging is done, Sign(x)=+1 or −

1, and D₊₋

represents a difference between a number of components with positive phase shifts and a number of components with negative phase shifts in a carrier group and its sign determines a direction for frequency offset adjustment.

116. A method according to claim 115, wherein:

N is chosen such that KN is a desired value.

117. A method according to claim 116, wherein:

KN is chosen to be at least 50.

118. A method according to claim 113, wherein:

said estimating includes comparing said D₊₋

to a predetermined threshold value T_d.

119. A method according to claim 118, wherein:

said estimating includes determining a frequency offset value for each carrier group as a function of an average offset of the majority components of that carrier group.

120. A method according to claim 118, wherein:

said estimating includes determining an adjustment direction Sign(φ

) according to

$\mathrm{Sign}<br><br>\left(\mathrm{\varphi <br><br>}\right)=\mathrm{Sign}<br><br>\left[\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br>\mathrm{Sign}<br><br>\left({\mathrm{dY}}_{\mathrm{kn}}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}+{\mathrm{dX}}_{\mathrm{kn}}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Delta <br><br>}}_{\mathrm{kn}}\right)\right].$

121. A method according to claim 85, wherein:

a first of said plurality of nodes utilizes a group of carriers including a first plurality of carriers and a second of said plurality of nodes utilizes a group of carrier including a second plurality of carriers different than said first plurality of carriers.

122. A method according to claim 85, wherein:

a first of said plurality of nodes utilizes a group of carriers including a single carrier and a second of said plurality of nodes utilizes a group of carrier including a plurality of carriers different than said single carrier.

123. A method according to claim 85, wherein:

said using said frequency offset parameters to implement frequency offset compensation in the time domain comprises utilizing an inverse fast Fourier transformer (IFFT) and a signal correction means coupled to the IFFT in each node for frequency offset compensation of data signals applied to and processed by the FFT.

124. A method according to claim 123, wherein:

said signal correction means corrects a data signal according to X_mc=X_m cos(mφ

)+Y_m sin(mφ

), Y_mc=Y_m cos(mφ

)−

X_m sin(mφ

), where X_m and Y_m are respectively real and imaginary parts of an m-th complex sample of said signal at an output of said IFFT after processing by said IFFT, where m is an integer changing from 1 to M, and M is the number of carriers in said multicarrier system, X_mc and Y_mc are respectively real and imaginary parts of the m-th corrected sample, and φ

is a function of said indication of said frequency offset estimation sent by the hub to the node.

125. A method according to claim 85, further comprising:

having at least two of the plurality of nodes transmit on at least one same carrier for transmission but at different times.