Carrier frequency offset estimation for OFDM systems

• US 7,570,722 B1
• Filed: 11/10/2004
• Issued: 08/04/2009
• Est. Priority Date: 02/27/2004
• Status: Active Grant

• Current Assignee: NXP USA, Inc. (NXP Semiconductors NV)
• Original Assignee: Marvell International Limited (Marvell Technology Group Limited)
• Inventors: Lee, Jungwon, Lou, Hui-Ling, Toumpakaris, Dimitrios-Alexandros
• Primary Examiner(s): Perilla; Jason M.
• Application Number:
  US10/986,082
• Time in Patent Office: 1,728 Days
• Field of Search: 375/260, 375/316, 375/354, 375/324, 375/327, 375/344, 375/346
• US Class Current: 375/344
• CPC Class Codes: H04B 7/01 Reducing phase shift
• CPC Class Codes: H04L 27/2657 Carrier synchronisation

Abstract

A system comprises a receiver module that receives a signal that is modulated using coherent orthogonal frequency division multiplexing (OFDM) modulation. A signal to noise ratio (SNR) module communicates with the receiver module and generates a SNR estimate based on the OFDM signal. An estimator module communicates with the SNR module and estimates carder frequency offset (CFO) based on the SNR estimate. System for orthogonal frequency division multiplexing (OFDM) signals such as frequency differential demodulation and time differential demodulation are also described.

Claims

1. A system comprising:

a receiver module that receives a signal that is modulated using coherent orthogonal frequency division multiplexing (OFDM) modulation;

a signal to noise ratio (SNR) module that communicates with said receiver module and that generates a SNR estimate based on said OFDM signal; and

an estimator module that communicates with said SNR module and that estimates a carrier frequency offset (CFO) of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between carrier frequencies of said receiver module and a remote transmitter, a number of subcarriers of said OFDM signal and a sampling period for said OFDM signal.

2. The system of claim 1 wherein said CFO estimate is based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 2 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 2 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

where

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

3. The system of claim 1 wherein said receiver module operates in a time-invariant frequency-selective channel.

4. The system of claim 1 wherein said receiver module operates in an additive white Gaussian noise (AWGN) channel.

5. The system of claim 1 wherein said receiver module operates in a multi-path fading channel.

6. The system of claim 1 wherein said estimator module includes a lookup table that outputs a table entry corresponding to said CFO estimate based on said SNR estimate.

7. The system of claim 1 wherein said receiver module is a wireless receiver.

8. The system of claim 1 wherein said receiver module is a wired receiver.

9. The system of claim 1 wherein said CFO estimate is based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 2 ⁡

( ɛ

) 1 - f N 2 ⁡

( ɛ

)

where,

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, N is equal to the number of subcarriers, and T is said sampling period.

10. A system comprising:

a receiver module that receives an orthogonal frequency division multiplexing (OFDM) signal that is modulated using differential OFDM modulation;

a signal to noise ratio (SNR) module that communicates with said receiver module and that generates a SNR estimate based on said OFDM signal; and

a carrier frequency offset (CFO) estimator module that communicates with said SNR module and that estimates a residual CFO of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between a carrier frequency of said receiver module and a carrier frequency of said remote transmitter, a number of subcarriers of said OFDM signal and a sampling period for said OFDM signal.

11. The system of claim 10 wherein said receiver module performs frequency domain differential demodulation.

12. The system of claim 11 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 4 ⁡

( ɛ

) ⁢

SNR 0 [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 and SNR₀ is a nominal SNR without CFO.

13. The system of claim 11 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 and N is equal to the number of subcarriers.

14. The system of claim 10 wherein said receiver module performs time domain differential demodulation.

15. The system of claim 14 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 4 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 4 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

16. The system of claim 14 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) 1 - f N 4 ⁡

( ɛ

) ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver module and said remote transmitter, T is said sampling period, and N is equal to the number of subcarriers.

17. The system of claim 10 wherein said CFO estimator module includes a lookup table that outputs a table entry corresponding to said CFO estimate based on said SNR estimate.

18. The system of claim 10 wherein said receiver module is a wireless receiver.

19. The system of claim 10 wherein said receiver module is a wired receiver.

20. A system comprising:

receiver means for receiving a signal that is modulated using coherent orthogonal frequency division multiplexing (OFDM) modulation;

signal to noise ratio (SNR) estimating means that communicates with said receiver means for generating a SNR estimate based on said OFDM signal; and

CFO estimating means that communicates with said SNR estimating means for estimating a carrier frequency offset (CFO) of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between a carrier frequency of said receiver means and a carrier frequency of a remote transmitter, a number of subcarriers of said OFDM signal and a sampling period for said OFDM signal.

21. The system of claim 20 wherein said CFO estimate is based on

$\mathrm{SNR}$

( ɛ

, k ) = f N 2 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 2 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

where

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

22. The system of claim 20 wherein said receiver means operates in a time-invariant frequency-selective channel.

23. The system of claim 20 wherein said receiver means operates in an additive white Gaussian noise (AWGN) channel.

24. The system of claim 20 wherein said receiver means operates in a multi-path fading channel.

25. The system of claim 20 wherein said CFO estimating means includes lookup means for outputting a table entry corresponding to said CFO estimate based on said SNR estimate.

26. The system of claim 20 wherein said receiver means is a wireless receiver.

27. The system of claim 20 wherein said receiver means is a wired receiver.

28. The system of claim 20 wherein said CFO estimate is based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 2 ⁡

( ɛ

) 1 - f N 2 ⁡

( ɛ

)

where

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, and T is said sampling period.

29. A system comprising:

receiver means for receiving an orthogonal frequency division multiplexing (OFDM) signal that is modulated using differential OFDM modulation;

signal to noise ratio (SNR) estimating means that communicates with said receiver means for generating a SNR estimate based on said OFDM signal; and

carrier frequency offset (CFO) estimating means that communicates with said SNR estimating means for estimating a residual CFO of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between a carrier frequency of said receiver module and a carrier frequency of a remote transmitter, a number of subcarriers of said OFDM signal and a sampling period for said OFDM signal.

30. The system of claim 29 wherein said receiver means performs frequency domain differential demodulation.

31. The system of claim 30 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 2 ⁡

( ɛ

) ⁢

SNR 0 [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 and SNR₀ is a nominal SNR without CFO.

32. The system of claim 29 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 equal to the number of subcarriers.

33. The system of claim 29 wherein said receiver means performs time domain differential demodulation.

34. The system of claim 33 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 4 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 4 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

35. The system of claim 33 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) 1 - f N 4 ⁡

( ɛ

) ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, T is said sampling period, and N is equal to the number of subcarriers.

36. The system of claim 29 wherein said CFO estimating means includes lookup means for outputting a table entry corresponding to said CFO estimate based on said SNR estimate.

37. The system of claim 29 wherein said receiver means is a wireless receiver.

38. The system of claim 29 wherein said receiver means is a wired receiver.

39. A method comprising:

receiving a signal in a receiver means for receiving that is modulated using coherent orthogonal frequency division multiplexing (OFDM) modulation;

generating a SNR estimate based on said OFDM signal; and

estimating a carrier frequency offset (CFO) of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between a carrier frequency of said receiver means and a carrier frequency of a remote transmitter, a number of subcarriers of said OFDM signal and a sampling period for said OFDM signal.

40. The method of claim 39 wherein said CFO estimate is based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 2 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 2 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

where

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

41. The method of claim 39 further comprising operating in a time-invariant frequency-selective channel.

42. The method of claim 39 further comprising operating in an additive white Gaussian noise (AWGN) channel.

43. The method of claim 39 further comprising operating in a multi-path fading channel.

44. The method of claim 39 further comprising outputting a table entry corresponding to said CFO estimate based on said SNR estimate.

45. The method of claim 39 wherein said CFO estimate is based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 2 ⁡

( ɛ

) 1 - f N 2 ⁡

( ɛ

)

where

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, and T is said sampling period.

46. A method comprising:

receiving an orthogonal frequency division multiplexing (OFDM) signal that is modulated using differential OFDM modulation;

generating a SNR estimate based on said OFDM signal; and

estimating a residual carrier frequency offset of said OFDM signal based on said SNR estimate, wherein said SNR estimate is based on a difference between a carrier frequency of a receiver means for receiving said OFDM signal and a carrier frequency of a remote transmitter, a number of subcarriers for said OFDM signal and a sampling period for said OFDM signal.

47. The method of claim 46 further comprising performing frequency domain differential demodulation.

48. The method of claim 47 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 4 ⁡

( ɛ

) ⁢

SNR 0 [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 and SNR₀ is a nominal SNR without CFO.

49. The method of claim 47 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) [ 1 - a N ⁡

( 1 - cos ⁡

( 2 ⁢

π

ɛ

) ) - f N 4 ⁡

( ɛ

) ] ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, T is said sampling period, a_N is approximated as

$\frac{1}{{\mathrm{\pi <br><br>}}^2}$

for N≧

64 and N is equal to the number of subcarriers.

50. The method of claim 46 further comprising operating using time domain differential demodulation.

51. The method of claim 50 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

, k ) = f N 4 ⁡

( ɛ

) ⁢

SNR 0 ( 1 - f N 4 ⁡

( ɛ

) ) ⁢

SNR 0 + 1 ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br><br><br>N<br><br><br><br>T,\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, N is equal to the number of subcarriers, k represents at least one of the subcarriers, T is said sampling period and SNR₀ is a nominal SNR without CFO.

52. The method of claim 50 wherein said CFO estimate is generated based on said SNR defined as

$\mathrm{SNR}$

( ɛ

) ≈

f N 4 ⁡

( ɛ

) 1 - f N 4 ⁡

( ɛ

) ,

wherein

$f_N<br><br>\left(\mathrm{\varepsilon <br><br>}\right)<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br><br><br>\frac{\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}\right)}{N<br><br><br><br>\sin <br><br>\left(\mathrm{\pi <br><br>\varepsilon <br><br>}/N\right)}<br><br>,\mathrm{\varepsilon <br><br>}<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{fNT},\mathrm{\Delta <br><br>}<br><br><br><br>f$

is said difference between said carrier frequencies of said receiver means and said remote transmitter, T is said sampling period, and N is equal to the number of subcarriers.

53. The method of claim 46 further comprising outputting a table entry corresponding to said CFO estimate based on said SNR estimate.