Maximum likelihood synchronization for a communications system using a pilot symbol

• US 20040081205A1
• Filed: 07/30/2003
• Published: 04/29/2004
• Est. Priority Date: 02/01/2001
• Status: Active Grant

• Current Assignee: Callaghan Innovation
• Original Assignee: Industrial Research Limited
• Inventors: Coulson, Alan James
• Granted Patent: US 7,627,067 B2
• Time in Patent Office: Days
• US Class Current: 370/503
• CPC Class Codes: H04L 27/2656 Frame synchronisation, e.g. packet synchronisation, time division duplex [TDD] switching point detection or subframe synchronisation
• CPC Class Codes: H04L 27/2657 Carrier synchronisation
• CPC Class Codes: H04L 27/2662 Symbol synchronisation
• CPC Class Codes: H04L 27/2675 Pilot or known symbols

Abstract

A method and apparatus for detecting and synchronising packets of data with a repeated sequence as a pilot symbol received by a communications system are provided. The method and apparatus include receiving data, detecting a packet within the received data, producing an estimate of the time-varying frequency offset of the received data, estimating the start of the packet of the received data, estimating the time-varying phase offset of the received data and estimating the time-varying time offset of the received data. Methods for assessing each one of the time-varying frequency offset, the time-varying phase offset, the time-varying time offset and the start of packet are also provided.

Claims

1. A method of detecting and synchronising packets of data with a repeated sequence as a pilot symbol received by a communications system including the steps of receiving data, detecting a packet within the received data, producing an estimate of the time-varying frequency offset of the received data, estimating the start of the packet of the received data, estimating the time-varying phase offset of the received data and estimating the time-varying time offset of the received data.

2. A method of detecting and synchronising packets of data with a repeated sequence as claimed in claim 1 further including the step of estimating the time-varying frequency offset of the received data again after the packet start has been estimated.

3. A method of detecting and synchronising packets of data with a repeated sequence as claimed in claim 1 or claim 2 further including the step of applying a correction to the received data based on the estimated frequency offset of the received data before the step of estimating the start of packet.

4. A method for detecting and synchronising packets of data with a repeated sequence as claimed in any one of claims 1 to 3 further including the step of applying corrections based on the frequency and phase offsets to the received data before the step of estimating the time varying time offset.

5. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence including the steps of:

receiving the data at a receiver as a series of data samples,

producing an autocorrelation of a first vector of the received data,

producing a cross correlation between the first vector of the received data and a second vector of the received data,

determining a timing metric representing the approximate start of a data packet for the current data sample as a function of the autocorrelation, the cross correlation and a threshold value,

assessing whether the timing metric is positive,

if the timing metric is not positive returning to the step of producing an autocorrelation of a first vector of the received data, and

if or when the timing metric is or becomes positive estimating the frequency offset from the phase of the cross correlation.

6. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in claim 5 further including the steps of:

determining the phase of the cross correlation of the first vector and the second vector once the start of a data packet has been detected, and

estimating the frequency offset from the phase of the cross correlation.

7. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in claim 5 or claim 6 wherein the pilot symbol includes at least two sequences with constant envelope in both the frequency and time domains.

8. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 7 wherein the length of the vectors used to determine the autocorrelation and the cross correlation of the received data are the length of a constant envelope sequence in the pilot symbol.

9. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 8 wherein the step of determining the timing metric includes determining the result of:

|P_l|−

T_C1{square root}{square root over (R_lR_l+L)}

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value,

R_l represents the autocorrelation of the received data beginning at sample l, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

10. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 8 wherein the step of determining the timing metric includes determining the result of:

|P_l|−

T_C1max(R_lR_l+L)

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value,

max represents taking the maximum value of those in the brackets,

R_l represents the autocorrelation of the received data beginning at sample l, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

11. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 8 wherein the step of determining the timing metric includes determining the result of:

|P_l|−

T_C1R_l

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l represents the autocorrelation of the received data beginning at sample l.

12. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 8 wherein the step of determining the timing metric includes determining the result of:

|P_l|−

T_C1R_l+L

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

13. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 8 wherein the step of determining the timing metric includes determining the result of:

P_l²−

T_C1²R_l²

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l represents the autocorrelation of the received data beginning at sample l.

14. A method of determining the frequency offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 5 to 13 wherein the step of determining the frequency offset includes determining the result of:

15. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence including the steps of:

receiving the data at a receiver as a series of data samples,

applying a correction based on an estimate of a frequency offset of the received data to a first vector of the received data to form a matched filter,

producing an autocorrelation of the first vector of the received data,

applying the matched filter to the received data to produce an output,

determining a timing metric for the current sample of data as a function of the output of the matched filter, the autocorrelation of the first vector of the received data, the magnitude of the constant envelope of a sequence of the pilot symbol and a first threshold value,

assessing whether the first timing metric is positive,

if the first timing metric is not positive returning to the step of producing an autocorrelation at the first vector of the received data, and

when the first tithing metric becomes positive estimating the start of packet from the current data sample.

16. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in claim 15 wherein the pilot symbol includes at least two sequences with constant envelope in both the frequency and time domains.

17. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in claim 15 or claim 16 wherein the length of the matched filter is equal to the length of a sequence within the pilot symbol.

18. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 17 wherein the length of the vector used to produce the autocorrelation is equal to the length of a sequence within the pilot symbol.

19. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 18 wherein the vector of data used to produce the autocorrelation and the vector of data used to produce the output of the matched filter are the same.

20. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 19 further including the step of ensuring that a second timing metric is positive before estimating the start of the data packet.

21. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in claim 20 wherein the second timing metric is a function of a second threshold value, the autocorrelation of the received data and a cross correlation between the first vector of data and a second vector of the received data.

22. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 21 wherein the step of determining the first timing metric includes the step of determining the result of:

|Q_l+Q_l+1|−

T_C2{square root}{square root over (LS)}{square root}{square root over (R_l)}

where Q_l represents the output of the matched filter for a vector of the received data starting at sample l,

Q_l+1 represents the output of the matched filter for a vector of the received data starting at sample l+1,

T_C2 represents the threshold value,

L represents the length of a constant envelope sequence in the pilot symbol,

S represents the per-sample magnitude of a constant envelope sequence in the pilot symbol, and

R_l represents the autocorrelation of the first vector of the received data.

23. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 21 wherein the step of determining the first timing metric includes the step of determining the result of:

|Q_l+Q_l+1|²−

T_C2²LS²R_l

where Q_l represents the output of the matched filter for a vector of the received data starting at sample l,

Q_l+1 represents the output of the matched filter for a vector of the received data staring at sample l+1,

T_C2 represents the threshold value,

L represents the length of a constant envelope sequence in the pilot symbol,

S represents the per-sample magnitude of a constant envelope sequence in the pilot symbol, and

R_l represents the autocorrelation of the first vector of the received data.

24. A method of determining the start of a packet of data including a pilot symbol including a repeated sequence as claimed in any one of claims 15 to 23 wherein the step of determining the start of packet includes the step of determining the result of:

{circumflex over (l)}+2L−

1|_{{circumflex over (l)}}=0

where {circumflex over (l)} represents the range of samples of the received data for which both the first and second timing metrics are positive.

25. A method for estimating the phase offset of data including a pilot symbol including a repeated sequence including the steps of:

receiving the data at a receiver as a series of data samples,

applying a correction based on an estimate of a frequency offset of the data to a vector of received data to form a matched filter,

applying the matched filter to the received data,

determining the correlation peak of the matched filter, and

estimating the phase offset from the phase of the correlation peak.

26. A method for estimating the phase offset of data including a pilot symbol including a repeated sequence as claimed in claim 25 wherein the pilot symbol includes at least two sequences with constant envelope in both the frequency and time domains.

27. A method for estimating the phase offset of data including a pilot symbol including a repeated sequence as claimed in claim 25 or claim 26 wherein the length of the data vector used to form the matched filter is equal to the length of a sequence in the pilot symbol.

28. A method for estimating the phase offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 25 to 27 wherein the step of determining the phase offset includes the step of determining the result of:

29. A method of determining the timing offset of data including a pilot symbol including a repeated sequence including the steps of:

receiving the data at a receiver as a series of data samples,

determining the start of a second sequence within the pilot symbol of the received data to an accuracy of half a data sample,

taking a discrete Fourier transform of a vector of the received data,

forming a vector product of the output of the discrete Fourier transform and the data sample of the second sequence, and

estimating the timing offset from the vector product.

30. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in claim 29 wherein the pilot symbol includes at least two sequences with constant envelope in both the frequency and time domains.

31. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in claim 29 or claim 30 further including the step of applying a frequency offset correction to the received data before the step of taking the discrete Fourier transform of the data.

32. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 29 to 31 further including the step of applying a phase offset correction to the received data before the step of taking the discrete Fourier transform of the data.

33. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 29 to 32 wherein the discrete Fourier transform is an L-point discrete Fourier transform where L represents the length of one constant envelope sequence in the pilot symbol.

34. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 29 to 33 wherein the step of determining the start of a second constant envelope sequence in the pilot symbol includes the steps of:

producing an autocorrelation of a first vector of the received data,

applying a correction based on an estimate of a frequency offset of the received data to the first vector of the received data to form a matched filter,

applying the matched filter to the received data to produce an output,

determining a timing metric for the current sample of data as a function of the output of the matched filter, the autocorrelation of the first vector of the received data, the magnitude of the constant envelope of a sequence of the pilot symbol and a first threshold value,

assessing when the first timing metric becomes positive, and

estimating the start of packet from the current data sample.

35. A method of determining the timing offset of data including a pilot symbol including a repeated sequence as claimed in any one of claims 29 to 34 wherein the step of estimating the timing offset from the vector product includes the step of determining the result of:

36. A receiver for detecting and synchronising packets received by a communications system including:

a front end arranged to receive data, a packet detect estimator arranged to detect a packet within the received data, a frequency offset estimator arranged to produce an estimate of the time-varying frequency offset of the received data, a start of packet estimator arranged to estimate the start of the packet of the received data, a phase offset estimator arranged to estimate the time-varying phase offset of the received data and a time offset estimator arranged to estimate the time-varying time offset of the received data.

37. A receiver for detecting and synchronising packets received by a communications system as claimed in claim 36 wherein the frequency offset estimation means is further arranged to estimate the time-varying frequency offset of the received data again after the packet start has been estimated.

38. A receiver for detecting and synchronising packets received by a communications system as claimed in claim 36 or 37 further including correction means arranged to apply a correction based on the estimated frequency offset to the received data before the start of packet estimation means estimates the start of packet.

39. A receiver for detecting and synchronising packets received by a communications system as claimed in any one of claims 36 to 38 wherein the time offset estimation means is further arranged to apply corrections based on the frequency and phase offsets to the received data before estimating the time varying time offset.

40. A frequency offset estimator arranged to determine the frequency offset of the received data including a pilot symbol including a repeated sequence including:

first correlation means arranged to produce an autocorrelation of a first vector of the received data,

second correlation means arranged to produce a cross correlation between the first vector of the received data and a second vector of the received data, and

computation means arranged to determine a timing metric as a function of the autocorrelation, the cross correlation and a threshold value, assess when the timing metric becomes positive, and when the timing metric becomes positive estimate the frequency offset from the phase of the cross correlation.

41. A frequency offset estimator as claimed in claim 40 wherein the calculation means is further arranged to:

determine the phase of the cross correlation of the first vector and the second vector once the start of a data packet has been detected, and

estimate the frequency offset from the phase of the cross correlation.

42. A frequency offset estimator as claimed in claim 40 or claim 41 wherein the pilot symbol includes at least two sequences with constant envelope in both the frequency and time domains.

43. A frequency offset estimator as claimed in any one of claims 40 to 42 wherein the length of the vectors used to determine the autocorrelation and the cross correlation of the received data are the same length as a sequence in the pilot symbol.

44. A frequency offset estimator as claimed in any one of claims 40 to 43 wherein the computation means is arranged to assess the timing metric as:

|P_l|−

T_C1{square root}{square root over (R_lR_l+L)}

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value,

R_l represents the autocorrelation of the received data beginning at sample l, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

45. A frequency offset estimator as claimed in any one of claims 40 to 43 wherein the computation means is arranged to assess the timing metric as:

|P_l|−

T_C1max(R_lR_l+L)

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value,

max represents taking the maximum value of those in the brackets,

R_l represents the autocorrelation of the received data beginning at sample l, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

46. A frequency offset estimator as claimed in any one of claims 40 to 43 wherein the computation means is arranged to assess the timing metric as:

|P_l|−

T_C1R_l

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l represents the autocorrelation of the received data beginning at sample l.

47. A frequency offset estimator as claimed in any one of claims 40 to 43 wherein the computation means is arranged to assess the liming metric as:

|P_l|−

T_C1R_l+L

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l+L represents the autocorrelation of the received data beginning at sample l+L.

48. A frequency offset estimator as claimed in any one of claims 40 to 43 wherein the computation means is arranged to assess the timing metric as:

P_l²−

T_C1²R_l²

where P_l represents the cross correlation of the received data,

T_C1 represents the threshold value, and

R_l represents the autocorrelation of the received data beginning at sample l.

49. A frequency offset estimator as claimed in any one of claims 40 to 48 wherein the computation means is further arranged to estimate the frequency offset as:

50. A start of packet estimator arranged to estimate the start of a packet of a series of samples of data including a pilot symbol including a repeated sequence including:

correlator means arranged to produce an autocorrelation of a first vector of the received data,

matched filter forming means arranged to apply a correction based on an estimate of a frequency offset of the received data to the first vector of the received data to form a matched filter,

matched filter means arranged to apply the matched filter to the received data to produce an output, and

computation means arranged to determine a timing metric for the current sample of data as a function of the output of the matched filter, the autocorrelation of the first vector of the received data, the magnitude of the constant envelope of a sequence within the pilot symbol and a first threshold value, assess when the first timing metric becomes positive, and estimate the start of packet from the current data sample.

51. A start of packet estimator as claimed in claim 50 wherein the length of the matched filter is equal to the length of a constant envelope sequence within the pilot symbol.

52. A start of packet estimator as claimed in claim 50 or claim 51 wherein the length of the vector used to produce the autocorrelation is equal to the length of a constant envelope sequence within the pilot symbol.

53. A start of packet estimator as claimed in any one of claims 50 to 52 wherein the vector of data used to produce the autocorrelation and the vector of data used to produce the output of the matched filter are the same.

54. A start of packet estimator as claimed in any one of claims 50 to 53 wherein the computation means is further arranged to ensure that a second timing metric is positive before estimating the start of the data packet.

55. A start of packet estimator as claimed in claim 54 wherein the second timing metric is a function of a second threshold value, the autocorrelation of the received data and a cross correlation between the first vector of data and a second vector of the received data.

56. A start of packet estimator as claimed in any one of claims 50 to 55 wherein the computation means is arranged to assess the timing metric as:

|Q_l+Q_l+1|−

T_C2{square root}{square root over (LS)}{square root}{square root over (R_l)}

where Q_l represents the output of the matched filter for a vector of the received data starting at sample l,

Q_l+1 represents the output of the matched filter for a vector of the received data starting at sample l+1,

T_C2 represents the threshold value,

L represents the length of a constant envelope sequence in the pilot symbol,

S represents the per-sample magnitude of a constant envelope sequence in the pilot symbol, and

R_l represents the autocorrelation of the first vector of the received data.

57. A start of packet estimator as claimed in any one of claims 50 to 55 wherein the computation means is arranged to assess the timing metric as:

|Q_l+Q_l+1|²−

T_C2²LS²R_l

where Q_l represents the output of the matched filter for a vector of the received data starting at sample l,

Q_l+1 represents the output of the matched filter for a vector of the received data starting at sample l+1,

T_C2 represents the threshold value,

L represents the length of a constant envelope sequence in the pilot symbol,

S represents the per-sample magnitude of a constant envelope sequence in the pilot symbol, and

R_l represents the autocorrelation of the first vector of the received data.

58. A start of packet estimator as claimed in any one of claims 50 to 57 wherein the computation means is arranged to assess the start of packet as:

{circumflex over (l)}+2L−

1|{circumflex over (l)}=0

where {circumflex over (l)} represents the range of samples of the received data for which both the first and second timing metrics are positive.

59. A phase offset estimator arranged to estimate the phase offset of data including a pilot symbol including a repeated sequence including:

computation means arranged to apply a correction based on an estimate of a frequency offset of the data to a vector of received data to form a matched filter,

a matched filter arranged to filter to the received data, and

the computation means further arranged to determine the correlation peak of the matched filter, and estimate the phase offset from the phase of the correlation peak.

60. A phase offset estimator as claimed in claim 59 wherein the length of the data vector used to form the matched filter is equal to the length of a sequence in the pilot symbol.

61. A phase offset estimator as claimed in claim 59 or claim 60 wherein the computation means is further arranged to estimate the phase offset as:

62. A timing offset estimator arranged to estimate the timing offset of a received series of samples of data including a pilot symbol including a repeated sequence including:

computation means arranged to determine the start of a second sequence within the pilot symbol of the received data to an accuracy of half a data sample,

Fourier transform means arranged to perform a discrete Fourier transform on a vector of the received data, and

the computation means further arranged to form a vector product of the output of the discrete Fourier transform and the data sample of the second constant envelope sequence, and estimate the timing offset from the vector product.

63. A timing offset estimator as claimed in claim 62 wherein the computation means is further arranged to apply a frequency offset correction to the received data before the Fourier transform means takes the discrete Fourier transform of the data.

64. A timing offset estimator as claimed in claim 62 or claim 63 wherein the computation means is further arranged to apply a phase offset correction to the received data before the Fourier transform means takes the discrete Fourier transform of the data.

65. A timing offset estimator as claimed in any one of claims 62 to 64 wherein the discrete Fourier transform is an L-point discrete Fourier transform where L represents the length of a sequence in the pilot symbol.

66. A timing offset estimator as claimed in any one of claims 62 to 65 wherein the computation means is further arranged to determine the start of a second sequence in the pilot symbol by:

producing an autocorrelation of a first vector of the received data,

applying a correction based on an estimate of a frequency offset of the received data to the first vector of the received data to form a matched filter,

applying the matched filter to the received data to produce an output,

determining a timing metric for the current sample of data as a function of the output of the matched filter, the autocorrelation of the first vector of the received data, the magnitude of the constant envelope of a sequence of the pilot symbol and a first threshold value,

assessing when the first timing metric becomes positive, and

when the first timing metric becomes positive estimating the start of packet from the current data sample.

67. A timing offset estimator as claimed in any one of claims 62 to 66 wherein the computation means is further arranged to estimate the timing offset from the vector product by determining the result of: