Apparatus and method for using training sequences to estimate timing error in a digital signal receiver
First Claim
1. An apparatus for determining an estimate of timing error in a digital signal receiver, said apparatus comprising a timing error controller that is capable of determining said estimate of timing error from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in said digital signal receiver, wherein said timing error controller is capable of extracting y1 data around said first training sequence received at time t1 where said y1 data is represented by:
-
y1(t)=Σ
akh1(t−
kT)+e1(t)where ak represents said training sequence, h1(t) represents a channel impulse response at time t1, e1(t) represents an error term, and T represents a clock period of a transmitter; and
wherein said timing error controller is capable of sampling said y1 data at a rate T2 that is approximately equal to said value T of said clock period of said transmitter to obtain sampled y1 data represented by;
y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2).
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Abstract
An apparatus and method is disclosed for estimating timing error in a digital signal receiver from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in the digital signal receiver. Time domain representations of the timing sequence data are converted into frequency domain representations and used to calculate a complex cross power spectrum. The timing error is obtained by determining an average phase of the complex cross power spectrum. The timing error is then used to calculate an accurate value for the clock rate of the digital signal transmitter.
6 Citations
36 Claims
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1. An apparatus for determining an estimate of timing error in a digital signal receiver, said apparatus comprising a timing error controller that is capable of determining said estimate of timing error from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in said digital signal receiver, wherein said timing error controller is capable of extracting y1 data around said first training sequence received at time t1 where said y1 data is represented by:
-
y1(t)=Σ
akh1(t−
kT)+e1(t)where ak represents said training sequence, h1(t) represents a channel impulse response at time t1, e1(t) represents an error term, and T represents a clock period of a transmitter; and
wherein said timing error controller is capable of sampling said y1 data at a rate T2 that is approximately equal to said value T of said clock period of said transmitter to obtain sampled y1 data represented by;
y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
-
-
10. A digital receiver system comprising an apparatus for determining an estimate of timing error in a digital signal receiver of said digital receiver system, said apparatus comprising a timing error controller that is capable of determining said estimate of timing error from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in said digital signal receiver, wherein said timing error controller is capable of extracting y1 data around said first training sequence received at time t1 where said y1 data is represented by:
-
y1(t)=Σ
akh1(t−
kT)+e1(t)where ak represents said training sequence, h1(t) represents a channel impulse response at time t1, e1(t) represents an error term, and T represents a clock period of a transmitter; and
wherein said timing error controller is capable of sampling said y1 data at a rate T2 that is approximately equal to said value T of said clock period of said transmitter to obtain sampled y1 data represented by;
y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2).- View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18)
where ak represents said training sequence, h2(t) represents a channel impulse response at time t2, e2(nT2) represents an error term, T represents a clock period of said transmitter, and τ
represents said timing error.
-
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12. A digital receiver system as claimed in claim 11 wherein said timing error controller is capable of obtaining said y2(nT2) data in terms of said channel impulse response h1(t) at time t1, where said y2(nT2) data is represented by:
-
y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2)where e3(nT2) represents an error term that is equal to e2(nT2) plus Δ
h(t){circle around (x)}ak where Δ
h(t) is a difference between h1(t) and h2(t), and where {circle around (x)} represents a convolution operation.
-
-
13. A digital receiver system as claimed in claim 12 wherein said timing error controller is capable of converting a time domain representation of y1(nT2)=Σ
- akh1(nT2−
kT)+e1(nT2) to a frequency domain representation Y1(ejω
)=P(ejω
)+E1(ejω
) where P(ejω
) is a frequency domain representation of Σ
akh1(nT2−
kT) and where E1(ejω
) is a frequency domain representation of the term e1(nT2); andwhere said timing error controller is capable of converting a time domain representation of y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2) to a frequency domain representation Y2(ejω
)=P(ejω
)ejω
τ
+E3(ejω
) where P(ejω
)ejω
τ
is a frequency domain representation of Σ
akh1(nT2−
kT−
τ
) and where E3(ejω
) is a frequency domain representation of the term e3(nT2).
- akh1(nT2−
-
14. A digital receiver system as claimed in claim 13 wherein said timing error controller is capable of multiplying said frequency domain representation Y1(ejω
- ) by a complex conjugate of said frequency domain representation Y2(ejω
) to calculate a complex cross power spectrum equal to;
Y1(ejω
)Y2(e−
jω
)=|P(ejω
)|2e−
jω
+E4(ejω
)where E4(ejω
) is a frequency domain representation of terms that are functions of ejω
.
- ) by a complex conjugate of said frequency domain representation Y2(ejω
-
15. A digital receiver system as claimed in claim 14 wherein said timing error controller is capable of determining a value of said timing error τ
- by determining an average phase of said complex cross power spectrum.
-
16. A digital receiver system as claimed in claim 15 wherein said timing error controller is capable of determining said value of said timing error τ
- by finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- by finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
-
17. A digital receiver system as claimed in claim 15 wherein said timing error controller is capable of determining said value of said timing error τ
- by finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- by finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
-
18. A digital receiver system as claimed in claim 15 wherein said timing error controller is capable of determining a value T of said transmitter clock period using:
- τ
=MT−
MT2=M(T−
T2) where said value of said timing error τ
is known, and where M represents a known number of symbols between said first training sequence and said second training sequence, and where T2 represents a known value of an approximate value of said transmitter clock period T.
- τ
-
19. A method for determining an estimate of timing error in a digital signal receiver, said method comprising the step of:
-
determining said estimate of timing error from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in said digital signal receiver, wherein said step of determining said estimate of timing error comprises the steps of; extracting y1 data around said first training sequence received at time t1 where said y1 data is represented by;
y1(t)=Σ
akh1(t−
kT)+e1(t)where ak represents said training sequence, h1(t) represents a channel impulse response at time t1, e1(t) represents an error term, and T represents a clock period of a transmitter; and sampling said y1 data at a rate T2 that is approximately equal to said value T of said clock period of said transmitter to obtain sampled y1 data represented by;
y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2).- View Dependent Claims (20, 21, 22, 23, 24, 25, 26, 27)
where ak represents said training sequence, h2(t) represents a channel impulse response at time t2, e2(nT2) represents an error term, T represents a clock period of said transmitter, and τ
represents said timing error.
-
-
21. A method as claimed in claim 20 further comprising the step of:
-
obtaining said y2(nT2) data in terms of said channel impulse response h1(t) at time t1, where said y2(nT2) data is represented by;
y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2)where e3(nT2) represents an error term that is equal to e2(nT2) plus Δ
h(t){circle around (x)}ak where Δ
h(t) is a difference between h1(t) and h2(t), and where {circle around (x)} represents a convolution operation.
-
-
22. A method as claimed in claim 21 further comprising the steps of:
-
converting a time domain representation of y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2) to a frequency domain representation Y1(ejω
)=P(ejω
)+E1(ejω
) where P(ejω
) is a frequency domain representation of Σ
akh1(nT2−
kT) and where E1(ejω
) is a frequency domain representation of the term e1(nT2); andconverting a time domain representation of y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2) to a frequency domain representation Y2(ejω
)=P(ejω
)ejω
τ
+E3(ejω
) where P(ejω
)ejω
τ
is a frequency domain representation of Σ
akh1(nT2−
kT−
τ
) and where E3(ejω
) is a frequency domain representation of the term e3(nT2).
-
-
23. A method as claimed in claim 22 further comprising the step of:
-
multiplying said frequency domain representation Y1(ejω
) by a complex conjugate of said frequency domain representation Y2(ejω
) to calculate a complex cross power spectrum equal to;
Y1(ejω
)Y2(e−
jω
)=|P(ejω
)|2e−
jω
τ
+E4(ejω
)where E4(ejω
) is a frequency domain representation of terms that are functions of ejω
.
-
-
24. A method as claimed in claim 23 further comprising the step of:
determining a value of said timing error τ
by determining an average phase of said complex cross power spectrum.
-
25. A method as claimed in claim 24 wherein said step of determining a value of said timing error τ
- comprises the step of;
finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- comprises the step of;
-
26. A method as claimed in claim 24 wherein said step of determining a value of said timing error τ
- comprises the step of;
finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- comprises the step of;
-
27. A method as claimed in claim 24 further comprising the step of:
determining a value T of said transmitter clock period using;
τ
=MT−
MT2=M(T−
T2) where said value of said timing error τ
is known, and where M represents a known number of symbols between said first training sequence and said second training sequence, and where T2 represents a known value of an approximate value of said transmitter clock period T.
-
28. A computer executable process steps, stored on a computer readable storage medium, for determining an estimate of timing error in a digital signal receiver comprising the step of:
-
determining said estimate of timing error from a difference between an arrival time of a first training sequence and an arrival time of a second training sequence in said digital signal receiver, wherein said step of determining said estimate of timing error comprises the steps of; extracting y1 data around said first training sequence received at time t1 where said y1 data is represented by;
y1(t)=Σ
akh1(t−
kT)+e1(t)where ak represents said training sequence, h1(t) represents a channel impulse response at time t1, e1(t) represents an error term, and T represents a clock period of a transmitter; and sampling said y1 data at a rate T2 that is approximately equal to said value T of said clock period of said transmitter to obtain sampled y1 data represented by;
y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2).- View Dependent Claims (29, 30, 31, 32, 33, 34, 35, 36)
where ak represents said training sequence, h2(t) represents a channel impulse response at time t2, e2(nT2) represents an error term, T represents a clock period of said transmitter, and τ
represents said timing error.
-
-
30. The computer executable process steps, stored on a computer readable medium, as claimed in claim 29 further comprising the step of:
-
obtaining said y2(nT2) data in terms of said channel impulse response h1(t) at time t1, where said y2(nT2) data is represented by;
y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2)where e3(nT2) represents an error term that is equal to e2(nT2) plus Δ
h(t){circle around (x)}ak where Δ
h(t) is a difference between h1(t) and h2(t), and where {circle around (x)} represents a convolution operation.
-
-
31. The computer executable process steps, stored on a computer readable medium, as claimed in claim 30 further comprising the steps of:
-
converting a time domain representation of y1(nT2)=Σ
akh1(nT2−
kT)+e1(nT2) to a frequency domain representation Y1(ejω
)=P(ejω
)+E1(ejω
) where P(ejω
) is a frequency domain representation of Σ
akh1(nT2−
kT) and where E1(ejω
) is a frequency domain representation of the term e1(nT2); andconverting a time domain representation of y2(nT2)=Σ
akh1(nT2−
kT−
τ
)+e3(nT2) to a frequency domain representation Y2(ejω
)=P(ejω
)ejω
τ
+E3(ejω
) where P(ejω
)ejω
τ
is a frequency domain representation of Σ
akh1(nT2−
kT−
τ
) and where E3(ejω
) is a frequency domain representation of the term e3(nT2).
-
-
32. The computer executable process steps, stored on a computer readable medium, as claimed in claim 31 further comprising the step of:
-
multiplying said frequency domain representation Y1(ejω
) by a complex conjugate of said frequency domain representation Y2(ejω
) to calculate a complex cross power spectrum equal to;
Y1(ejω
)Y2(e−
jω
)=|P(ejω
)|2e−
jω
τ
+E4(ejω
)where E4(ejω
) is a frequency domain representation of terms that are functions of ejω
.
-
-
33. The computer executable process steps, stored on a computer readable medium, as claimed in claim 32 further comprising the step of:
determining a value of said timing error τ
by determining an average phase of said complex cross power spectrum.
-
34. The computer executable process steps, stored on a computer readable medium, as claimed in claim 33 wherein said step of determining a value of said timing error τ
- comprises the step of;
finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- comprises the step of;
-
35. The computer executable process steps, stored on a computer readable medium, as claimed in claim 33 wherein said step of determining a value of said timing error τ
- comprises the step of;
finding an average of a phase of each frequency bin in an N-point Fast Fourier Transform (FFT) unit that calculates said complex cross power spectrum Y(k) by calculating;
- comprises the step of;
-
36. The computer executable process steps, stored on a computer readable medium, as claimed in claim 33 further comprising the step of:
determining a value T of said transmitter clock period using;
τ
=MT−
MT2=M(T−
T2) where said value of said timing error τ
is known, and where M represents a known number of symbols between said first training sequence and said second training sequence, and where T2 represents a known value of an approximate value of said transmitter clock period T.
Specification