Blind cost criterion timing recovery
First Claim
1. A method of timing recovery of symbols in a received signal, comprising the steps of:
- (a) generating a sequence of samples from the received signal with a sample period and sample phase related to a symbol rate of the symbols;
(b) generating a phase error for a current sample from the sequence based on a gradient of a blind cost criterion of Bussgang-class cost functions;
(c) adjusting at least one of the sample period and sample phase based on the phase error such that a magnitude of the phase error is driven to a predetermined point; and
(d) repeating steps (a), (b), and (c) for subsequent samples so as to substantially recover timing of the symbols in the received signal, wherein step (b) comprises the steps of;
(b1) calculating a blind cost error term based on the sample; and
(b2) forming an approximation of a derivative of the received signal with respect to the sampling phase.
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Accused Products
Abstract
Symbol timing recovery employs a blind cost criterion from the Bussgang class of functions, and its stochastic gradient, to generate a timing phase error used to adjust sampling of received symbols. For one implementation, the estimate is derived in accordance with the Constant Modulus (CM) criterion and its gradient via the CM algorithm (CMA), and the estimate is calculated from a sequence of samples. This estimate is then used to adjust the period and phase of the sample sequence toward the period and phase of the transmitted symbols, driving the timing phase error to zero. The values used may be either i) samples themselves, ii) processed (e.g., interpolated) samples, or iii) equalized and processed samples. In addition, timing phase error estimates for other cost criteria, including the least mean squares algorithm, may be generated. These timing phase error estimates are selected either alone or in combination for deriving the timing phase error used to adjust the period and phase of the sample sequence.
66 Citations
41 Claims
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1. A method of timing recovery of symbols in a received signal, comprising the steps of:
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(a) generating a sequence of samples from the received signal with a sample period and sample phase related to a symbol rate of the symbols; (b) generating a phase error for a current sample from the sequence based on a gradient of a blind cost criterion of Bussgang-class cost functions; (c) adjusting at least one of the sample period and sample phase based on the phase error such that a magnitude of the phase error is driven to a predetermined point; and (d) repeating steps (a), (b), and (c) for subsequent samples so as to substantially recover timing of the symbols in the received signal, wherein step (b) comprises the steps of; (b1) calculating a blind cost error term based on the sample; and (b2) forming an approximation of a derivative of the received signal with respect to the sampling phase. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
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18. Apparatus for timing recovery of a symbol rate for symbols in a received signal, comprising:
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a timing reference providing a reference signal; a sample generator configured to generate a sequence of samples from the received signal with a sample period and sample phase based on the reference signal and related to the symbol rate; a blind cost error term generator configured to generate a blind cost error term for a current sample of the sequence in accordance with a gradient of a blind cost criterion of Bussgang-class cost functions; and a timing phase detector configured to generate a phase error for the current sample from the sequence and based on the blind cost error term; wherein the timing reference modifies the reference signal based on the phase error to adjust at least one of the sample period and sample phase such that a magnitude of the phase error is driven to zero so as to substantially recover timing of the symbols in the received signal; and wherein the timing phase detector forms an approximation of a derivative of the received signal with respect to the sampling phase. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
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38. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to implement a method for timing recovery of symbols in a received signal, the method comprising the steps of:
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(a) generating a sequence of samples from the received signal with a sample period and sample phase related to a symbol rate of the symbols; (b) generating a phase error for a current sample from the sequence based on a gradient of a blind cost criterion of Bussgang-class cost functions; (c) adjusting at least one of the sample period and sample phase based on the phase error such that a magnitude of the phase error is driven to zero; and (d) repeating steps (a), (b), and (c) for subsequent samples so as to substantially recover timing of the symbols in the received signal wherein step (b) comprises the steps of; (b1) calculating a blind cost error term based on the sample; and (b2) forming an approximation of a derivative of the received signal with respect to the sampling phase. - View Dependent Claims (39)
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40. A method of timing recovery of symbols in a received signal, comprising the steps of:
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(a) generating a sequence of samples from the received signal with a sample period and sample phase related to a symbol rate of the symbols; (b) generating a phase error for a current sample from the sequence based on a gradient of a blind cost criterion of Bussgang-class cost functions; (c) adjusting at least one of the sample period and sample phase based on the phase error such that a magnitude of the phase error is driven to a predetermined point; and (d) repeating steps (a), (b), and (c) for subsequent samples so as to substantially recover timing of the symbols in the received signal, wherein; for step (b), the phase error is generated in accordance with a phase error calculation derived for a cost function error criterion having a corresponding cost function error term, the phase error calculation substituting the blind cost error term for the cost function error term; step (b) comprises the steps of; (b1) calculating a blind cost error term for a current sample yn(τ
) and a blind cost error term for a previous sample yn−
1(τ
), based on a gradient of a constant modulus (CM) cost criterion; and(b2) combining the current and previous blind cost error terms with the current and previous samples generated at the sampling period to generate the timing phase error as;
yn(τ
)yn−
1(τ
) ((ρ
2−
|yn(τ
)|2)−
(ρ
2−
|yn−
1(τ
)|2))where ρ
2 is a dispersion constant and τ
represents the sampling phase.
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41. Apparatus for timing recovery of a symbol rate for symbols in a received signal, comprising:
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a timing reference providing a reference signal; a sample generator configured to generate a sequence of samples from the received signal with a sample period and sample phase based on the reference signal and related to the symbol rate; a blind cost error term generator configured to generate a blind cost error term for a current sample of the sequence in accordance with a gradient of a blind cost criterion of Bussgang-class cost functions; and a timing phase detector configured to generate a phase error for the current sample from the sequence and based on the blind cost error term, wherein; the timing reference modifies the reference signal based on the phase error to adjust at least one of the sample period and sample phase such that a magnitude of the phase error is driven to zero so as to substantially recover timing of the symbols in the received signal; the phase detector generates the phase error in accordance with a phase error calculation derived for a cost function error criterion having a corresponding cost function error term, the phase error calculation substituting the blind cost error term for the cost function error term; the blind-cost error term is based on a gradient of a constant modulus (CM) cost criterion for the current sample defined as
dJCM/dτ
=(dJCM/dyn(τ
))dyn(τ
)/dτ
,wherein JCM=E[(p2−
|yn(τ
)|2] is the CM cost criterion, ρ
2 is a dispersion constant, yn(τ
) is a discrete value representing the current sample generated at the sampling period, τ
represents the sampling phase, and dyn(τ
)/dτ
is a derivative of the received signal with respect to the sampling phase, and a derivative of JCM with respect to yn(τ
) is defined as the blind cost error term eCMA[n] given by
eCMA[n]=yn(τ
)(ρ
2−
|yn(τ
)|2); andwherein the timing phase detector combines a current blind cost error term eCMA[n] and a previous blind cost error term eCMA[n−
1] with the current sample yn(τ
) and previous sample yn−
1(τ
) to generate the timing phase error as;
yn(τ
)yn−
1(τ
) ((ρ
2−
|yn(τ
)|2)−
(ρ
2−
|yn−
1(τ
)|2)).
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Specification