Frequency, phase, and gain estimation technique for use in a read channel receiver of a hard disk drive

A method of synchronizing a read channel of a hard disk drive, in reference to data that is read by said read channel, said method comprising:

• first generating two or more preliminary phase estimates based on one or more preambles of one or more data sectors in said hard disk drive;
• second generating a frequency offset and a phase offset by applying linear regression to said two or more preliminary phase estimates;
• and
• using said frequency offset and said phase offset to perform said synchronizing, said phase offset obtained using the equation:
• θ
• ^
• 0
• ⁡
• (
• k
• )
• =
• 1
• 8
• +
• γ
• ⁡
• (
• k
• )
• ⁢
• R
• xy
• +
• δ
• ⁡
• (
• k
• )
• ⁢
• R
• y
• ,
• as determined by computing an inverse matrix,
• (
• x
• T
• ⁢
• x
• x
• T
• ⁢
• I
• L
• ×
• 1
• I
• 1
• ×
• L
• ⁢
• x
• L
• )
• -
• 1
• ,
• wherein X=(1, . . ., L)T, and IL×1 comprises a L by 1 vector of ones, and I1×L comprises a 1 by L vector of all ones, said γ(k) comprises the row 2, column 1 term of said inverse matrix, and said δ(k) comprises the row 2, column 2 term of said inverse matrix, and wherein Rxy is equal to XT multiplied by a vector comprising L of said two or more preliminary phase estimates and Ry is equal to I1×L multiplied by said vector comprising L of said two or more preliminary phase estimates.

A system for synchronizing a read channel of a hard disk drive, in reference to data that is read by said read channel, said system comprising:

• at least one circuitry for first generating two or more preliminary phase estimates based on one or more preambles of one or more data sectors in said hard disk drive, for second generating a frequency offset and a phase offset by applying linear regression to said two or more preliminary phase estimates, and for using said frequency offset and said phase offset to perform said synchronizing, said frequency offset obtained using the equation:
• Δ{circumflex over (f)}(k)=α(k)Rxy+β(k)Ry,
• as determined by computing an inverse matrix,
• (
• x
• T
• ⁢
• x
• x
• T
• ⁢
• I
• L
• ×
• 1
• I
• 1
• ×
• L
• ⁢
• x
• L
• )
• -
• 1
• ,
• wherein X=(1, . . ., L)T, and IL×1 comprises a L by 1 vector of ones, and I1×L comprises a 1 by L vector of all ones, said α(k) comprises the row 1, column 1 term of said inverse matrix, and said β(k) comprises the row 1, column 2 term of said inverse matrix, and wherein Rxy is equal to XT multiplied by a vector comprising L of said two or more preliminary phase estimates and Ry is eciual to I1×L multiplied by said vector comprising L of said two or more preliminary phase estimates.

A system for synchronizing a read channel of a hard disk drive, in reference to data that is read by said read channel, said system comprising:

• at least one circuitry for first generating two or more preliminary phase estimates based on one or more preambles of one or more data sectors in said hard disk drive, for second generating a frequency offset and a phase offset by applying linear regression to said two or more preliminary phase estimates, and for using said frequency offset and said phase offset to perform said synchronizing, said phase offset obtained using the equation:
• θ
• ^
• 0
• ⁡
• (
• k
• )
• =
• 1
• 8
• +
• γ
• ⁡
• (
• k
• )
• ⁢
• R
• xy
• +
• δ
• ⁡
• (
• k
• )
• ⁢
• R
• y
• ,
• as determined by computing an inverse matrix,
• (
• x
• T
• ⁢
• x
• x
• T
• ⁢
• I
• L
• ×
• 1
• I
• 1
• ×
• L
• ⁢
• x
• L
• )
• -
• 1
• ,
• wherein X=(1, . . .,L)T, and IL×1 comprises a L by 1 vector of ones, and I1×L comprises a 1 by L vector of all ones, said γ(k) comprises the row 2, column 1 term, of said inverse matrix, and said δ(k) comprises the row 2, column 2 term of said inverse matrix, and wherein Rxy is equal to XT multiplied by a vector comprising L of said two or more preliminary phase estimates and Ry is equal to I1×L multiplied by said vector comprising L of said two or more preliminary phase estimates.

A method of determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said method comprising:

• determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive;
• using said sine and cosine projections to generate two or more preliminary phase estimates;
• and
• using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said sine projections described by the equation,
• P
• ⁢
• ⁢
• sin
• ⁡
• (
• k
• )
• =
• a
• ⁢
• ⁢
• cos
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples, while P sin(k) represents a sine projection of said consecutive samples.

A method of determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said method comprising:

• determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive;
• using said sine and cosine projections to generate two or more preliminary phase estimates;
• and
• using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said cosine projections described by the equation,
• P
• ⁢
• ⁢
• cos
• ⁡
• (
• k
• )
• =
• a
• ⁢
• ⁢
• sin
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples, while P cos(k) represents a cosine projection of said consecutive samples.

A system for determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said system comprising:

• at least one circuitry for determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive, for using said sine and cosine projections to generate two or more preliminary phase estimates, and for using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said sine projections described by the equation,
• P
• ⁢
• ⁢
• sin
• ⁡
• (
• k
• )
• =
• a
• ⁢
• ⁢
• cos
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples, while P sin(k) represents a sine projection of said consecutive samples.

A system for determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said system comprising:

• at least one circuitry for determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive, for using said sine and cosine projections to generate two or more preliminary phase estimates, and for using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said cosine projections described by the equation,
• P
• ⁢
• ⁢
• cos
• ⁡
• (
• k
• )
• =
• a
• ⁢
• ⁢
• sin
• ⁢
• ⁢
• 2
• ⁢
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples, while P cos(k) represents a cosine projection of said consecutive samples.

A method of determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said method comprising:

• determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive;
• using said sine and cosine projections to generate two or more preliminary phase estimates;
• and
• using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said generating two or more phase estimates accomplished by determining two or more quotients, each of said two or more quotients determined by dividing a corresponding cosine projection by a corresponding sine projection of said sine and cosine projections, wherein each of said two or more quotients, Q(k), is described by the following equation:
• Q(k)=tan2πφ(k),
• wherein
• ϕ
• ⁡
• (
• k
• )
• =
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• ,
• wherein said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples.

A system for determining a frequency offset and a phase offset during reading of a data sector of a hard disk drive, said system comprising:

• at least one circuitry for:
• determining sine and cosine projections using a number of consecutive samples obtained from a preamble of said data sector of said hard disk drive;
• using said sine and cosine projections to generate two or more preliminary phase estimates;
• and
• using linear regression to generate said frequency offset and said phase offset using said two or more preliminary phase estimates, said generating two or more phase estimates accomplished by determining two or more quotients, each of said two or more quotients determined by dividing a corresponding cosine projection by a corresponding sine projection of said sine and cosine projections, wherein each of said two or more quotients, Q(k), is described by the following equation:
• Q(k)=tan2πφ(k),
• wherein
• ϕ
• ⁡
• (
• k
• )
• =
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• ,
• wherein said frequency offset given by Δf and said phase offset given by θ0, wherein k represents an integer variable that indexes said consecutive samples.

A method of estimating the gain or amplitude of a data stream read by a read channel receiver of a hard disk drive comprising determining one or more sine and cosine projections of a number of consecutive samples of one or more preambles of one or more data sectors in said hard disk drive, said one or more sine and cosine projections computed using the following equations:

• P
• ⁢
• ⁢
• sin
• =
• a
• ⁢
• ⁢
• cos
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• P
• ⁢
• ⁢
• cos
• =
• a
• ⁢
• ⁢
• sin
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• wherein said frequency offset is given by Δf and said phase offset is given by θ0, wherein k represents an integer variable that indexes said consecutive samples and wherein P sin and P cos represent a sine and cosine projections of said consecutive samples.

A system for estimating the gain or amplitude of a data stream read by a read channel receiver of a hard disk drive comprising:

• at least one circuitry for determining one or more sine and cosine projections of a number of consecutive samples of one or more preambles of one or more data sectors in said hard disk drive, said one or more sine and cosine projections computed using the following equations:
• P
• ⁢
• ⁢
• sin
• =
• a
• ⁢
• ⁢
• cos
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• P
• ⁢
• ⁢
• cos
• =
• a
• ⁢
• ⁢
• sin
• ⁢
• ⁢
• 2
• ⁢
• π
• ⁡
• (
• Δ
• ⁢
• ⁢
• fk
• +
• θ
• 0
• -
• 1
• 8
• )
• ,
• wherein said frequency offset is given by Δf and said phase offset is given by θ0, wherein k represents an integer variable that indexes said consecutive samples and wherein P sin and P cos represent a sine and cosine projections of said consecutive samples.