Fast computation of linear equalizer coefficients from channel estimate
View Patent ↗Computing optimal Linear Equalizer (LE) coefficients g opt from a channel estimate h. A channel impulse response h is first estimated based upon either a known training sequence or an unknown sequence. The channel estimate is formulated as a convolution matrix H. The convolution matrix H is then related to the LE coefficients in a matrix format equation, the matrix format equation based upon the structure of the LE, the convolution matrix, and an expected output of the LE. A Fast Transversal Filter (FTF) algorithm is then used to formulate a recursive least squares solution to the matrix format equation. Computing the recursive least squares solution yields the LE coefficients using structured equations.
1. A method for directly computing Linear Equalizer (LE) coefficients from a channel estimate, the method comprising:
formulating the channel estimate as a convolution matrix H;
relating the convolution matrix H to the LE coefficients in a matrix format equation, the matrix format equation based upon the structure of the LE, the convolution matrix, and an expected output of the LE;
using a Fast Transversal Filter (FTF) algorithm to formulate a recursive least squares solution to the matrix format equation, wherein a length of the LE is chosen to force the FTF algorithm to use a lower triangular matrix; and
computing the recursive least squares solution to yield the LE coefficients using structured equations.
2. The method of claim 1 , wherein the recursive least squares solution is formulated as a Kalman gain solution using the FTF algorithm.
3. The method of claim 2 , wherein the Kalman gain solution is determined using an Array Form Algorithm.
4. The method of claim 3 , wherein a length of the LE is chosen to force the Array Form Algorithm to use a lower triangular matrix.
5. The method of claim 1 , wherein the matrix format equation comprises:
g opt =[σ v 2 I+H*H] −1 H*d
where:
H is the convolution matrix;
g opt is a vector of the LE coefficients;
σ v 2 is the power spectral density of the channel estimate;
I is the identity matrix; and
d as a vector of all zeros except for the δ th element, which is unity, δ representing a system delay.
6. The method of claim 5 , wherein the system delay is a combination of a length of the channel and a length of the LE.
7. The method of claim 1 , wherein the channel estimate is based upon a known preamble sequence of a data packet upon which the LE operates.
8. The method of claim 1 , further comprising the LE using the LE coefficients to equalize received data.
9. The method of claim 7 , wherein the LE services at least one a receiver used in a High Definition Television, a receiver used in a Wireless Local Area Network, and a receiver used in a Cellular Telephone.
10. A Linear Equalizer System comprising:
a Liner Equalizer (LE) having an input that receives an uncompensated signal and an output; and
a LE coefficients processor that is operable to:
formulate the channel estimate as a convolution matrix H;
relate the convolution matrix H to the LE coefficients in a matrix format equation, the matrix format equation based upon the structure of the LE, the convolution matrix, and an expected output of the LE;
use a Fast Transversal Filter (FTF) algorithm to formulate a recursive least squares solution to the matrix format equation;
choose a length of the LE to force the FTF algorithm to use a lower triangular matrix; and
solve the recursive least squares solution to yield the LE coefficients.
11. The Linear Equalizer System of claim 10 , wherein the LE coefficients processor is operable to formulate the recursive least squares solution as a Kalman gain solution using the FTF algorithm.
12. The Linear Equalizer System of claim 11 , wherein the LE coefficients processor is operable to determine the Kalman gain solution using an Array Form Algorithm.
13. The Linear Equalizer System of claim 12 , the LE coefficients processor is operable to choose a length of the LE to force the Array Form Algorithm to use a lower triangular matrix.
14. The Linear Equalizer System of claim 10 , wherein the matrix format equation comprises:
g opt =[σ v 2 I+H*H] −1 H*d
where:
H is the convolution matrix;
g opt is a vector of the LE coefficients;
σ v 2 is the power spectral density of the channel estimate;
I is the identity matrix; and
d as a vector of all zeros except for the δ th element, which is unity, δ representing a system delay.
15. The Linear Equalizer System of claim 14 , wherein the system delay is a combination of a length of the channel and a length of the LE.
16. The Linear Equalizer System of claim 10 , wherein the channel estimate is based upon a known preamble sequence of a data packet upon which the LE operates.
17. The Linear Equalizer System of claim 10 , wherein the LE is operable to equalize received data using the LE coefficients.
18. The Linear Equalizer System of claim 16 , wherein the LE is operable to service at least one of a receiver used in a High Definition Television, a receiver used in a Wireless Local Area Network, and a receiver used in a Cellular Telephone.