Signal processor for estimating signal parameters using an approximated inverse matrix
A device that estimates information from a signal includes a receiver for receiving an input signal and electronic processing circuitry. The electronic processing circuitry generates a matrix associated with the input signal and determines an approximation of an inverse of the matrix based on the adjoint of the matrix and a scaling factor associated with the determinant of the matrix. This approximation avoids possible mathematical difficulties that may be encountered in certain situations when a typical matrix inversion is calculated. The approximated inverse matrix is applied to the input signal to transform the input signal into an output signal. Information associated with the input signal is then determined based on the output signal.
1. A device for estimating information from a signal, comprising:
a receiver for receiving an input signal, and electronic processing circuitry coupled to the receiver and configured to:
generate a matrix associated with the input signal;
determine an approximation of an inverse of the matrix based on the adjoint of the matrix and a scaling factor associated with the determinant of the matrix;
apply the approximated inverse matrix to the input signal to transform the input signal into an output signal; and
determine information associated with the input signal based on the output signal,
wherein the electronic processing circuitry is configured to digitally filter the input signal using weights derived from the approximated inverse matrix.
2. The device in claim 1 , wherein the electronic processing circuitry is configured to approximate the inverse of the matrix by multiplying the adjoint of the matrix by the scaling factor associated with a determinant of the matrix.
3. The device in claim 1 , wherein the electronic processing circuitry is configured to apply the adjoint of the matrix to the input signal to transform the input signal into an intermediate signal and then to apply the scaling factor to the intermediate signal to produce the output signal.
4. The device in claim 1 , wherein the electronic processing circuitry is configured to approximate the inverse of the matrix by an adjoint of the matrix and a scaling function associated with a determinant of the matrix, said scaling function comprising thresholding a function of the determinant of the matrix.
5. The device in claim 4 , wherein the electronic processing circuitry is configured to compensate the output signal for the approximation.
6. The device in claim 1 , wherein the electronic processing circuitry is configured to scale the output signal to offset scaling associated with the scaling function.
7. The device in claim 1 , wherein the matrix R is Hermitian symmetric.
8. The device in claim 1 , wherein the inverse of matrix R is defined as:
R
-
1
=
(
1
det
(
R
)
)
adj
(
R
)
where
(
1
det
(
R
)
)
where is the determinant of matrix R and adj(R) is the adjoint of matrix R, wherein the electronic processing circuitry is configured to approximate the inverse of matrix R using: R −1 ≈ƒ(R)adj(R), wherein
f
(
R
)
=
{
1
/
det
(
R
)
,
det
(
R
)
>
1
/
f
max
f
max
,
otherwise
,
and wherein 1/ƒ max is a threshold value.
9. The device in claim 1 , wherein the receiver is a wireless receiver or the receiver is a wired receiver.
10. The device in claim 1 , wherein the electronic processing circuitry is configured to equalize the input signal or estimate a communications channel used to convey the input signal using the approximated inverse matrix.
11. The device in claim 1 , wherein the electronic processing circuitry is configured to determine a signal quality associated with the input signal using the approximated inverse matrix.
12. The device in claim 1 , wherein the electronic processing circuitry is configured to perform multi-user detection using the approximated inverse matrix.
13. The device in claim 1 , wherein the receiver is a one of a G-RAKE radio receiver and a chip equalizer.
14. The device of claim 1 , wherein the device is one of a radar receiver and a sonar receiver.
15. The device of claim 1 , wherein the electronic processing circuitry is configured to compute minors or cofactors of the matrix and to use the computed minors or cofactors of the matrix in computing the adjoint and the scaling factor.
16. A method for estimating information from a signal, comprising:
receiving in a receiver an input signal from one or more sensors, and
electronic processing circuitry coupled to the receiver and performing the following steps:
generating a matrix associated with the input signal;
determining an approximation of an inverse of the matrix based on the adjoint of the matrix and a scaling factor associated with the determinant of the matrix;
applying the approximated inverse matrix to the input signal to transform the input signal into an output signal; and
determining and providing information associated with the input signal based on the output signal,
wherein the electronic processing circuitry digitally filters the input signal using weights derived from the approximated inverse matrix.
17. The method in claim 16 , wherein the electronic processing circuitry approximates the inverse of the matrix by multiplying the adjoint of the matrix by the scaling factor associated with a determinant of the matrix.
18. The method in claim 16 , wherein the electronic processing circuitry applies the adjoint of the matrix to the input signal to transform the input signal into an intermediate signal and then to apply the scaling factor to the intermediate signal to produce the output signal.
19. The method in claim 16 , wherein the electronic processing circuitry approximates the inverse of the matrix by an adjoint of the matrix and a scaling function associated with a determinant of the matrix, said scaling function comprising thresholding a function of the determinant of the matrix.
20. The method in claim 19 , wherein the electronic processing circuitry compensates the output signal for the approximation.
21. The method in claim 16 , wherein the electronic processing circuitry computes minors or cofactors of the matrix and shares them in computing the adjoint and the scaling factor.
22. The method in claim 16 , wherein the matrix R is Hermitian symmetric.
23. The method in claim 16 , wherein the inverse of matrix R is defined as:
R
-
1
=
(
1
det
(
R
)
)
adj
(
R
)
where
(
1
det
(
R
)
)
is the determinant of matrix R and adj(R) is the adjoint of matrix R, wherein the electronic processing circuitry is configured to approximate the inverse of matrix R using: R −1 ≈ƒ(R)adj(R) , wherein
f
(
R
)
=
{
1
/
det
(
R
)
,
det
(
R
)
>
1
/
f
max
f
max
,
otherwise
,
and wherein ƒ max is a threshold value.
24. The method in claim 16 , wherein the receiver is a wireless receiver or the receiver is a wired receiver.
25. The method in claim 16 , wherein the electronic processing circuitry equalizes the input signal or estimate a communications channel used to convey the input signal using the approximated inverse matrix.
26. The method in claim 16 , wherein the electronic processing circuitry determines a signal quality associated with the input signal using the approximated inverse matrix.
27. The method in claim 16 , wherein the electronic processing circuitry performs multi-user detection using the approximated inverse matrix.