# US 2017/0117878 A1 · Method and Apparatus for Determining Stability Factor of Adaptive Filter

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- Number: US 2017/0117878 A1
- Document ID: US20170117878A1
- Status: Published application
- Kind: A1
- Application number: 15/400,147
- Filed: 2017-01-06
- Published: 2017-04-27
- Earliest claimed: 2014-08-22
- Assignees: Huawei Technologies Co., Ltd.
- Applicants: Huawei Technologies Co., Ltd.
- Inventors: Eyal Shlomot; Yuanyuan Liu; Haiting Li
- Web page: https://patentgrep.com/patent/US20170117878A1

## CPC

- H03H 21/0043: {Adaptive algorithms}
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- H03H 2021/0054: {Affine projection}
- H03H 2021/0061: {Normalized LMS [NLMS]}
- H03H: IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS (waveguides, resonators, lines or other devices of the waveguide type H01P)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method and an apparatus for determining a stability factor of an adaptive filter is presented. The method includes: determining, according to first input signal that are input to an adaptive filter, a reference input matrix of the first input signal; determining a stability parameter of the first input signal according to the reference input matrix; and determining a stability factor of the adaptive filter according to the stability parameter. According to the method and apparatus for determining a stability factor of an adaptive filter provided in the embodiments of the present application, the stability factor of the adaptive filter can be adaptively obtained according to a stability feature of the first input signal, and the adaptive filter can reach a balance between a convergence speed and steady state error performance.

## Claims

### Claim 1

A method for determining a stability factor of an adaptive filter, comprising:
determining, according to a first input signal that is input to the adaptive filter, a reference input matrix of the first input signal;
determining a stability parameter of the first input signal according to the reference input matrix; and
determining the stability factor of the adaptive filter according to the stability parameter.

### Claim 2 (depends on 1)

The method according to claim 1, wherein determining the stability factor of the adaptive filter according to the stability parameter comprises determining the stability factor of the adaptive filter according to the stability parameter and a decreasing function relation between the stability factor and the stability parameter.

### Claim 3 (depends on 2)

The method according to claim 2, wherein determining the stability factor of the adaptive filter according to the stability parameter and the decreasing function relation between the stability factor and the stability parameter comprises determining, when the stability parameter is greater than or equal to a first threshold and is less than or equal to a second threshold, the stability factor according to the following function relational expression:
kδ=Aα+B,
wherein kδ is the stability factor, wherein α is the stability parameter, wherein A is a real number less than 0, and wherein B is a real number greater than 0.

### Claim 4 (depends on 1)

The method according to claim 1, wherein determining the stability factor of the adaptive filter according to the stability parameter comprises:
determining that the stability factor is a first constant when the stability parameter is less than or equal to a third threshold; or
determining that the stability factor is a second constant when the stability parameter is greater than or equal to a fourth threshold, wherein the third threshold is less than the fourth threshold, wherein both the first constant and the second constant are numbers greater than 0, and wherein the first constant is greater than the second constant.

### Claim 5 (depends on 1)

The method according to claim 1, wherein determining the stability parameter of the first input signal according to the reference input matrix comprises:
transposing the reference input matrix in order to obtain a transposed matrix;
multiplying the transposed matrix by the reference input matrix in order to obtain a first matrix; and
determining a value of a determinant of the first matrix as the stability parameter.

### Claim 6 (depends on 1)

The method according to claim 1, wherein determining the stability parameter of the first input signal according to the reference input matrix comprises:
transposing the reference input matrix in order to obtain a transposed matrix;
multiplying the transposed matrix by the reference input matrix in order to obtain a second matrix; and
determining, as the stability parameter, a result obtained by taking a logarithm of a value of a determinant of the second matrix.

### Claim 7 (depends on 1)

The method according to claim 1, further comprising:
determining, according to second input signal that is input to the adaptive filter, an input vector of the second input signal;
determining an output signal at a current time according to a coefficient of the adaptive filter at the current time, the input vector, and the reference input matrix; and
determining a filtering coefficient of the adaptive filter according to the reference input matrix, the output signal, the stability factor, and an update step of the adaptive filter.

### Claim 8

An apparatus for determining a stability factor of an adaptive filter, comprising:
a memory storing executable instructions; and
a processor coupled to the memory and configured to:
determine, according to a first input signal that is input to the adaptive filter, a reference input matrix of the first input signal;
determine a stability parameter of the first input signal according to the reference input matrix; and
determine the stability factor of the adaptive filter according to the stability parameter.

### Claim 9 (depends on 8)

The apparatus according to claim 8, wherein the processor is further configured to determine the stability factor of the adaptive filter according to the stability parameter and a decreasing function relation between the stability factor and the stability parameter.

### Claim 10 (depends on 9)

The apparatus according to claim 9, wherein the processor is further configured to determine, when the stability parameter is greater than or equal to a first threshold and is less than or equal to a second threshold, the stability factor according to the following function relational expression:
kδ=Aα+B,
wherein kδ is the stability factor, wherein α is the stability parameter, wherein A is a real number less than 0, and wherein B is a real number greater than 0.

### Claim 11 (depends on 8)

The apparatus according to claim 8, wherein the processor is further configured to:
determine that the stability factor is a first constant when the stability parameter is less than or equal to a third threshold; and
determine that the stability factor is a second constant when the stability parameter is greater than or equal to a fourth threshold, wherein the third threshold is less than the fourth threshold, wherein both the first constant and the second constant are numbers greater than 0, and wherein the first constant is greater than the second constant.

### Claim 12 (depends on 8)

The apparatus according to claim 8, wherein the processor is further configured to:
transpose the reference input matrix in order to obtain a transposed matrix;
multiply the transposed matrix by the reference input matrix in order to obtain a first matrix; and
determine a value of a determinant of the first matrix as the stability parameter.

### Claim 13 (depends on 8)

The apparatus according to claim 8, wherein the processor is further configured to:
transpose the reference input matrix, to obtain a transposed matrix;
multiply the transposed matrix obtained by the reference input matrix, to obtain a second matrix; and
determine, as the stability parameter, a result obtained by taking a logarithm of a value of a determinant of the second matrix.

### Claim 14 (depends on 8)

The apparatus according to claim 8, wherein the processor is further configured to:
determine, according to second input signal that is input to the adaptive filter, an input vector of the second input signal;
determine an output signal at a current time according to a coefficient of the adaptive filter at the current time, the input vector, and the reference input matrix; and
determine a filtering coefficient of the adaptive filter according to the reference input matrix, the output signal, the stability factor, and an update step of the adaptive filter.