# US 7,746,186 B2 · Wideband quadrature imbalance compensation system and method

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- Number: US 7,746,186 B2
- Document ID: US7746186B2
- Status: Granted
- Kind: B2
- Application number: 12/011,672
- Filed: 2008-01-29
- Published: 2009-07-30
- Granted: 2010-06-29
- Earliest claimed: 2008-01-29
- Assignees: Analog Devices, Inc.
- Inventors: Ganesh Ananthaswamy
- Web page: https://patentgrep.com/patent/US7746186B2

## CPC

- H04L 27/3863: {Compensation for quadrature error in the received signal}
- H04L 27/366: {Arrangements for compensating undesirable properties of the transmission path between the modulator and the demodulator}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

Compensating for wideband quadrature imbalance error by introducing inverse complex inputs to phase quadrature estimator filters to generate estimated quadrature distortion; summing estimator quadrature distortion with a delayed version of the actual complex input to obtain estimated quadrature output; comparing the output with the true output to obtain residual quadrature imbalance error; applying a least mean square to the inverse input and imbalance residual error to obtain an updated estimate of filter coefficients; updating the filter coefficients of the phase quadrature estimator; and updating the filter coefficients of a phase quadrature compensator with the filter coefficients of the phase quadrature estimator to obtain a quadrature output pre-compensated for quadrature imbalance error.

## Claims

### Claim 1

A wideband quadrature imbalance error compensation system, comprising:
an in-phase channel for receiving an in-phase input, the in-phase channel having a first in-phase filter circuit;
a quadrature channel for receiving a quadrature input, the quadrature channel having a first quadrature filter circuit;
a first cross-coupled filter responsive to the quadrature input;
a second cross-coupled filter responsive to the in-phase input;
a first in-phase summing circuit responsive to the first in-phase filter circuit and the first cross-coupled filter to provide a first complex signal;
a first quadrature summing circuit responsive to the first quadrature filter circuit and the second cross-coupled filter to provide a second complex signal;
a complex circuit for rotating the second complex signal by 90°;
a first output summing circuit responsive to the first complex signal and second rotated complex signal to provide a quadrature output pre-compensated for a quadrature imbalance error in an output of a quadrature modulator; and
a phase quadrature estimator for determining the coefficients of the first and second cross-coupled filters to minimize the quadrature imbalance error;
wherein the phase quadrature estimator includes:
a comparator responsive to the output of the quadrature modulator and an estimate of the output of the quadrature modulator to determine a residual quadrature imbalance error; and
a least mean square estimator responsive to the residual quadrature imbalance error and an input of the wideband quadrature imbalance error compensation system to update the coefficients of the first and second cross-coupled filters.

### Claim 2 (depends on 1)

The wideband quadrature imbalance error compensation system of claim 1, wherein the cross-coupled filters are complex coefficient filters.

### Claim 3 (depends on 2)

The wideband quadrature imbalance error compensation system of claim 2 further including a phase quadrature estimator for determining the complex coefficients for the first and second cross-coupled filters for minimizing quadrature imbalance error.

### Claim 4

A wideband quadrature imbalance error compensation system, comprising:
an in-phase channel for receiving an in-phase input, the in-phase channel having a first in-phase filter circuit;
a quadrature channel for receiving a quadrature input, the quadrature channel having a first quadrature filter circuit;
a first cross-coupled filter responsive to the quadrature input;
a second cross-coupled filter responsive to the in-phase input;
a first in-phase summing circuit responsive to said first in-phase filter circuit and the first cross-coupled filter to provide a first complex signal;
a first quadrature summing circuit responsive to the first quadrature filter circuit and the second cross-coupled filter to provide a second complex signal;
a complex circuit for rotating the second complex signal by 90°;
a first output summing circuit responsive to the first complex signal and second rotated complex signal to provide a quadrature output pre-compensated for a quadrature imbalance error in an output of a quadrature modulator;
a phase quadrature estimator for determining the complex coefficients for the first and second cross-coupled filters for minimizing the quadrature imbalance error;
wherein the first and second cross-coupled filters are complex coefficient filters;
wherein the phase quadrature estimator further includes:
an in-phase channel for receiving the in-phase input, the in-phase channel of the phase quadrature estimator having a second in-phase filter circuit;
a quadrature channel for receiving the quadrature input, the quadrature channel of the phase quadrature estimator having a second quadrature filter circuit;
a third cross-coupled filter responsive to the quadrature input;
a fourth cross-coupled filter responsive to the in-phase input;
a second in-phase summing circuit responsive to the second in-phase filter circuit and the third cross-coupled filter to provide a third complex signal;
a second quadrature summing circuit unit responsive to the second quadrature filter circuit and the fourth cross-coupled filter to provide a fourth complex signal;
a second complex circuit for rotating the fourth complex signal by 90°; and
a second output summing circuit responsive to the third complex signal and fourth rotated complex signal to provide a complex output which is an estimate of the output of the quadrature modulator.

### Claim 5 (depends on 4)

The wideband quadrature imbalance error compensation system of claim 4, wherein the in-phase and quadrature channels include delay circuits.

### Claim 6 (depends on 4)

The wideband quadrature imbalance error compensation system of claim 4, wherein the cross-coupled filters are FIR filters.

### Claim 7 (depends on 4)

The wideband quadrature imbalance error compensation system of claim 4 in which the phase quadrature estimator includes a comparator responsive to the output of the quadrature modulator and the estimate of the output of the quadrature modulator for determining a residual quadrature imbalance error.

### Claim 8 (depends on 7)

The wideband quadrature imbalance error compensation system of claim 7 in which the phase quadrature estimator includes a least mean square device responsive to the residual quadrature imbalance error and an input of the wideband quadrature imbalance error compensation system to modify the third and fourth cross-coupled filter coefficients in the phase quadrature estimator to reduce the residual quadrature imbalance error.

### Claim 9 (depends on 8)

The wideband quadrature imbalance error compensation system of claim 8 in which the phase quadrature estimator includes a control circuit to update the filter coefficients of the first and second cross-coupled filters based on modifications to the coefficients of the third and fourth cross-coupled filters.

### Claim 10

A method for compensating for wideband quadrature modulator imbalance error, comprising:
introducing inverse complex inputs to phase quadrature estimator filters to generate an estimated quadrature distortion;
summing the estimated quadrature distortion with a delayed version of the actual complex input to obtain an estimated quadrature modulator output;
comparing the estimated quadrature modulator output with an output of a quadrature modulator to obtain a residual quadrature imbalance error;
applying a least mean square algorithm to the inverse complex inputs and the residual quadrature imbalance error to obtain an updated estimate of filter coefficients;
updating the filter coefficients of the phase quadrature estimator filters; and
updating the filter coefficients of a phase quadrature compensator with the filter coefficients of the phase quadrature estimator filters to obtain a quadrature output pre-compensated for the quadrature modulator imbalance error.

### Claim 11

A quadrature imbalance error compensation system, comprising:
a quadrature modulator having (1) an input terminal and (2) an output terminal;
a phase quadrature compensator having (1) an input terminal for receiving an input signal and (2) an output terminal that is coupled to the input terminal of the quadrature modulator, wherein the phase quadrature compensator includes a pair of cross-coupled filters; and
a phase quadrature estimator having (1) an input terminal that is coupled to the input terminal of the phase quadrature compensator and (2) an output terminal for outputting updates to coefficients of the pair of cross-coupled filters of the phase quadrature compensator,
wherein the phase quadrature estimator includes:
a pair of cross-coupled filters having (1) an input terminal that is coupled to the input terminal of the phase quadrature estimator for receiving the input signal and (2) an output terminal for outputting an estimate of the output of the quadrature modulator;
a comparator responsive to the output of the quadrature modulator and the estimate of the output of the quadrature modulator to compute a residual quadrature imbalance error; and
a least mean square estimator responsive to the residual quadrature imbalance error and the input signal to modify the coefficients of the pair of cross-coupled filters of the phase quadrature estimator and output the updates at the output terminal of the quadrature estimator.

### Claim 12 (depends on 11)

The quadrature imbalance error compensation system of claim 11, wherein the phase quadrature compensator further includes:
an in-phase channel for receiving an in-phase of the input signal, the in-phase channel having a first in-phase filter circuit;
a quadrature channel for receiving a quadrature phase of the input signal, the quadrature channel having a first quadrature filter circuit;
a first cross-coupled filter responsive to the quadrature phase;
a second cross-coupled filter responsive to the in-phase;
a first in-phase summing circuit responsive to the first in-phase filter circuit and the first cross-coupled filter to provide a first complex signal;
a first quadrature summing circuit responsive to the first quadrature filter circuit and the second cross-coupled filter to provide a second complex signal;
a complex circuit for rotating the second complex signal by 90°; and
a first output summing circuit responsive to the first complex signal and the rotated second complex signal to provide a quadrature output pre-compensated for the quadrature imbalance error.