Measuring I/Q impairments from sampled complex signals
Systems and methods for measuring transmitter and/or receiver I/Q impairments are disclosed, including iterative methods for measuring transmitter I/Q impairments using shared local oscillators, iterative methods for measuring transmitter I/Q impairments using intentionally-offset local oscillators, and methods for measuring receiver I/Q impairments. Also disclosed are methods for computing I/Q impairments from a sampled complex signal, methods for computing DC properties of a signal path between the transmitter and receiver, and methods for transforming I/Q impairments through a linear system.
1. A method for estimating I/Q impairment information associated with a sampled complex signal produced by a receiver, the method comprising:
(a) computing, by digital circuitry, a transform value C I at frequency f of an I component of the sampled complex signal, wherein the sampled complex signal is a baseband signal produced by the receiver in response to the receiver being stimulated with a stimulus signal including a tone at displacement frequency f and a void interval at displacement frequency −f, wherein displacement frequencies f and −f are displacements with respect to a local oscillator frequency of the receiver;
(b) computing, by the digital circuitry, a transform value C Q at frequency f of a Q component of the sampled complex signal;
(c) performing one or more of:
computing, by the digital circuitry, a gain imbalance g of the sampled complex signal at frequency f based on magnitudes of the values C I and C Q , wherein the gain imbalance g includes a gain imbalance of the receiver; or
computing, by the digital circuitry, a phase skew φ of the sampled complex signal at frequency f based on phases of the values C I and C Q , wherein the phase skew φ includes a phase skew of the receiver;
wherein data including the gain imbalance g and/or the phase skew φ is usable to at least partially correct I/Q impairments of the receiver.
2. The method of claim 1 , wherein the gain imbalance g and/or the phase skew φ is partially dependent on I/Q impairments of a device that generates the stimulus signal.
3. The method of claim 1 , wherein the stimulus signal is generated by a transmitter whose local oscillator frequency is offset from the receiver's local oscillator frequency by a non-zero amount.
4. The method of claim 1 , wherein the stimulus signal is generated by a calibration tone generator.
5. The method of claim 1 , further comprising:
applying a time-domain window to the sampled complex signal prior to said computing the value C I and said computing the value C Q .
6. The method of claim 1 , further comprising:
computing correction information based on said data; and
configuring the receiver using the correction information to at least partially correct the I/Q impairments of the receiver.
7. The method of claim 1 , wherein the digital circuitry includes a programmable hardware element.
8. The method of claim 1 , wherein the digital circuitry includes a processor configured to execute program instructions.
9. A computer system for estimating I/Q impairment information associated with a sampled complex signal produced by a receiver, the computer system comprising:
a processor; and
memory storing program instructions, wherein the program instructions, when executed by the processor, cause the processor to:
compute a transform value C I at frequency f of an I component of the sampled complex signal, wherein the sampled complex signal is a baseband signal produced by the receiver in response to the receiver being stimulated with a stimulus signal including a tone at displacement frequency f and a void interval at displacement frequency −f, wherein displacement frequencies f and −f are displacements with respect to a local oscillator frequency of the receiver;
compute a transform value C Q at frequency f of a Q component of the sampled complex signal;
perform one or more of:
computing a gain imbalance g of the sampled complex signal at frequency f based on magnitudes of the values C I and C Q , wherein the gain imbalance g includes a gain imbalance of the receiver; or
computing a phase skew φ of the sampled complex signal at frequency f based on phases of the values C I and C Q , wherein the phase skew φ includes a phase skew of the receiver;
wherein data including the gain imbalance g and/or the phase skew φ is usable to at least partially correct I/Q impairments of the receiver.
10. The computer system of claim 9 , wherein the gain imbalance g and/or the phase skew φ is partially dependent on I/Q impairments of a device that generates the stimulus signal.
11. The computer system of claim 9 , wherein the stimulus signal is generated by a transmitter whose local oscillator frequency is offset from the receiver's local oscillator frequency by a non-zero amount.
12. The computer system of claim 9 , wherein the stimulus signal is generated by a calibration tone generator.
13. The computer system of claim 9 , wherein the program instructions, when executed by the processor, further cause the processor to:
apply a time-domain window to the sampled complex signal prior to said computing the value C I and said computing the value C Q .
14. The computer system of claim 9 , wherein the program instructions, when executed by the processor, further cause the processor to:
compute correction information based on said data; and
configure the receiver using the correction information to at least partially correct the I/Q impairments of the receiver.
15. A non-transitory computer-accessible memory medium for estimating I/Q impairments associated with a sampled complex signal produced by a receiver, wherein the memory medium stores program instructions, wherein the program instructions, when executed by a processor, cause the processor to:
(a) compute a transform value C I at frequency f of an I component of the sampled complex signal, wherein the sampled complex signal is a baseband signal produced by the receiver in response to the receiver being stimulated with a stimulus signal including a tone at displacement frequency f and a void interval at displacement frequency −f, wherein displacement frequencies f and −f are displacements with respect to a local oscillator frequency of the receiver;
(b) compute a transform value C Q at frequency f of a Q component of the sampled complex signal;
(c) perform one or more of:
computing a gain imbalance g of the sampled complex signal at frequency f based on magnitudes of the values C I and C Q , wherein the gain imbalance g includes a gain imbalance of the receiver; or
computing a phase skew φ of the sampled complex signal at frequency f based on phases of the values C I and C Q , wherein the phase skew φ includes a phase skew of the receiver;
wherein data including the gain imbalance g and/or the phase skew φ is usable to at least partially correct I/Q impairments of the receiver.
16. The non-transitory computer-accessible memory medium of claim 15 , wherein the gain imbalance g and/or the phase skew φ is partially dependent on I/Q impairments of a device that generates the stimulus signal.
17. The non-transitory computer-accessible memory medium of claim 15 , wherein the stimulus signal is generated by a transmitter whose local oscillator frequency is offset from the receiver's local oscillator frequency by a non-zero amount.
18. The non-transitory computer-accessible memory medium of claim 15 , wherein the stimulus signal is generated by a calibration tone generator.
19. The non-transitory computer-accessible memory medium of claim 15 , wherein the program instructions, when executed by the processor, further cause the processor to:
compute correction information based on said data; and
configure the receiver using the correction information to at least partially correct the I/Q impairments of the receiver.
20. A method performed by a device for estimating I/Q impairment information associated with a sampled complex signal produced by a receiver, the method comprising:
receiving the sampled complex signal from the receiver, wherein the sampled complex signal is a baseband signal produced by the receiver in response to the receiver being stimulated with a stimulus signal including a tone at displacement frequency f and a void interval at displacement frequency −f, wherein displacement frequencies f and −f are displacements with respect to a local oscillator frequency of the receiver;
computing, by the device, a transform value C I at frequency f of an I component of the sampled complex signal;
computing, by the device, a transform value C Q at frequency f of a Q component of the sampled complex signal;
computing, by the device, a gain imbalance g of the sampled complex signal at frequency f based on magnitudes of the values C I and C Q , wherein the gain imbalance g includes a gain imbalance of the receiver;
wherein the gain imbalance g is usable to at least partially correct I/Q impairments of the receiver.
21. The method of claim 20 , further comprising:
computing correction information based on the gain imbalance g; and
configuring the receiver using the correction information to at least partially correct the I/Q impairments of the receiver.
22. The method of claim 20 , further comprising:
the receiver generating the sampled complex signal in response to being stimulated with the stimulus signal.
23. The method of claim 20 , wherein the stimulus signal is generated by a transmitter whose local oscillator frequency is offset from the receiver's local oscillator frequency by a non-zero amount.
24. A method performed by a device for estimating I/Q impairment information associated with a sampled complex signal produced by a receiver, the method comprising:
receiving the sampled complex signal from the receiver, wherein the sampled complex signal is a baseband signal produced by the receiver in response to the receiver being stimulated with a stimulus signal including a tone at displacement frequency f and a void interval at displacement frequency −f, wherein displacement frequencies f and −f are displacements with respect to a local oscillator frequency of the receiver;
computing, by the device, a transform value C I at frequency f of an I component of the sampled complex signal;
computing, by the device, a transform value C Q at frequency f of a Q component of the sampled complex signal;
computing, by the device, a phase skew φ of the sampled complex signal at frequency f based on phases of the values C I and C Q , wherein the phase skew φ includes a phase skew of the receiver;
wherein the phase skew φ is usable to at least partially correct I/Q impairments of the receiver.
25. The method of claim 24 , further comprising:
computing correction information based on the phase skew φ; and
configuring the receiver using the correction information to at least partially correct the I/Q impairments of the receiver.
26. The method of claim 24 , further comprising:
the receiver generating the sampled complex signal in response to being stimulated with the stimulus signal.
27. The method of claim 24 , wherein the stimulus signal is generated by a transmitter whose local oscillator frequency is offset from the receiver's local oscillator frequency by a non-zero amount.