Memoryless spectrum correction algorithm for non-ideal I/Q demodulators
An algorithm for correcting the output of an analog I/Q demodulator without the need for calibration or storing state information. The output of the analog I/Q demodulator is digitized, and the discrete-time samples are divided into segments. A digital frequency transform (e.g., a Discrete Fourier Transform) is computed for each segment. The effects of the non-ideal I/Q demodulator are removed by identifying a set of image frequency candidates for each digital frequency transform, and for each image frequency candidate, estimating a set of demodulator imbalance parameters to characterize the demodulator imbalance at that frequency and correcting the digital frequency transform at the image frequency candidate using the imbalance parameters in order to minimize the effects of the imbalance. Each digital frequency transform is corrected independently and consequently no persistent state information needs to be saved between transforms.
1. A device, comprising:
a. a radio receiver that receives radio frequency signals and includes an analog demodulator that demodulates the radio frequency signals;
b. a processor coupled to the radio receiver that:
i. computes a digital frequency transform for each sample of a time-based output of the analog demodulator;
ii. analyzes the digital frequency transform to identify image frequency candidates; and
iii. removes an image frequency candidate if it actually is an image, otherwise, not removing the image frequency candidate.
2. The device of claim 1 , the processor computes I/Q demodulator imbalance parameters for an image frequency candidate such that when applied to the digital frequency transform at the image frequency candidate it has the effect of removing a component of the digital frequency transform that is the image of a signal at the negative frequency and leaving the rest of the digital frequency transform unaltered.
3. The device of claim 2 , wherein the processor removes an image frequency candidate by computing Y′ m =γ(Y m −βY* −m ), where Y m is an uncorrected value of the frequency transform at the image frequency candidate m and Y′ m is the corrected value of the digital frequency transform at the image frequency candidate m, and where the I/Q demodulator imbalance parameters comprise γ and β.
4. The device of claim 3 , wherein when a value of the digital frequency transform at the image frequency candidate appears as an image of a relatively narrow-band signal, the processor computes Y′ m as an average of the values of the digital frequency transform at neighboring image frequency candidates.
5. The device of claim 1 , wherein the processor analyzes the digital frequency transform and identifies a frequency of the frequency domain transform that has a power that is a predetermined amount lower than the power of the frequency domain transform at a corresponding negative frequency.
6. The device of claim 1 , wherein the processor computes I/Q demodulator imbalance parameters for an image frequency candidate such that the digital frequency transform is conjugate symmetric at the image frequency candidate.
7. A processor readable medium storing instructions that, when executed by a processor, cause the processor to:
a. computes a digital frequency transform for a time-based output of an analog demodulator;
b. analyzes the digital frequency transform to identify image frequency candidates; and
c. removes an image frequency candidate if it actually is an image, otherwise, not removing the image frequency candidate.
8. The processor readable medium of claim 7 , wherein the instructions that (b) analyzes comprises instructions that compute I/Q demodulator imbalance parameters for an image frequency candidate such that when applied to the digital frequency transform at the image frequency candidate it has the effect of removing a component of the digital frequency transform that is the image of a signal at the negative frequency and leaving the rest of the digital frequency transform unaltered.
9. The processor readable medium of claim 8 , wherein the instructions that (c) removes comprise instructions that compute Y′ m =γ(Y m −βY* −m ), where Y m is an uncorrected value of the frequency transform at the image frequency candidate m and Y′ m is the corrected value of the digital frequency transform at the image frequency candidate m, and where the I/Q demodulator imbalance parameters comprise γ and β.
10. The processor readable medium of claim 9 , wherein the instructions that (c) removes comprise instructions that compute Y′ m as an average of the values of the digital frequency transform at neighboring image frequency candidates if a value of the digital frequency transform at the image frequency candidate appears as an image of a relatively narrow-band signal.
11. The processor readable medium of claim 7 , wherein the instructions that (b) analyze comprise instructions that identify a frequency of the frequency domain transform that has a power that is a predetermined amount lower than the power of the frequency domain transform at a corresponding negative frequency.
12. The processor readable medium of claim 7 , wherein the instructions that (b) analyzes comprise instructions that compute the I/Q demodulator imbalance parameters for an image frequency candidate such that the digital frequency transform is conjugate symmetric at the image frequency candidate.
13. A device, comprising:
a. a radio receiver that receives radio frequency signals and includes an analog demodulator that demodulates the radio frequency signals;
b. a digital frequency transform module that computes a time-based sequence of digital frequency transforms for a time-domain output of the analog demodulator;
c. a spectrum correction module coupled to the digital frequency transform module that analyzes the digital frequency transforms to identify image frequency candidates and removes an image frequency candidate if it actually is an image, and otherwise, does not remove the image frequency candidate.
14. The device of claim 13 , wherein the spectrum correction module computes I/Q demodulator imbalance parameters for an image frequency candidate such that when applied to the digital frequency transform at the image frequency candidate it has the effect of removing a component of the digital frequency transform that is the image of a signal at the negative frequency and leaving the rest of the digital frequency transform unaltered.
15. The device of claim 14 , wherein the spectrum correction module removes an image frequency candidate by computing Y′ m =γ(Y m −βY* −m ), where Y m is an uncorrected value of the frequency transform at the image frequency candidate m and Y′ m is the corrected value of the digital frequency transform at the image frequency candidate m, and where the demodulator imbalance parameters comprise γ and β.
16. The device of claim 15 , wherein when a value of the digital frequency transform at the image frequency candidate appears as an image of a relatively narrow-band signal, the spectrum correction module computes Y′ m as an average of the values of the digital frequency transform at neighboring image frequency candidates.
17. The device of claim 13 , wherein the spectrum correction module identifies a an image frequency candidate as a frequency of the digital frequency transform that has a power that is a predetermined amount lower than the power of the frequency domain transform at a corresponding negative frequency.
18. The device of claim 13 , wherein the spectrum correction module computes I/Q demodulator imbalance parameters for an image frequency candidate such that the digital frequency transform is conjugate symmetric at the image frequency candidate.
19. The device of claim 13 , wherein the digital frequency transform module and the spectrum correction module are implemented with fixed or programmable digital logic gates.