A Novel Digital IQ Demodulation for Interferometric Radiometers
Abstract
:1. Introduction
2. Materials and Methods
2.1. Visibility and Correlation
2.2. In-Phase and Quadrature
2.3. Normalized Cross-Correlation Function
2.4. Data Processing
2.4.1. Decorrelation of the Imaginary Part
2.4.2. Center Frequency Error
2.5. Fringe Washing Function Shape
2.5.1. Three-Delay Measurements
- Delaying receiver k (Figure 3):
- Delaying receiver j (Figure 4).
2.5.2. The system of Equations
3. Results
3.1. Power Measurements
3.2. Correlation Measurements
3.2.1. Self-IQ Correlation
3.2.2. Cross-Correlation
3.2.3. Fringe Washing Function Shape
3.2.4. Sensitivity Circles
3.3. Effective Integration Time
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ALR | Advanced Receiver for the Future L-Band Radiometer |
DUT | Device Under Test |
ESA | European Space Agency |
EBB | Elegant Breadboard |
IF | Intermediate Frequency |
IQ | In-phase and Quadrature |
LICEF | Lightweight Cost-Effective Front-end |
LO | Local Oscillator |
MIRAS | Microwave Imaging Radiometer with Aperture Synthesis |
NOSU | Noise Source |
PMS | Power Measurement System |
RF | Radio Frequency |
SMOS | Soil Moisture and Ocean Salinity |
Appendix A. The Fringe Washing Function
- If the product is real, then , so the real part is even and the imaginary part odd. This happens either if both receivers have identical frequency responses or if a single receiver is considered (the case of or ).
- If both frequency responses are symmetrical around the reference frequency (that is, if ), then the fringe washing function is real.
- A group delay difference between both receivers, defined as , is equivalent to a linear phase shift in the frequency domain. As a consequence, the integrand of (A1) can be written as the product of two filter responses with equal group delay multiplied by . After some mathematical operations, it is easily found that the fringe washing function becomes:
- Changing the reference frequency of the fringe washing function only adds a linear term to the phase, with no change in the amplitude:
- If the product can be approximated by a rectangular function of width B centered at , then the fringe washing function referenced to this frequency becomes:
- Independent of the reference frequency, the fringe washing function at the origin is:
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DUT | Offset (Hz) | Gain (Hz/K) | Noise Figure (dB) |
---|---|---|---|
ALR01 H | 8503 | 9.56 | 1.02 |
ALR01 V | 7143 | 11.59 | 0.99 |
ALR02 H | 7399 | 9.58 | 1.20 |
ALR02 V | 7306 | 7.92 | 1.18 |
Baseline | Amplitude | Phase (deg) |
---|---|---|
H1-V1 | 0.9876 | −6.13 |
H1-H2 | 0.9939 | −159.44 |
H1-V2 | 0.9694 | −106.37 |
V1-H2 | 0.9982 | −153.75 |
V1-V2 | 0.9961 | −100.42 |
H2-V2 | 0.9928 | 53.67 |
Baseline | A-1 (cu) | B (MHz) | C (ns) | E (kHz) |
---|---|---|---|---|
H1-V1 | 100.163 | 19.688 | 3.945 | 600.290 |
H1-H2 | 19.602 | 18.398 | 1.875 | 359.365 |
H1-V2 | 191.575 | 18.733 | 5.723 | 177.256 |
V1-H2 | 29.676 | 18.976 | −2.236 | 173.539 |
V1-V2 | 18.610 | 19.112 | 1.759 | 42.783 |
H2-V2 | 104.440 | 19.036 | 4.166 | −99.463 |
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Corbella, I.; Martín Neira, M.; Vilaseca, R.; Catalan, A.; Torres, F.; Suess, M. A Novel Digital IQ Demodulation for Interferometric Radiometers. Remote Sens. 2021, 13, 1156. https://doi.org/10.3390/rs13061156
Corbella I, Martín Neira M, Vilaseca R, Catalan A, Torres F, Suess M. A Novel Digital IQ Demodulation for Interferometric Radiometers. Remote Sensing. 2021; 13(6):1156. https://doi.org/10.3390/rs13061156
Chicago/Turabian StyleCorbella, Ignasi, Manuel Martín Neira, Roger Vilaseca, Albert Catalan, Francesc Torres, and Martin Suess. 2021. "A Novel Digital IQ Demodulation for Interferometric Radiometers" Remote Sensing 13, no. 6: 1156. https://doi.org/10.3390/rs13061156
APA StyleCorbella, I., Martín Neira, M., Vilaseca, R., Catalan, A., Torres, F., & Suess, M. (2021). A Novel Digital IQ Demodulation for Interferometric Radiometers. Remote Sensing, 13(6), 1156. https://doi.org/10.3390/rs13061156