@article{hong_floyd_2022, title={Beamformer Calibration Using Coded Correlations}, ISSN={["1554-8422"]}, DOI={10.1109/PAST49659.2022.9975099}, abstractNote={Code-modulated embedded test (CoMET) has been investigated for simultaneous testing and calibration of phased-array elements using phase-shifter modulation and a single scalar detector together with an off-line equation solver. To improve the speed and reduce the complexity of the calibration, this work presents a revised methodology relying only on correlations and eliminating equation solvers within the calibration loop. The new technique, “beamformer calibration using coded correlations” (BC3), operates by calibrating the phased-array's in-phase and quadrature-phase correlations between elements. Within BC3, a first method calibrates the array's response by using two two-dimensional (2-D) correlations. A second method further reduces the total calibration time and improves accuracy by using two one-dimensional (1-D) correlations together with an empirical model to predict gain-dependent phase variation. Also, we investigate ways to improve the speed of calibration by reducing the code length and the number of searching states per iteration. The phase and gain accuracy, calibration time, and antenna beam patterns are measured and compared using original and proposed calibration methods on an eight-element receiver at 10 GHz. The most accurate BC3 method achieves 1.4 deg. and 0.23 dB root-mean-squared (RMS) phase and gain error, 1.1 dB maximum gain error and -37.8 dB calculated residual sidelobe level (RSL) for the calibrated array, with 12X speedup compared to CoMET. The fastest BC3 method achieves 2.1 deg. and 0.27 dB root-mean-squared (RMS) phase and gain error, 1.2 dB maximum gain error and -35.3 dB RSL for the array with 33X speedup compared to CoMET.}, journal={2022 IEEE INTERNATIONAL SYMPOSIUM ON PHASED ARRAY SYSTEMS & TECHNOLOGY (PAST)}, author={Hong, Zhangjie and Floyd, Brian A.}, year={2022} }
 @article{almahmoud_hong_floyd_2022, title={Simultaneous Phased-Array Element Testing Using Orthogonal Amplitude Modulation}, ISSN={["1554-8422"]}, DOI={10.1109/PAST49659.2022.9975103}, abstractNote={This work introduces an orthogonal amplitude modulation (AM) technique for simultaneous measurement of phased-array elements. The approach leverages a code-modulated embedded test (CoMET) technique in which a test signal is injected to the array, on-off keying is applied to each element using the existing variable-gain amplifiers and vector interpolators, signals are combined and then squared using a power detector, correlations are demodulated from the squared response, and then amplitude and phase are estimated using an equation solver. The amplitude modulation technique can be used in systems where phase modulation is either difficult or erroneous. This paper presents the theory for AM-CoMET and demonstrates its operation using an eight-element phased array transmitter operating at 8 GHz. The extracted gain and phase from the new technique are compared with a vector network analyzer (VNA), showing that AM-CoMET extracted gain and phase are accurate to within 0.25 dB gain error and 2° phase error.}, journal={2022 IEEE INTERNATIONAL SYMPOSIUM ON PHASED ARRAY SYSTEMS & TECHNOLOGY (PAST)}, author={Almahmoud, Saleh and Hong, Zhangjie and Floyd, Brian A.}, year={2022} }
 @article{chauhan_hong_schoenherr_floyd_2021, title={An X-Band Code-Modulated Interferometric Imager}, volume={69}, ISSN={["1557-9670"]}, url={https://doi.org/10.1109/TMTT.2021.3101243}, DOI={10.1109/TMTT.2021.3101243}, abstractNote={Code-modulated interferometry (CMI) enables a lens-less approach to imaging in which incoming signals are code modulated, combined, and processed through a shared hardware path; visibility functions are demodulated from an aggregate power-detected response; and an image is obtained using an inverse Fourier transform of the visibility samples. CMI allows the imager to be constructed using low-cost conventional beamforming hardware. This article presents the theory of operation of a code-modulated interferometer array intended for active imaging. This includes the selection of codes, the use of phase shifters for modulation, the demodulation of visibility functions, the necessary calibration, and the image processing. The architecture and design of an active imaging prototype is then presented, where it is created using a commercially available 16-element 8–16 GHz beamforming receiver along with a sparse antenna array that generates 169 distinct visibility samples. The imaging capabilities are demonstrated through the detection of multiple point sources at 10 GHz. Finally, the feasibility of creating a larger 64-element imager with 961 visibility samples is demonstrated through construction and measurements of a single row within that array.}, number={11}, journal={IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chauhan, Vikas and Hong, Zhangjie and Schoenherr, Simon and Floyd, Brian A.}, year={2021}, month={Nov}, pages={4856–4868} }
 @article{hong_chauhan_schoenherr_floyd_2021, title={Code-Modulated Embedded Test and Calibration of Phased-Array Transceivers}, volume={69}, ISSN={["1557-9670"]}, url={https://doi.org/10.1109/TMTT.2020.3041022}, DOI={10.1109/TMTT.2020.3041022}, abstractNote={We present improved methods for built-in test and calibration of phased arrays in free-space using a code-modulated embedded test (CoMET). Our approach employs the Cartesian modulation of test signals within each element using existing phase shifters, the combination of these signals into a code-multiplexed response, creation of code-modulated element-to-element “interference products” using a built-in power detector, demodulation of correlations from the digitized interference response, and parallel in situ extraction of amplitude and phase per element using an equation solver. In this article, we review CoMET’s methodology and then analyze the impact of noise within the system. To improve CoMET accuracy, a reference-element methodology is introduced, where all measurements are referred to as one element in the array whose phase is held constant. This is compared with another method in which the modulation axes are rotated to allow accurate extraction of phase near the original 0°/90°/180°/270° axes. Our techniques are demonstrated for both receive and transmit modes using an eight-element 8–16-GHz phased-array packaged and assembled together with patch antennas. Compared with network analyzer measurements, CoMET-extracted gain and phase using the reference-element method are accurate to within 0.4 dB and 2°–3° for free-space measurements, respectively. CoMET is then used within a calibration loop to equalize elemental gain and achieve a 7-bit phase resolution. In free space, the maximum gain and phase offsets between active antenna elements are reduced from 3.5 dB and 20°–90° to 1.1 dB and 0°, respectively. Calibrated beam patterns show significant improvement with peak-to-null ratios of >30 dB.}, number={3}, journal={IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Hong, Zhangjie and Chauhan, Vikas and Schoenherr, Simon and Floyd, Brian A.}, year={2021}, month={Mar}, pages={1846–1859} }