KalCal: a novel calibration framework for radio interferometry using the Kalman Filter and Smoother
- Authors: Welman, Brian Allister
- Date: 2024-10-11
- Subjects: Radio interferometers , Calibration , Kalman filtering , Bayesian inference , Signal processing , Radio astronomy , MeerKAT
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/467127 , vital:76818
- Description: Calibration in radio interferometry is essential for correcting measurement errors. Traditional methods employ maximum likelihood techniques and non-linear least squares solvers but face challenges due to the data volumes and increased noise sensitivity of contemporary instruments such as MeerKAT. A common approach for mitigating these issues is using “solution intervals”, which helps manage the data volume and reduces overfitting. However, inappropriate interval sizes can degrade calibration quality, and determining optimal sizes is challenging, often relying on brute-force methods. This study introduces Kalman Filtering and Smoothing in Calibration (KalCal), a new framework for calibration that combines the Kalman Filter, Kalman Smoother, and the energy function: the negative logarithm of the Bayesian evidence. KalCal offers Bayesian-optimal solutions as probability densities and models calibration effects with lower computational requirements than iterative approaches. Unlike traditional methods, which require all the data for a particular solution to be in memory simultaneously, KalCal’s recursive computations only need a single pass through the data with appropriate prior information. The energy function provides the means for KalCal to determine this prior information. Theoretical contributions include additions to complex optimisation literature and the “Kalman-Woodbury Identity” that reformulates the traditional Kalman Filter. A Python implementation of the KalCal framework was benchmarked against solution intervals as implemented in the QuartiCal package. Simulations show KalCal matching solution intervals in high Signal-to-Noise Ratio (SNR) scenarios and surpassing them in low SNR conditions. Moreover, the energy function produced minima that coincide with KalCal’s Mean Square Error (MSE) on the true gain signal. This result is significant as the MSE is unavailable in real applications. Further research is needed to assess the computational feasibility and intricacies of KalCal. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2024
- Full Text:
- Date Issued: 2024-10-11
- Authors: Welman, Brian Allister
- Date: 2024-10-11
- Subjects: Radio interferometers , Calibration , Kalman filtering , Bayesian inference , Signal processing , Radio astronomy , MeerKAT
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/467127 , vital:76818
- Description: Calibration in radio interferometry is essential for correcting measurement errors. Traditional methods employ maximum likelihood techniques and non-linear least squares solvers but face challenges due to the data volumes and increased noise sensitivity of contemporary instruments such as MeerKAT. A common approach for mitigating these issues is using “solution intervals”, which helps manage the data volume and reduces overfitting. However, inappropriate interval sizes can degrade calibration quality, and determining optimal sizes is challenging, often relying on brute-force methods. This study introduces Kalman Filtering and Smoothing in Calibration (KalCal), a new framework for calibration that combines the Kalman Filter, Kalman Smoother, and the energy function: the negative logarithm of the Bayesian evidence. KalCal offers Bayesian-optimal solutions as probability densities and models calibration effects with lower computational requirements than iterative approaches. Unlike traditional methods, which require all the data for a particular solution to be in memory simultaneously, KalCal’s recursive computations only need a single pass through the data with appropriate prior information. The energy function provides the means for KalCal to determine this prior information. Theoretical contributions include additions to complex optimisation literature and the “Kalman-Woodbury Identity” that reformulates the traditional Kalman Filter. A Python implementation of the KalCal framework was benchmarked against solution intervals as implemented in the QuartiCal package. Simulations show KalCal matching solution intervals in high Signal-to-Noise Ratio (SNR) scenarios and surpassing them in low SNR conditions. Moreover, the energy function produced minima that coincide with KalCal’s Mean Square Error (MSE) on the true gain signal. This result is significant as the MSE is unavailable in real applications. Further research is needed to assess the computational feasibility and intricacies of KalCal. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2024
- Full Text:
- Date Issued: 2024-10-11
Higher order modulation formats for high speed optical communication systems with digital signal processing aided receiver
- Chabata, Tichakunda Valentine
- Authors: Chabata, Tichakunda Valentine
- Date: 2016
- Subjects: Optical communications , Modulation (Electronics) , Signal processing
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10948/4775 , vital:20677
- Description: The drastic increase in the number of internet users and the general convergence of all other communication systems into an optical system have brought a sharp rise in demand for bandwidth and calls for high capacity transmission networks. Large unamplified transmission reach is another contributor in reducing deployment costs of an optical communication system. Spectrally efficient modulation formats are suggested as a solution to overcome the problems associated with limited channels and bandwidth of dense wavelength division multiplexing (DWDM) optical communication systems. Higher order modulation formats which are considered to be spectrally efficient and can increase the transmission capacity by transmitting more information in the amplitude, phase, polarization or a combination of all was studied. Different detection technologies are to be implemented to suit a particular higher order modulation format. In this research multilevel modulation formats, different detection technologies and a digital signal processing aided receiver were studied in a practical optical transmission system. The work in this thesis started with the implementation of the traditional amplitude shift keying (ASK) modulation and a differential phase shift keying (DPSK) modulation systems as they form the basic building block in the design of higher order modulation formats. Results obtained from using virtual photonics instruments (VPI)simulation software, receiver sensitivity for 10Gbpsnon-return-to-zero (NRZ), amplitude phase shift keying (ASK) and DPSK signals were measured to be -22.7 dBm and -22.0 dBm respectively. Performance comparison for the two modulation formats were done over different transmission distances. ASK also known as On-Off keying (OOK) performed better for shorter lengths whereas DPSK performed better for longer lengths of up to90km.Experimental results on a 10 Gbps NRZ- ASK signal gave a receiver sensitivity of -21.1 dBm from digital signal processing (DSP) aided receiver against -19.8 dBm from the commercial bit error ratio tester (BERT) yielding a small difference of 1.3 dB hence validating the reliability and accuracy of the digital signal processing (DSP) assisted receiver. Traditional direct detection scheme and coherent detection scheme performances were evaluated again on a 10 Gbps NRZ ASK signal. Coherent detection that can achieve a large unamplified transmission reach and has a higher passive optical splitting ratio was first evaluated using the VPI simulation software. Simulation results gave a receiver sensitivity of -30.4 dBm forcoherent detection and -18.3 dBm for direct detection, yielding a gain in receiver sensitivity of 12.1 dB. The complex coherently detected signal, from the experimental setup gave a receiver sensitivity of -20.6 dBm with a gain in receiver sensitivity of 3.5 dBm with respect to direct detection. A multilevel pulse amplitude modulation (4-PAM) that doubles the data rate per channel from10 Gbps to 20 Gbps by transmitting more information in the amplitude of the carrier signal was implemented. This was achieved by modulating the optical amplitude with an electrical four level amplitude shift keyed (ASK) signal. A receiver consisting of a single photodiode, three decision circuits and a decoding logic circuit was used to receive and extract the original transmitted data. A DSP aided receiver was used to evaluate the link performance. A receiver sensitivity of -12.8 dBm is attained with a dispersion penalty of about 7.2 dB after transmission through 25 km of G.652 fibre.
- Full Text:
- Date Issued: 2016
- Authors: Chabata, Tichakunda Valentine
- Date: 2016
- Subjects: Optical communications , Modulation (Electronics) , Signal processing
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10948/4775 , vital:20677
- Description: The drastic increase in the number of internet users and the general convergence of all other communication systems into an optical system have brought a sharp rise in demand for bandwidth and calls for high capacity transmission networks. Large unamplified transmission reach is another contributor in reducing deployment costs of an optical communication system. Spectrally efficient modulation formats are suggested as a solution to overcome the problems associated with limited channels and bandwidth of dense wavelength division multiplexing (DWDM) optical communication systems. Higher order modulation formats which are considered to be spectrally efficient and can increase the transmission capacity by transmitting more information in the amplitude, phase, polarization or a combination of all was studied. Different detection technologies are to be implemented to suit a particular higher order modulation format. In this research multilevel modulation formats, different detection technologies and a digital signal processing aided receiver were studied in a practical optical transmission system. The work in this thesis started with the implementation of the traditional amplitude shift keying (ASK) modulation and a differential phase shift keying (DPSK) modulation systems as they form the basic building block in the design of higher order modulation formats. Results obtained from using virtual photonics instruments (VPI)simulation software, receiver sensitivity for 10Gbpsnon-return-to-zero (NRZ), amplitude phase shift keying (ASK) and DPSK signals were measured to be -22.7 dBm and -22.0 dBm respectively. Performance comparison for the two modulation formats were done over different transmission distances. ASK also known as On-Off keying (OOK) performed better for shorter lengths whereas DPSK performed better for longer lengths of up to90km.Experimental results on a 10 Gbps NRZ- ASK signal gave a receiver sensitivity of -21.1 dBm from digital signal processing (DSP) aided receiver against -19.8 dBm from the commercial bit error ratio tester (BERT) yielding a small difference of 1.3 dB hence validating the reliability and accuracy of the digital signal processing (DSP) assisted receiver. Traditional direct detection scheme and coherent detection scheme performances were evaluated again on a 10 Gbps NRZ ASK signal. Coherent detection that can achieve a large unamplified transmission reach and has a higher passive optical splitting ratio was first evaluated using the VPI simulation software. Simulation results gave a receiver sensitivity of -30.4 dBm forcoherent detection and -18.3 dBm for direct detection, yielding a gain in receiver sensitivity of 12.1 dB. The complex coherently detected signal, from the experimental setup gave a receiver sensitivity of -20.6 dBm with a gain in receiver sensitivity of 3.5 dBm with respect to direct detection. A multilevel pulse amplitude modulation (4-PAM) that doubles the data rate per channel from10 Gbps to 20 Gbps by transmitting more information in the amplitude of the carrier signal was implemented. This was achieved by modulating the optical amplitude with an electrical four level amplitude shift keyed (ASK) signal. A receiver consisting of a single photodiode, three decision circuits and a decoding logic circuit was used to receive and extract the original transmitted data. A DSP aided receiver was used to evaluate the link performance. A receiver sensitivity of -12.8 dBm is attained with a dispersion penalty of about 7.2 dB after transmission through 25 km of G.652 fibre.
- Full Text:
- Date Issued: 2016
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