In radio astronomy interferometers where the number of stations is large (in the \ac{ALMA} case 66 antennas, where 8 digitizers are deployed in each antenna) tuning the digitizers parameters: thresholds and bias, is a process which needs to be repeated several times, therefore finding an algorithm that allows to speed up this process is a critical task. It is quite important to keep the digitizers properly adjusted in order to reach the maximal efficiency of the correlator, especially in a regime of coarse quantization (88\% for 2 bits, 96\% for 3 bits), and also is critical for avoiding signal artifacts which can degrade the collected data (DC bias or harmonics). This work presents a set of different approaches for automatically tune the digitizers, primary selected as \ac{PID} controller, Fuzzy Logic controller, and a hybrid scheme combining PID and Fuzzy Logic for a rapid and accurate tuning process. In the PID controller, we define a system to process a coupled \ac{MIMO} system as two uncoupled \ac{SISO}. For the Fuzzy Control controller, we make an extensive advantage of the expert operator knowledge where this controller relies on.
The work aims to evaluate the performance of each tuning method based on metrics like required tuning time, stability and robustness under different extreme boundary conditions. Besides, we suggest the means for collecting the needed information considering a usual interferometer architecture.
Furthermore, we provide an automated approach to find the best sampler’s clock timing profile. This work provides a guideline for implementing an algorithm which allows tuning a broad set of digitizers under different conditions in a fast and precise automated process. The produced report will come in handy for integration into interferometer projects comprising a large number of individual stations (\ac{ALMA}, \ac{SKA}, \ac{VLA}, \ac{CHIME}, \ac{MeerKAT}).
The study began with a characterization of the of signals in radio astronomy as Gaussian distribution like for a discrete space. Based on figures of maximum efficiency factor and expected standard distribution, we were able to build theoretical probability values and their appropriate weights in each state. Those findings pave the way to obtain equations for the error offset and error amplitude of the measured signal with respect to the theoretical ideal and discrete Gaussian distribution.
The current \ac{ALMA} digitizer was then showcased, it is a monolithic \ac{ASIC} based analog to digital converter implemented in a \ac{BiCMOS} 0.25µm \ac{SiGe} process, the main features are its flash \ac{ADC} architecture, 4 \ac{Gsps} speed and Gray code codification scheme. The user is able to control the reference voltages that can be interpreted as the input signal’s offset and amplitude, parameters that are tightly related to the first two moments of Gaussian distribution (offset and distribution respectively). A variable-sweep in these two control variables shows the digitizer response, suggesting zones of linearity and dependency between both variables.
The controllers are later introduced into this work, first it is recognized how digitizers are adjusted by means of manual control or by basic control approaches. The \ac{PID} controller is then presented as one of the most used controllers in the industry, thanks for its easiness to adjust its major parameters. We present the continuous time version and then transform it into its discrete time version since we expect to integrate it into a digital platform. The tuning parameters for this controller are expressed with plots that confirm the controller is properly tuned. The second controller alternative, inspired by the way trained personnel used to adjust the digitizer, is brought into study. The \ac{FLC} represents an appropiate candidate for retrieving expert-operator knowledge under a system that is not completely characterized. The research displays \ac{FLC} primary functions that compound the core of the controller (fuzzification interface, knowledge base, decision making logic and defuzzification interface), after the core stages presentation, it is demonstrated its performance and its tuned parameters.
Additionally, as a complementary step for providing a complete digitizer tuning process, a 250[MHz] delay word adjustment method is proposed. This “only one of its kind” technique performs a search of the largest convergence zone by testing the trace of the co-variance matrix of the offset and distribution error by sweeping the 250[MHz] delay word. The points with the lowest traces are considered stable, and areas of stability are defined; the chosen 250[MHz] adjustment will lie in the middle of the main stable zone.