Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Calibration of aperture arrays using self-holography
Thesis (PhD)--Stellenbosch University, 2021.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2021
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613734427426816 |
|---|---|
| access_status_str | Open Access |
| author | Wilke, Cornelis |
| author2 | Gilmore, Jacki |
| author_browse | Gilmore, Jacki Wilke, Cornelis |
| author_facet | Gilmore, Jacki Wilke, Cornelis |
| author_sort | Wilke, Cornelis |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2021. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/123698 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:40:51.455Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/123698 Calibration of aperture arrays using self-holography Wilke, Cornelis Gilmore, Jacki Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering. Aperture Arrays UCTD Calibration Holographic interferometry Thesis (PhD)--Stellenbosch University, 2021. ENGLISH ABSTRACT: The calibration methods that are commonly applied to aperture array instru- ments typically rely on knowledge of the array covariance matrix. This implies an associated compute load and data volume that scale with the square of the number of receive paths, P , in the array. This trend might become prohibitive for large arrays or arrays with limited computing resources. Alternative methods are being developed to address this issue. One of these methods is self-holography (SH) which derives the complex-valued receive path gains from the correlations between the individual receive path signals, and a reference signal obtained with the array itself. As this only involves P correlations, the compute load and data volume scale only linearly with P . In its original formulation, the receive path gains are derived directly from the crosscorrelations. Since the reference signal is obtained by the array itself, the crosscorrelations contain an unwanted correlation in the thermal noise of the array. This leads to a bias in the amplitude of the gain estimates while the corresponding phase estimates converge to their true values after sufficient solving iterations. In this dissertation, it was discovered that this bias can be remedied by accurately compensating the thermal noise in the measured crosscorrelations. However, this is not a trivial process and in reality, will be challenging to implement accurately. These limitations lead to a revised formulation in which the receive path gains and noise powers are estimated simultaneously. But thermal noise is not the only factor that dictates the accuracy of SH. Up to this point, it was assumed that the calibration scenario resembles the situation with a single probe in an anechoic chamber, i.e, no other signals other than the reference signal is present. In reality, this assumption will be violated due to the unavoidable presence of interference and the accuracy of the gain estimates will be affected to an extent that is dependent on the actual isolation of the reference signal. n this dissertation, a detailed analysis was performed on the mathematics underlying the second formulation of SH and an analytical expression for the signal-to-interference ratio (SIR) of the reference signal was extracted. This was followed by a detailed simulation study in which the accuracy of the gain estimates was determined as a function of the SIR for a given calibration sce- nario and array configuration. As expected, the accuracy of the gain estimates was found to be inversely proportional to the SIR. It was also determined that the results are independent of the array configuration which confirms that the SIR expression is universal and can be used, together with the simulation results, to calculate the expected accuracy of the gain estimates given any analytical calibration scenario. An analysis was also done on the effectiveness of using null placement to minimize the interference received by the array. It was determined that nulling can be very effective in scenarios where the SIR is low due to one or two strong interferers. This is an especially promising result for the application of SH in commercial applications where small (lower directivity) arrays are typically used in the presence of strong interferers. The simulation study was followed by a first-ever practical application of SH calibration on data that was recorded by a Low-Frequency Array (LOFAR) low-band antenna (LBA) and high-band antenna (HBA) station. A visual inspection of the before and after imaged data proved that SH calibration was applied successfully. By estimating the level of interference in the recorded data, it was estimated that the SIR for the LBA data had a maximum of around 15 dB when using Cassiopeia A as the calibration source which corresponds to an RMS relative gain error of around 0.04 according to the results from the simulation study. Similarly, when using Cygnus A as a calibration source for the HBA recorded data, a maximum SIR of around 19 dB was calculated which corresponds to an RMS relative gain error of around 0.02. The gain estimates obtained with SH corresponded closely with those obtained with the standard LOFAR calibration pipeline, which further confirmed its successful application. n the final part of this dissertation, a study was performed to determine the suitability of applying SH to a Mid-Frequency Aperture Array (MFAA) station of the Square Kilometre Array (SKA). A Mid-Frequency Aperture Array Transient and Intensity-Mapping System (MANTIS) station was used as a reference and an appropriate sky model was simulated by carefully combining multiple resources. The SIR was calculated for various potential calibration sources at 10-minute intervals over 24 hours and the results showed that SIR’s well above 20 dB can be expected for most of a sidereal day. This confirms that SH will be perfectly suitable to calibrate an MFAA station which is a promising result for the future of the SKA. AFRIKAANSE OPSOMMING: Die kalibrasiemetodes wat gewoonlik op apertuur samestelling instrumente toegepas word, berus gewoonlik op kennis van die samestelling kovariansiema- triks. Dit impliseer ’n gepaardgaande rekenlading en datavolume wat skaal met die kwadraat van die aantal ontvangspaaie, P , in die samestelling. Hi- erdie tendens kan onbetaalbaar word vir groot samestellings of samestellings met beperkte rekenaarhulpbronne. Alternatiewe metodes word ontwikkel om hierdie kwessie aan te spreek. Een van hierdie metodes is self-holografie (SH), wat die komplekswaardige ontvangspadaanwinste verkry uit die korrelasies tussen die individuele ont- vangspadseine, en ’n verwysingssein wat met die samestelling self verkry word. Aangesien dit slegs P korrelasies behels, skaal die rekenbelasting en datavolume slegs liner met P . In sy oorspronklike formulering word die ontvangspadaan- winste direk verkry uit die kruiskorrelasies. Aangesien die verwysingsein deur die samestelling self verkry word, bevat die kruiskorrelasies ’n ongewenste ko- rrelasie in die termiese geraas van die samestelling. Dit lei tot ’n vooroordeel in die amplitude van die aanwinsberamings, terwyl die ooreenstemmende fase- beramings na genoeg oplossings iterasies na hul werklike waardes konvergeer. In hierdie proefskrif is dit ontdek dat hierdie vooroordeel reggestel kan word deur die termiese geraas in die gemete kruiskorrelasies akkuraat te vergoed. Dit is egter nie ’n onbenullige proses nie en sal in werklikheid moeilik wees om akkuraat te implementeer. Hierdie beperkings het gelei tot ’n hersiende formu- lering waarin die ontvangspadaanwinste en geraasdrywings gelyktydig geskat word. Maar, termiese geraas is nie die enigste faktor wat die akkuraatheid van SH bepaal nie. Tot hiertoe is dit aanvaar dat die kalibrasiescenario die situ- asie met ’n enkele probe in ’n anekoese kamer voorstel, d.w.s. dat daar geen ander seine as die verwysings sein is nie. In werklikheid sal hierdie aanname geskend word as gevolg van die onvermydelike teenwoordigheid van steuring, en die akkuraatheid van die aanwinsberamings sal benvloed word in ’n mate wat afhang van die werklike isolasie van die verwysingssein. In hierdie proefskrif is ’n gedetailleerde ontleding van die wiskunde on- derliggend aan die tweede formulering van SH uitgevoer, en ’n analitiese uit- drukking vir die sein-tot-interferensieverhouding (SIV) van die verwysingssein is onttrek. Dit is gevolg deur ’n gedetailleerde simulasie-studie waarin die akkuraatheid van die winsberamings bepaal is as ’n funksie van die SIV vir ’n gegewe kalibrasiescenario en samestellingkonfigurasie. Soos verwag, is dit gevind dat die akkuraatheid van die aanwinsberamings omgekeerd eweredig is aan die SIV. Daar is ook vasgestel dat die resultate onafhanklik is van die samestellingkonfigurasie wat bevestig dat die SIV-uitdrukking universeel is en tesame met die simulasie-resultate gebruik kan word om die verwagte akku- raatheid van die winsberamings te bereken gegewe enige analitiese kalibrasi- escenario. ’n Analise is ook gedoen oor die effektiwiteit van die gebruik van nulplasing om die steuring wat die samestelling ontvang, te verminder. Daar is vasgestel dat nulplasing baie effektief kan wees in scenario’s waar die SIV laag is as gevolg van een of twee sterk steuraars. Dit is ’n baie belowende resultaat vir die toepassing van SH in kommersile toepassings, waar klein samestellings (laer direktiwiteit) gewoonlik gebruik word in die teenwoordigheid van sterk steuraars. Die simulasie-studie is gevolg deur ’n eerste-ooit praktiese toepassing van SH-kalibrasie op data wat deur ’n ”Low-Frequency Array (LOFAR) low-band antenna (LBA)” en ”high-band antenna (HBA)” -stasie opgeneem is. ’n Vi- suele inspeksie van die voor- en na- gebeelde data bewys dat SH-kalibrasie suksesvol toegepas was. Deur ’n skatting van die vlak van interferensie in die aangetekende data te maak, is dit beraam dat die SIV vir die LBA-data ’n maksimum van ongeveer 15 dB gehad het wanneer Cassiopeia A as die kali- brasiebron gebruik is, wat ooreenstem met ’n RMS-aanwinsfout van ongeveer 0,04 volgens die resultate uit die simulasie-studie. Net so is ’n maksimum SIV van ongeveer 19 dB bereken wanneer Cygnus A as kalibrasiebron vir die HBA- aangetekende data gebruik word, wat ooreenstem met ’n RMS-aanwinsfout van ongeveer 0,02. Die aanwinsberamings wat met SH verkry is, stem goed ooreen met di wat verkry is met die standaard LOFAR-kalibrasiepyplyn, wat die suksesvolle toepassing daarvan verder bevestig. In die laaste gedeelte van hierdie proefskrif is ’n studie uitgevoer om die geskiktheid van die toepassing van SH op ’n ”Mid-Frequency Aperture Array (MFAA)” -stasie van die ”Square Kilometer Array (SKA)” te bepaal. ’n ”Mid- Frequency Aperture Array Transient and Intensity-Mapping System (MAN- TIS)” -stasie is as verwysing gebruik en ’n toepaslike lugmodel is gesimuleer deur die versigtige samestelling van menigte hulpbronne. Die SIV is bereken vir verskillende potensile kalibrasiebronne vir tussenpouses van tien minute oor 24 uur en die resultate het getoon dat SIV’s bo 20 dB die grootste deel verwag kan word. Dit bevestig dat SH perfek geskik sal wees om ’n MFAA-stasie te kalibreer, wat ’n belowende resultaat vir die toekoms van die SKA is. Doctoral 2021-10-12T07:05:21Z 2021-12-22T14:16:30Z 2021-10-12T07:05:21Z 2021-12-22T14:16:30Z 2021-12 Thesis http://hdl.handle.net/10019.1/123698 en_ZA Stellenbosch University 95 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Aperture Arrays UCTD Calibration Holographic interferometry Wilke, Cornelis Calibration of aperture arrays using self-holography |
| title | Calibration of aperture arrays using self-holography |
| title_full | Calibration of aperture arrays using self-holography |
| title_fullStr | Calibration of aperture arrays using self-holography |
| title_full_unstemmed | Calibration of aperture arrays using self-holography |
| title_short | Calibration of aperture arrays using self-holography |
| title_sort | calibration of aperture arrays using self holography |
| topic | Aperture Arrays UCTD Calibration Holographic interferometry |
| url | http://hdl.handle.net/10019.1/123698 |
| work_keys_str_mv | AT wilkecornelis calibrationofaperturearraysusingselfholography |