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z%+%BfO|zMqg#o&cO^poAOwiPs8X1~mNra}BXdbDzurM?;LQOQFpf)u}QwVY(dLlG5 zG&e-cc7~vMM~^y7b4x=rw6tYmVQ6k*sZftx{u+QBgYIgO7@Dg=+0NVm)q#eFW=3Xc z1q~>Ujm%MVlcAxR2~tSc!wP-_OA8EzhK6V*CnzBqqeT-)%nXY<3$)w>a-cC<nPO<j zYGz_-WITQTWkH(+3lnEkb0Y&oR~JJ=S2ssPHw$wE6BiRV6E`Ds7c*mLI~#&3V!7<> cxQa^>i%KerQq#CV6`F~W0hg+(tG^o;0KE6``~Uy| diff --git a/doc/papers/2008/IEEE-SIG/lofar.tex b/doc/papers/2008/IEEE-SIG/lofar.tex index f9887146226..67f8a8f9353 100644 --- a/doc/papers/2008/IEEE-SIG/lofar.tex +++ b/doc/papers/2008/IEEE-SIG/lofar.tex @@ -755,11 +755,32 @@ of 38~m each. \subsection{Receiver} -In interferometry it is important to keep the signal paths equal in (electrical) characteristics (because differences between signals received are measured). This also applies to the signals before beamforming. Any difference in gain or phase introduced prior to the beamforming operation will degrade the signal to noise ratio (here defining "signal" as the signal of interest, the sky noise, and the "noise" as the noise generated by the system). For these reasons early sampling and digitization is preferred and therefore done prior to beamforming in the LOFAR stations (an exception are the HBA arrays, where an analog beamformer stage is used as well for cost reasons). - -For the receiver a wide-band direct digital conversion architecture is adopted. This reduces the number of analog devices used in the signal path. The maximum sampling rate is 200~MHz, which is sufficient to directly convert the analog signals. To fill the gaps in between the Nyquist zones, a sample frequency of 160 MHz can be chosen as well. The Nyquist zones I to III of the A/D converter with a sample frequency of 200 MHz and 160 MHz respectively are depicted in Figure~\ref{fig:nyquistzones}. - -Since the LOFAR stations are installed in populated areas the dynamic range of the A/D converter must be sufficient to handle the Radio Frequency Interference (RFI) signals in the band of interest. Hence, the A/D converter converts the analog signal into a 12 bit digital signal. +In interferometry it is important to keep the signal paths equal in +(electrical) characteristics (because differences between signals received +are measured). +This also applies to the signals before beamforming. +Any difference in gain or phase introduced prior to the beamforming operation +will degrade the signal-to-noise ratio (here defining ``signal'' as the signal +of interest, the sky noise, and the ``noise'' as the noise generated by the +system). +For these reasons early sampling and digitization is preferred and therefore +done prior to beamforming in the LOFAR stations (an exception are the HBA +arrays, where an analog beamformer stage is used as well for cost reasons). + +For the receiver a wide-band direct digital conversion architecture is adopted. +This reduces the number of analog devices used in the signal path. +The maximum sampling rate is 200~MHz, which is sufficient to directly convert +the analog signals. +To fill the gaps in between the Nyquist zones, a sample frequency of 160~MHz +can be chosen as well. +The Nyquist zones I to III of the A/D converter with a sample frequency of +200~MHz and 160~MHz respectively are depicted in Figure~\ref{fig:nyquistzones}. + +Since the LOFAR stations are installed in populated areas, the dynamic range +of the A/D converter must be sufficient to handle the Radio Frequency +Interference (RFI) signals in the bands of interest. +Hence, the A/D converter converts the analog signal into a 12-bit digital +signal. \begin{figure} \begin{center} @@ -769,13 +790,23 @@ Since the LOFAR stations are installed in populated areas the dynamic range of t \label{fig:nyquistzones} \end{figure} -The three types of antennas are all connected via coaxial cables to the receiver, which selects one out of these three antennas. After selecting an antenna, the signal is filtered with one of the integrated filters. These filters select one of the four available observing bands. After filtering, the signal is amplified and filtered again to reduce the out of band noise contribution (anti-aliasing). A pre-amplifier in front of the A/D converter converts the single ended signal into a differential signal prior to A/D conversion. +The three types of antennas are all connected via coaxial cables to the +receiver, which selects one out of the three antenna inputs (LBL, LBH, and +HBA). +After selecting an antenna, the signal is filtered with one of the integrated +filters. +These filters select one of the four available observing bands. +After filtering, the signal is amplified and filtered again to reduce the +out-of-band noise contribution (anti-aliasing). +A pre-amplifier in front of the A/D~converter converts the single-ended signal +into a differential signal prior to A/D~conversion. \subsection{Digital Processing} -To form a phased array at station level, the analog antenna signals must be delayed and added which results in a beam on the sky. Moreover the beamformer should be able to track sources on the sky and be flexible in exchanging beams for bandwidth. - -The beamformer can be implemented by using true time delays or by applying phase shifts on narrow subbands. The time resolution required for using true time delays is smaller than the time resolution available (one over 200~MHz). On the other hand phase shifts can be applied only if the subband width is narrow enough. The error which is made at the edges of each subband is shown in Figure~\ref{fig:phasebeamf}, since the phase is frequency dependent and only one phase can be set per subband. The choice between both approaches depends also on the frequency resolution required further down the stream. +To form a phased array at station level, the analog antenna signals are delayed +and added, which results in a beam on the sky. +Moreover, the beamformer is able to track sources on the sky and can exchange +beams for bandwidth. \begin{figure} \begin{center} @@ -785,15 +816,72 @@ The beamformer can be implemented by using true time delays or by applying phase \label{fig:phasebeamf} \end{figure} -The correlator in the LOFAR system is an FX correlator as is explained in Section~\ref{sec:corr}. The correlator requires a frequency resolution of order 1~kHz. This frequency resolution is sufficient for a beamformer implemented by phase shifts. However, implementing a filterbank with this resolution for each antenna signal path is extremely expensive. For a phase shift beamformer a frequency resolution of order 200~kHz is sufficient which is determined by the error made at the edges of each subband. Hence, it was chosen to use a first stage filter bank which operates at antenna level to result in a frequency resolution sufficient for the phase shift beamforming. The remainder of the required frequency resolution before the correlator is achieved by a second stage filter bank which operates on station beams (which are a factor 48 smaller than the number of antennas). Since no extra significant data reduction will be done after the second stage filterbank, that functionality is implemented in the central systems. - -The first stage filter bank in the stations splits up the total band into 512 equidistant subbands resulting in order 195~kHz subbands for the 200~MHz sample frequency and 156~kHz for the 160~MHz sample frequency. The filter bank is efficiently implemented as a Poly-Phase Filter bank (PPF) on Field Programmable Gate Arrays (FPGA). - -After the filtering operation, a subset of the subbands can be selected. The selected subbands can be arbitrary over the band and will add up to in total 32~MHz. This bandwidth is matched to the current capacity of the central processor. - -To form beams, the antenna signals are combined in a complex weighted sum for each selected subband. Each subband gets its own phase shift and all subbands are treated independent of each other. In this way the number of pointings on the sky can be exchanged against the bandwidth per pointing, i.e. a user can choose between 1 beam of 32~MHz to a maximum of 8 beams of 4~MHz. This is limited by the processing power of the Local Control Unit (LCU) which has to calculate the weights each second, given a certain direction on the sky. - -The weights applied in the beamformer have a phase component and a gain component. Both are also used to correct for gain and phase differences in all the individual analog signal paths. The gain and phase differences are determined by a station calibration algorithm~\cite{stefan:06} which runs online with the observations. As an input to the station calibration algorithm the full cross correlation matrix of all dipoles in the stations is calculated for one subband each second. Each second another subband can be selected, so that the station calibration algorithm can tune over the complete band in about 512~seconds. Additionally the cross correlation algorithm will be used for Radio Frequency Interference (RFI) detection as well~\cite{Boonstra:05}. +A beamformer can be implemented by using true time delays or by applying phase +shifts on narrow subbands. +The time resolution required for using true time delays is smaller than the +time resolution available (one over 200~MHz). +On the other hand, phase shifts can be applied only if the subband width is +narrow enough. +The error which is made at the edges of each subband is shown in +Figure~\ref{fig:phasebeamf}, since the phase is frequency dependent and only +one phase can be set per subband. +The choice between both approaches depends also on the frequency resolution +required further down the stream. + +The correlator in the LOFAR system is an FX correlator as is explained in +Section~\ref{sec:corr}. +The correlator uses a frequency resolution of less than 1~kHz. +This frequency resolution is sufficient for a beamformer implemented by +phase shifts. +However, implementing a filterbank with this resolution for each antenna +signal path is extremely expensive. +For a phase shift beamformer, a frequency resolution of order 200~kHz is +sufficient, which is determined by the error made at the edges of each subband. +Hence, it was chosen to use a first stage filter bank which operates at antenna +level, to result in a frequency resolution sufficient for the phase shift +beamforming. +The remainder of the required frequency resolution before the correlator is +achieved by a second-stage filter bank, which operates on station beams +(which are a factor 48 smaller than the number of antennas). +Since no extra significant data reduction is done after the second stage +filterbank, that functionality is implemented in the central systems. + +The first-stage filter bank in the stations splits up the total band into +512~equidistant subbands, resulting in 195~kHz subbands for the 200~MHz +sample frequency and 156~kHz for the 160~MHz sample frequency. +The filter bank is efficiently implemented as a Poly-Phase Filter bank (PPF) +on Field Programmable Gate Arrays (FPGA). + +The observer selects a subset of the 512~subbands from the first-stage PPF. +The selected subbands can be arbitrary over the band and will add up to a +total of 32~MHz. +The capacity of the central processor matches this bandwidth. + +To form beams, the antenna signals are combined in a complex weighted sum +for each selected subband. +Each subband gets its own phase shift and all subbands are treated +independently of each other. +In this way, the number of pointings on the sky can be exchanged against +the bandwidth per pointing, i.e. a user can choose between 1~beam of 32~MHz +to a maximum of 8 beams of 4~MHz. +The number of beams is limited by the processing power of the Local Control +Unit, which has to calculate the weights each second, given a certain +direction on the sky. + +The weights applied in the beamformer have a phase component and a gain +component. +Both are also used to correct for gain and phase differences in all the +individual analog signal paths. +The gain and phase differences are determined by a station calibration +algorithm~\cite{stefan:06}, which runs online with the observations. +As an input to the station calibration algorithm the full cross correlation +matrix of all dipoles in the stations is calculated for one subband each +second. +Each second, another subband is selected, so that the station calibration +algorithm loops over the complete band in about 512~seconds. +Additionally, the cross correlation algorithm will be used for +Radio Frequency Interference (RFI) detection as well~\cite{Boonstra:05}. +\fixme{Maar hier doen we nog niets mee.} \section{Central Processing: the Correlator} \label{sec:corr} -- GitLab