Frequency and Subband selection

Frequency Definition

The combination of analogue and digital signal processing both at station level as well as at the Central Processing facility allows for the users a flexible definiton of the total frequency range, subband selection and spectral channel width.

The design of the A/D system allows for RFI detection of both broad- and narrow band features.

Setting the Observing Frequency

The Receiver Units (RCUs) which convert the antenna voltages to base-band frequencies are desinged to be sky noise limited. For this, a 12 bit Analogue to Digital converter along with multiple bandpass filters is used to select the frequency bands of LOFAR.

Two sampling clock frequencies, at 200 MHz and at 160 MHz, have been selected in the design to determine the standard obseving frequency bands shown below:

Freq. range (MHz)	Clock (MHz)	Array	Nyquist zone	Remarks
10—90	200	LBA*	1	Massive interference below 20 MHz during daytime.
10—70	160	LBA*	1	Aliasing of 80—90 MHz range into 80—70 MHz [This setup is not normally used in operations]
30—90	200	LBA*	1	Short wave radio suppressed. There may however still be some intermodulation products from shortwave radio during certain ionospheric conditions.
30—70	160	LBA*	1	Aliasing of 80—90 MHz range into 80—70 MHz [This setup is not normally used in operations]
110—190	200	HBA	2	HBA band with the least interference
170—230	160	HBA	3
210—250	200	HBA	3	This band contains many digital audio stations. Final frequency selection should be done in close collaboration with observers and science support staff.

Table 1: Frequency Ranges

LOFAR Frequency Bands

Selecting the frequency/subband range

After digitisation from the RCU boards the signal is further processed in the Remote Station Processing (RSP) boards which use Field Programmable Gate Arrays (FPGAs).

Initially the total bandwidth of the digitized signal (100 MHz for the 200 MHz clock and 80 MHz for the 160MHz clock) is split in 512 sub-bands via a poly-phase filter (PPF), followed by a 1024-point Fast Fourier Transform.

These subbands have bandwidths of 195.3 kHz and 156.2 KHz, respectively for the 200 MHz and 160 MHz clock. This is shown in Table 2.

Due to hardware and network restrictions only a total of 244 subbands, totaling 48MHz (or 38.25MHz) can be transmitted from the stations to the Central Processing Facility. These subbands can be selected arbitrarily over the selected frequency bands.

Clock	Total Bandwidth	Sub-band width	Channel width (256 channels)
(MHz)	(MHz)	(Hz)	(Hz)
200	100	195312.5	767.939
160	80	156250.0	610.352

Table 2: Subband and Spectral Line Channel Bandwidths

Following subsequent processing in the Central Processing Faciity, to realign the data streams in time, a poly-phase filter is applied to re-sample the data to the kHz level, splitting each sub-band into a fixed number of frequency channels.

Typically, 64 channels per subband have been routinely used and the maximum recommended number of 256 channels per subband (which creates channels of 763 Hz or 610 Hz respectively; see Table 2). Both allow for the offline processing to flag narrow-band RFI so that unaffected channels remain usable.

The number of spectral channels proportionaly increases the raw data size and the subsequent processing speed, so at the time of the definition of observations the Radio Observatory can reccomend the spectral resolution that offers the best compromise between the scientific aims and the practical considerations.

Subband Naming Convention

Due to the limit of processing only 244 of the total of 512 subbands, users will have to select the subbands they wish to observe when proposing and at the time of definition of the proposed observations.

In the convention of the observing system, each subband is identified by a number. This number is related to the sky frequency through the following formula:

The number of the sub-band S containing a certain frequency ν is given by

where n is the Nyquist zone (see Table above), ν_clk is the clock frequency (200 or 160 MHz), and ⌊ and ⌋ denotes the "floor" function.

Conversely, the central frequency of sub-band S is given by:

Because the sub-band separation is done using fixed poly-phase filters on a time series that is recorded at a fixed clock rate, LOFAR does not perform any Doppler tracking. That is, the frequencies are observed in a telescope based reference frame, not a geocentric, solar system barycentric, or sky frame. Such conversions should be performed offline by the PI, if necessary.

Some frequently used examples of subband selections are listed below:


LBA frequency	subband name	clock
30-78	154-397	-
HBA frequency	subband name	clock
115-163	77-320	200
148-196	245-488	200
180-210	128-371	160
210-250	52-255	200

Table 3. Naming convention of Recommended subbands

Interference in the LOFAR frequency bands

Following are typical plots of the RFI situation in the LBA and HBA bands. The HBA has been split into three parts (HBA low, mid and high), which were observed independently. Parts of the HBA high range (around 225 MHz) are contaminated by several broadband digital broadcast transmitters. Towards lower frequencies in the LBA band (below 30 MHz), the data are more affected by interferences.

Station Clock

The second clock system consists of a rubidium maser controlled by a GPS clock. Each station has its own independent GPS-controlled rubidium clock. In that sense, LOFAR operates by default in "VLBI mode", even on short baselines.

The stations of the "superterp" CS002, CS003, CS004, CS005, CS006 and CS007, since May 2010, share a common clock. They are suitable for tied-array observations because no clock corrections are needed at the BG/P.

Combining other stations into a tied-array will lead to decorrelation of the signal because the tied-array software currently does not correct for clock offsets and the offsets are comparable to the wavelength in the high band.

There are plans to extend the common clock to all core stations, by the end of the summer 2012.

Time offsets between two independent GPS controlled rubidium masers during the course of 60 hours.

During a 2.5 day long test run, the time offsets between two stations using two GPS-stabilized rubidium masers, had an RMS variation of 3.5 ns with peaks of the order of 10 ns. These time differences correspond to path length differences of 1 to 3 m respectively.

More information on the clock system can be found in LOFAR Report 057 (pdf) by Andre van Houwelingen and Gijs Schoonderbeek.

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