3 A model of acquisition chain

To test rigorously the efficiency of different compressors the best solution is to generate a realistically simulated signal for different mission hypotheses and apply to them the given compressors. To be realistical the simulation of the signal generation should contain both astrophysical and instrumental effects. It would be helpful that the final simulation would be able to given a hint about the influence of the various signal components and their variance. Of course it is useless to reproduce in full detail the LFI to obtain a signal simulation accurate enough to test compressors. A simplified model of the LFI, its front-end electronics and its operations will be enough.

At the base of the simplified model is the concept of acquisition pipeline. This pipeline is composed by all the modules which process the astrophysical signal: from its collection to the production of the final data streams which are compressed and then sent to Earth. In the real LFI, the equivalent of the acquisition pipeline may be obtained following the flow of the astrophysical information, from the telescope through the front-end electronics and the main Signal Processing Unit (SPU) to the memory of the Data Processing Unit (DPU) which is in charge to downlink it to the computer of the spacecraft and then to Earth. The acquisition pipeline is represented in Fig. 1.

Figure 1: Scheme for the functional model of the acquisition pipeline

Since its purpose is to describe the signal processing and its parameters it must not be regarded as a representation of the true on-board electronics since some functionalities may be shared between different real modules. In this scheme Front End operations of the true LFI are assigned to the first simulation level, while on-board processing and compression to the second one.

The simulated microwave signal from the sky is collected and compared with the temperature of a reference load which, in our simulations, is supposed to have exactly the CMB temperature T₀=2.725 K (Mather et al. 1999). The difference $\Delta T$ expressed in $\mu{\rm K}$ is sampled along a scan circle producing a data stream of 60 scan circles with 8640 samples (pointings).

Signal detection is simulated by (Bersanelli et al. 1996; Maris et al. 1998; Maris et al. 1999)

$$% \mbox{$V_{{\rm out}}$ } = \mbox{${\rm AFO}$ } + \mbox{${{\rm VOT}}$ } \cdot \Delta T,$$ (3)

where $V_{{\rm out}}$ is the detection chain output in Volts, ${{\rm VOT}}$ is the antenna temperature to the detector voltage conversion factor (-0.5 V/K $\leq \mbox{${{\rm VOT}}$ } \leq +1.5$ V/K) while ${\rm AFO}$ is a detection chain offset (-5 V $\leq \mbox{${\rm AFO}$ } \leq +5$ V). Of course in our simulation this offset takes into account all offset sources, including variations of the reference temperature, and not only of the electrical offset. Similarly the ${{\rm VOT}}$ factor takes into account also differences among the different detectors which affect the calibration of the temperature/voltage relation. The range for ${{\rm VOT}}$ and ${\rm AFO}$ is large enough to include the whole set of nominal instrumental configurations, allowing also for somewhat larger and smaller values.

The analog to digital conversion (ADC) is described by the formula:

$$% \mbox{$V_{{\rm out}}^{{\rm adu}}$ } {\rm (adu)} = \mbox{$... ...}}{\mbox{$V_{{\rm max}}$ } - \mbox{$V_{{\rm min}}$ }} \right),$$ (4)

where $\mbox{${\rm trunc}$ }(.)$ is the decimal truncation operator, $N_{{\rm bits}}$ is the number of quantization bits produced by the ADC, while $\mbox{$V_{{\rm min}}$ }$ and $\mbox{$V_{{\rm max}}$ }$ are the lower and upper limits of the voltage scale accepted in input by the ADC. In our case: $\mbox{$N_{{\rm bits}}$ } = 16$ bits, $\mbox{$V_{{\rm min}}$ } = -10$ V, $\mbox{$V_{{\rm max}}$ } = +10$ V. So the quantization unit "adu'' (analog/digital unit) is

$$% 1 \, \mbox{${\rm adu}$ } = \frac{\mbox{$V_{{\rm max}}$ } - ... ...{$V_{{\rm min}}$ } }{2^{\scriptsize\mbox{$N_{{\rm bits}}$ }} }$$ (5)

or in terms of antenna temperature the quantization step is

$$% \Delta = \frac{\mbox{$V_{{\rm max}}$ } - \mbox{$V_{{\rm mi... ...2^{\scriptsize\mbox{$N_{{\rm bits}}$ }} \mbox{${{\rm VOT}}$ }}$$ (6)

for a typical $\mbox{${{\rm VOT}}$ } = 1$ V/K, $\mbox{$N_{{\rm bits}}$ } = 16$ bits, $1\; \Delta \approx 3 \,\, 10^{-4}$ K/adu. After digitization the simulated signal is written into a binary file of 16 bits integers and sent to the compression pipeline.

The simplified model of the Low Frequency Instrument is composed of four acquisition pipelines, one for each frequency, each one being representative of the set of devices which form the full detection channel for the given frequency. The overall data-rate after loss-less compression for LFI should be obtained summing the contribution expected from each detector. Since in the real device each radiometer for a given frequency channel, will be characterized by different values of ${{\rm VOT}}$ and ${\rm AFO}$, the distribution of these parameters has to be taken in account computing the overall compression efficiency. In particular a greater attention should be devoted to the distribution of the ${{\rm VOT}}$ parameter since the compression efficiency is particularly sensitive to it. However, since the distribution of operating conditions and instrumental parameters are not yet fully defined, we assumed that all the detectors belonging to a given frequency channel are identical and located at the telescope focus.