of Interferometers and Comparison of R adio Interferometers with Analog and Digital Extraction of Recorded Signal

Introduction . Radio telescopes incorporated in very long baseline interferometry (VLBI) networks are used to record several narrowband signals (up to 32 MHz), which are extracted by means of base band converters (BBC) from an analog noise signal of an intermediate frequency (IF) with bands up to 1 GHz. When processing the as-obtained data, the method of frequency band synthesis is used. Novel compact radio telescopes (e.g., RT-13) digitalize wideband IF signals. A digital narrowband signal extraction module developed in 2019 provides the possibility of integrating RT-13 radio telescopes with the Russian Quasar VLBI Network. Aim. To assess the accuracy of measuring the interferometric group delay of a signal by a radio interferometer equipped with a digital narrow-band signal extraction module, as well as to compare the sensitivity of interferometers with analog and digital signal extraction systems. Materials and methods . Sensitivity losses of interferometers with different systems for detecting recorded signals were calculated. The accuracy of a multi-channel interferometer with the synthesis of a frequency band and an interferometer with recording of digital broadband IF signals without band synthesis was compared. The results were confirmed by VLBI observations in the observatories of the Quasar VLBI Network. Results. When replacing the analog system of signal extraction with the digital system, the sensitivity losses of the interferometer decreased slightly. The measurement accuracy of the interferometric group delay remained unchanged. An increase in accuracy was achieved when broadband IF signals were recorded digitally and when a frequency band significantly larger than the IF bandwidth was synthesized. Conditions and minimum synthesized bands were determined, under which the accuracy of the interferometer registering narrowband signals exceed that of the interferometer registering wideband IF signals. Conclusion. The problem of integrating RT-13 radio telescopes with VLBI networks, which record video frequency signals, was solved. The feasibility of installing digital signal conversion systems on radio telescopes was shown.

Introduction. Data acquisition systems (DAS) are widely used in radio telescopes with very long baseline interferometry (VLBI) networks. These systems are capable to extract signals with relatively narrow (up to 32 MHz) F ∆ bands from a wide (up to 1 GHz) band of intermediate frequencies (IF) that followed by their conversion to base band frequencies and digital recording [1,2]. This class of system also includes R1002M 16-channel DAS [3] which are installed on RT-32 VLBI radio telescopes in the Quasar VLBI Network [4]. Signals with F ∆ bands are extracted from a noise IF signal with a band of 0.1…1 GHz using analog quadrature frequency converters (QFC) and digital downconverter. The extracted signals are amplitude-quantized and formatted according to the international VDIF standard [5] or the VSI-H format [6], followed by the transmission of the received observation data for processing by VLBI correlators [7,8]. For VLBI observations by astrometry and geodetic programs the signals of 5-8 frequency channels with bands of 8 F ∆ = or 16 MHz are extracted from the IF band and processed using the method of wide band frequency synthesis [9].
In recent years the transition to compact radio telescopes with digital systems for recording broadband signals (from 0.5 to 1 GHz) has become the main direction in of the development of VLBI [10,11]. Such systems are essential both for the creation of new generation VLBI complexes [12,13] and for the development of radiometry as a whole [14]. For example, the RT-13 13-meter VLBI radio telescopes was incorporated with digital systems for converting broadband signals that have eight channels and able to record IF signals with 0 bands at a sampling frequency of d 1024 MHz = F [11]. Processing of high-speed data streams received by the system channels (2048 Mbit/s per channel) are carried out by specialized software VLBI correlators [15].
In order to integrate radio telescopes with broadband channels into existing VLBI networks, where narrowband signals of base band frequencies are recorded and processed, the signals with relatively narrow bands should be extracted from a high-speed digital IF signal and converted to base band frequencies ( ) 0... . F ∆ This operation can be performed by digital modules on a field programmable gate array (FPGA) that containing polyphase filters (PPF) and base band converters (BBC) [16]. In terms of structure and clock frequency the data stream generated by such modules is similar to that received using R1002M DAS. As a result, it becomes possible to integrate RT-13 radio telescopes registering broadband signals with both the Quasar VLBI Network and international VLBI networks that recording narrowband signals.
In this regard, it is important to determine the effect of replacing analog DAS with digital signal extraction modules on the sensitivity of radio interferometers and the measurement accuracy of interferometric group delays of the τ received radiosignal. This information is essential both for the rational planning of VLBI observations using heterogeneous signal conversion systems and for the selection of reference sources for radiosignals. In addition, this information can be used for developing multifunctional digital systems for converting signals with bands (sampling frequency of with the aim of upgrading the existing RT-32 radio telescopes and equipping new compact radio telescopes.
In this article we set out to investigate the effect of the loss of instrumental sensitivity by radio interferometers equipped with different systems for extracting recorded narrowband signals from a wide IF band. To this end we compare the sensitivity and accuracy of measuring the interferometric group delays of signals using an interferometer with extracting registered narrowband signals digitally and an interferometer with an R1002M DAS.
In connection with the development of VLBI radio telescopes with ultra wide-band radio astronomy receivers (RR) [17,18] and registration systems for broadband signals [10,11], the possibility of synthesizing a frequency band exceeding the passband of the receiving channel (up to 1 GHz) is of particular significance. The receivers of RT-13 radio telescopes [19] have three receiving channels for each frequency range and for any of two circular wave polarizations, thus allowing the frequency bands up to 2.5 and 6 GHz wide to be synthesized in the X (7…9.5 GHz) and K range (28…34 GHz), respectively. Since the effectiveness of such an approach has not been clarified yet, it is of interest to compare the parameters of a multichannel interferometer that registering narrowband signals (up to 16 MHz) digitally for a subsequent synthesis of a broadband signal, with those of an interferometer recording in parallel (without synthesis) up to three broadband (0.5 or 1 GHz) signals.
Determination of the sensitivity of interferometers based on different systems for extracting recorded signals. The sensitivity of a radio interferometer is characterized by the ratio of the correlation response peak to the root mean square deviation (RMSD) of the residual noise at the output of the correlator. For a single-channel interferometer with the F ∆ band of signal recording, the signal-to-noise ratio at the peak of the correlation response is defined as: where 1 χ ≤ is the coefficient that taking into account the loss of sensitivity in the receiving and recording channels of radio telescopes and in the correlator of the interferometer; s n = q T T is the ratio of the s T received signal noise temperature to the n T temperature of the radio telescope set noise at the RR input; o t is the source observation (scanning) time [8]. Subscripts 1 and 2 indicate the serial numbers of the interferometer radio telescopes. VLBI measurements are usually performed at 1 7.
R > Let us represent the coefficient of hardware sensitivity loss by the E 0 χ = χ χ product, where the first term represents the losses in the broadband receiving and amplifying channels, as well as in the device for separating the recorded base band frequency signals, while the second term represents the losses in the digital processing and correlation devices of the extracted base band frequency signals.
The 0 χ value is determined mainly by losses arising during amplitude quantization of digital samples of the noise signal (12 or 36.3 % for four-or two-level quantization, respectively), as well as by losses involved with the correlation processing of base band frequency signals, accounting together for about 13 % [9]. For radio interferometers with narrowband channels, including those in the Quasar VLBI Network with R1002M systems, as a first ap-proximation, 0 0.76 χ ≈ or 0 0.55 χ ≈ can be taken for four-or two-level quantization, respectively. These 0 χ values remain valid for an interferometer based on digital signal extraction systems, since the methods of amplitude quantization, formatting and correlation processing of narrowband signals remain the same.
For assessing the quality of signal extraction channels, it is sufficient to compare the E χ loss coefficients for interferometers with digital signal extraction systems ( ) and those with analog In RT-32 radio telescopes the RR is connected to the DAS by a coaxial transmission line containing power amplifiers with corrections for the nonuniformity of attenuation in the 0.1…1 GHz IF band ( Fig. 1). In the DAS IF signal is distributed over base band converters each of which comprises a quadrature frequency converter (QFC) equipped with diode mixers and F ∆ band analog low-pass filters (LPF), a pair of analog-to-digital converters (ADC) and a digital phase signal splitter (PSS) separating the signals of the upper and lower side bands. After the fourlevel quantization of amplitudes the digital signals with F ∆ bands are fed to the data formatter of the Mark 5B+ recording terminal [20] followed by transmission of the observation data to the correlation processing center.
When the A χ coefficient is calculated using an interferometer with an DAS R1002M, account is taken of the losses associated with the distortion of signals in the receiving-amplifying channel from the input of the RR to the ADC in the DAS base band converter. In general, η are the losses related to the i-th factor (in Fig. 1 10 percent). Losses of about 3 % result from distorting the signal by the phase noise from super-high frequency heterodynes of the RR. Distortions of the narrowband signal in the RR with a wide passband can be neglected, since the amplitude-frequency characteristic (AFC) and phase-frequency characteristic (PFC) of the receiving channel are formed by the narrowband low-pass filter of the base band converter. In the IF signal transmission line, due to the non-uniform AFC of power amplifiers and the residual slope in the AFC of the coaxial cable (uncompensated attenuation nonuniformity), signals with F ∆ bands in individual frequency channels are susceptible to distortion. The distortions of the channel AFC due to the slope of the spectrum leads to the loss of the interferometer sensitivity of up to 2 %. A significant loss of the interferometer sensitivity may occur due to the non-identity of the AFC of analog filters in the base band converters of an interferometer radio telescope pair. Technological variation in the filter parameters, temperature changes and aging of circuit elements can also result in the oscillation and slope of the AFC in the channel passband. In R1002M DAS base band converters, the AFC identity and PFC linearity of the channels are significantly increased due to digital filters forming the F ∆ band and digital PSS separating sideband signals with an isolation of more than 42 dB. The noise of the mirror channel is practically eliminated, while moire noise is suppressed by a pre-filter (switchable filters) at the input of the base band converter. Nonlinear distortion of signals in the channel with digital filters is also practically absent. The quantization noise of the analog signal can be neglected, when the number of ADC bits equal to at least 8. Losses arising for the aforementioned reasons account for about 2 %. Minor (about 1 %) sensitivity losses occur due to noise from heterodyne signals, the RMSD of which is reduced to 2° [3]. The loss of the interferometer sensitivity due to signal distortion in the R1002M DAS comprises about 3 % in total.
In general, for an interferometer with analog signal extraction channels of base band frequencies, the coefficient of hardware sensitivity loss can be taken as A 0 0.92 . χ ≈ χ In interferometers based on digital conversion systems for broadband signals, the ADC operates at the sampling frequencies of d 2048 From the received high-speed (broadband) digital signal, narrowband signals are extracted using an FPGA-formed PPF module and BBC (Fig. 2). A digital input signal with a d F sampling frequency is distributed by the demultiplexer (DM) over the N channels of PPF with decreasing frequency to the FPGA value of clock frequency т 550 MHz.
≤ F Complex signals at the PPF outputs are divided into N real signals with s 0 = B B N bands by the splitters (PSS) in phase-shifting filters. From the obtained band signals, signals with the F ∆ specified bands are extracted by BBC. The selected signals are quantized in amplitude and formatted similar to those in the DAS R1002M channels.
In radio astronomy equipment that based on FPGA, it is convenient to use BBC operating with a clock frequency of т 128 F = or 256 MHz [11] which are tuned by digital heterodynes [21] in the frequency bands up to 64 or 128 MHz, respectively. When using heterodynes with a clock frequency of 512 MHz [22], the tuning range of the BBC is expanded to 256 MHz. However, in the latter case, preliminary filtering of the input broadband signal is also necessary.
During polyphase filtering in the near-zero frequency range and at the frequencies multiple of т F the signals are distorted. Distortions also occur near the frequencies multiple of т 0.5F where the signal spectra partially overlap at the edges of adjacent s . B bands. Thus, in order to be capable of extracting signals of any frequencies without distortion, the mod- where n is the serial number of the output signal code; L is the order of the filters for the ( ) n h r weight functions; j is the imaginary unit. The weight function affecting the distribution of energy between the main and side lobes of the spectral function for the output signal has the form: In RT-13 radio telescopes, a digital broadband IF converter is located next to the RR by means of a fixed short (less than 1.5 m) coaxial. The signal spectrum at the ADC input is formed by a broadband IF filter. Here, the sensitivity losses associated with distortions of signals in the IF signal transmission lines are eliminated; however, the losses (up to 3 %) due to signal distortions in frequency converters by heterodyne phase noise are still present. All filters in the signal extraction channel are digital, thus ensuring a high stability of the receiving and recording channel parameters during the antenna movement and changes in external climatic conditions. Therefore, the PFC linearity is guaranteed, and distortions in the AFC shape of the receiving and recording channel are minimized (distortion and oscillation of AFC, deviations in the passband, frequency tuning shift). The loss of sensitivity due to the AFC nonidentity of the interferometer channels is lower than 0.3 %. The AFC side lobes of the PPF channel are attenuated by 30 dB. Due to out-of-band noise penetrating the side lobes, the signal-to-noise ratio in the 8-channel PPF decreases by about 0.7 %.
In digital signal extraction systems, insignificant losses appears due to the bit depth limitations (truncations) of the codes in the PPF, PSS and BBC. In calculations according to (1) products are summed. The codes obtained at this stage are truncated to 9 bits. At the stage of multiplying these codes by 16-bit codes of the exponential function and adding the 8 N = obtained results, the output signal codes are truncated to 12 bits. As a result of code truncations, the signal-to-noise ratio in the PPF channel decreases by 0.16 %. A decrease in the bit depth of the codes to 14 in the band signal phase selector does not result in any noticeable loss of sensitivity. In the BBC heterodyne, the resolution of the current phase codes decreases to 10, corresponding  12 to a RMS phase noise of the heterodyne signal of 0.1°. Losses associated with such a phase noise are negligible. Amplitude fluctuations of heterodyne signals represented by 10-bit codes have little effect on the signal-to-noise ratio in the frequency converter. Almost no change in the signals of the base band frequencies caused by signal-to-noise ratio is observed at the outputs of the QFC, while limiting their bit depth to 15. The total sensitivity loss introduced by the digital narrowband signal extraction module does not exceed 0.5 %.
In the digital module, the total decrease in the signal-to-noise ratio is significantly lower than the loss resulting from signal distortion by phase noise of the RR heterodynes. Taking into account all losses for an interferometer with digital narrowband signal extraction systems, the loss coefficient can be taken equal to D 0 0.96 . χ ≈ χ For an interferometer with the same antennas and RR, but with different types of narrowband signal extraction systems, A 0 0.94 . χ ≈ χ The sensitivity of interferometers can be slightly increased (up to 4 %) by replacing the standard R1002M DAS in RT-32 radio telescopes with the considered modules for digital extraction of narrowband signals. A slight improvement in sensitivity has little effect on the accuracy of determining the τ interferometric group delay of the received radio signal. Under 1 7 R > , the greatest effect is produced by factors unrelated to the signal registration system, including errors in tracking systems for Doppler frequencies and ephemeris, errors in measuring group delays of signals in the receiving and recording channels of radio telescopes and discrepancies in the time scales of data formatters in radio telescopes. In addition, for angular and coordinate-time measurements by VLBI methods, account should be taken of the state of the atmosphere; however, the accuracy of such corrections may be insufficient.
A radio telescope with a digital signal extraction module can be operated both in a multichannel interferometer mode with registration of narrowband signals and in an interferometer mode registering broadband IF signals. During the VLBI observations conducted at the Zelenchukskaya and Badary observatories, the parameters of the Quasar standard radio interferometer (two RT-32 radio telescopes with R1002M DAS) and an interferometer with different types of radio telescopes (RT-32 with DAS and RT-13 with a digital signal extraction module) were compared. The tests confirmed the possibility of integration radio telescopes with dif-ferent systems of signal conversion in the VLBI network and the possibility of operating a RT-13 radio telescope in the Quasar VLBI Network.
Accuracy assessment of a multichannel interferometer providing digital signal extraction. For an M-channel radio interferometer with the synthesis of a wide frequency band, the RMSD calculated by the interferometric delay correlator is defined as [8]: observations are chosen such that it could be possible to extrapolate the signal phases from one frequency to another without 2π uncertainty and to construct a linear dependence of the recorded signal phases to the frequency with the greatest possible accuracy. In one of the recommended options, the frequency spacing between adjacent channels doubles as the r channel number increases [8].  Radioelectronics. 2020, vol. 23, no. 2, pp. 6-18 13 telescope, the former option can be implemented using one RR channel and two channels of the standard digital signal recording system with bands. The latter option requires one channel with a 512 MHz band.
In the synthesis of a frequency band not exceed- mean square error of the M-channel interferometer is always greater than that of a single-channel interferometer with a 0 B recording band defined in [9] as Provided that the interferometer contains m parallel channels registering broadband IF signals and after averaging m results, the RMSD of the calculated interference group delay will be Based on (2) and (3), in the synthesis of the frequency band within the passband of the receiving the relation is formed: This formula can be used to determine the minimum value of the synthesized frequency band, under which the accuracy of determining the interferometric delay exceed that obtained by an interferometer with broadband channels without band synthesis.
Results. The use of the digital method for extracting narrowband signals at radio telescopes provides a minor (about 4%) reduction in the sensitivity loss of the radio interferometer, without affecting the accuracy of measuring the interference group delay of the signal. When replacing analog narrowband signal extraction systems with digital systems, the accuracy of a multi-channel radio interferometer with frequency band synthesis remains unchanged.
As follows from (4) One direction in the development of VLBI (international projects VLBI 2010 and VGOS) involves the synthesis of a frequency band significantly exceeding 1 GHz. The antenna irradiator and threechannel RR of the RT-13 radio telescope with the bandwidths [19] allow a frequency band of up to 2.5 and 6 GHz in the X and K wavelength range, respectively, to be synthesized. This task can be achieved by using three RR channels, four ADCs of a standard signal recording system with bands of 512 MHz and a module for digital extraction of narrowband signals (Fig. 4). The signal extraction device is realized in the FPGA of the XC7K325T type. After formatting the extracted signals with the F ∆ bands according to the VDIF standard, an Ethernet 10G data stream is generated and transmitted through the X2 electron-optical transceiver to the radio telescope server and to the center of correlation data processing.
For  14 mission channel. The channel RR 1, extracting a broadband signal in the lower part of the operating frequency range, is connected to two ADCs through filters with adjacent passband (1024-1536 and 1536-2048 MHz). It is sufficient to connect one ADC with a filter of 1024-1536 MHz to the two remaining channels of the RR.
In the X frequency range, when synthesizing a frequency band up to 2.5 GHz, 2 RR channels with 1 GHz bandwidths, 3 ADCs digitizing signals with bands, 3 PPF modules and 7 ADCs can be used (Fig. 5, a) (Fig. 5, a) Across the K frequency range, a frequency band of up to 6 GHz can be synthesized using three RR channels, four PPF modules and seven BBCs with the 16 MHz ∆ = F bands (Fig. 5, b). Under 45 MHz = w and a similar arrangement of signals in terms of frequency, the number of extracted signals can be potentially increased to 8. However, due to the absence of a fourth RR channel, the registration is limited to 7 signals (excluding the signal at a frequency of  with the interferometer operating in the registration mode of the broadband IF signals. However, in the mode of registering several F ∆ narrowband signals, the total stream speed of data transmitted to the correlation data processing center decreases significantly, thus permitting the connection of the radio telescope to VLBI networks using narrowband signal correlators [8]. For example, in an interferometer recording 8 signals with 16 MHz bands (see Fig. 5, b), the total speed of the information stream under four-level quantization is 512 Mbit/s. An interferometer recording 4 signals with 512 MHz bands provides a stream with a total speed of 8192 Mbit/s. An increase in the speed of the data stream leads to stricter requirements for radio telescope servers, fiber-optic communication lines between radio telescopes and data processing centers, as well as VLBI correlators.
Discussion. According to the obtained results, a conclusion can be made about the advisability of installing digital signal conversion systems on the RT-32 and RT-70 (Ussuriysk) radio telescopes instead of the standard R1002M DAS with analogue extraction of narrowband signals. This replacement will improve slightly the sensitivity of the interferometer (approximately 4%), at the same time as leaving the accuracy of measuring the interferometric group delays of the received signals practically unchanged. However, in digital systems, the complex channels for amplifying and transmitting broadband analog IF signals are replaced with fiber-optic digital signal transmission lines. Therefore, in terms of performance and reliability, digital systems provide distinct advantages.
In addition, the use of the developed digital system allows radio telescopes to be operated in the registration mode of broadband IF signals, thus significantly increasing the sensitivity of interferometers and expanding the list of available reference sources used in VLBI observations.
After completion of the ongoing development of antenna irradiators and ultra-wideband receivers for RT-32 radio telescopes, it will be possible to synthesize frequency bands wider than 1 GHz and to improve the accuracy of VLBI measurements.
The developed method for a digital extraction of narrowband signals from the IF bandwidth is applied in a new multifunctional signal conversion and registration system aimed at upgrading existing radio telescopes of the Russian Quasar VLBI Network and equipping novel compact radio telescopes [24]. This system is capable of rapidly switching the modes of radio astronomy observations.