Performance of a Highly Sensitive, 19-element, Dual-polarization, Cryogenic L-band Phased-array Feed on the Green Bank Telescope

Radio astronomy is primarily an observational science, in which high-sensitivity, large-scale surveys are an essential tool for new discoveries (Condon et al. 1998; Barnes et al. 2001; Manchester 2001; DeZotti et al. 2010; Bekhti et al. 2016). While large apertures enhance sensitivity, they have a more limited field of view (FoV) when equipped with a single feed. The survey speed of a telescope is proportional to its FoV and the square of the signal-to-noise ratio (S/N) required for the survey. In this paper, we describe a new 1.4 GHz (L-band) phased-array feed (PAF) system, built for the Robert C. Byrd Green Bank Telescope (GBT) as part of the Focal L-band Array for the GBT (FLAG) project, which can enhance the FoV of the telescope by a factor of 7 and has sensitivity comparable to the existing single-feed 1.4 GHz receiver.

There are wide-ranging scientific interests to increase the FoV of the GBT near the L band. Here we focus on two scientific motivations. It is now known that galaxies must be accreting gas to sustain their star formation. With the current known gas content of galaxies, current star formation rates can be sustained only for a few billion yr. However, there is evidence that the gas content of galaxies has remained roughly constant for the past 10 billion yr, implying that galaxies must be accreting gas from the intergalactic medium (Prochaska et al. 2005). Current theories suggest that this accretion occurs in one of two modes: a hot mode, where the gas is heated to 10⁶ K, or a cold mode, where the gas remains below 10⁵ K (Kereš et al. 2005, 2009; Sancisi et al. 2008). The cold mode, in particular, should be the dominant form of accretion for low-mass galaxies in low-density environments. Such accretion should be detectable via observations of neutral hydrogen at 21 cm (H i) at column densities of N(H i) ≲ 10¹⁸ cm² (Popping et al. 2009). To detect H i emission from the cold accretion flows from nearby galaxies, sensitive single-dish observations are essential (Chynoweth et al. 2008; Mihos et al. 2012; Wolfe et al. 2013; de Blok et al. 2014; Pisano 2014; Wolfe et al. 2016). Since the expected line strengths are weak, such surveys require enormous amounts of observing time. To reduce the observing time, it is essential to increase the FoV of the telescope with high-sensitivity multibeam systems.

The discovery of fast radio bursts (FRBs) has generated renewed interest in exploring the transient radio sky (Lorimer et al. 2007; Katz 2016). FRBs are bright, approximately millisecond-duration individual pulses from compact sources exhibiting pulse-dispersive delays over a wide bandwidth. The dispersive delays far exceed the values expected from the interstellar medium of our Galaxy, indicating that they are extragalactic in origin. This has been confirmed by the localization and optical counterpart identification for FRB 121103, the only known repeating burst source (Chatterjee et al. 2017). So far, about 24 FRBs have been detected (Petroff et al. 2016), with most of the detections made near 1.4 GHz. The physical nature of and mechanism producing the burst are not known. Studies of such short-duration radio transients are poised for a revolution with large FoV telescopes and flexible, high-throughput back ends (see, for example, Bannister et al. 2017).

The FoV of a radio telescope when equipped with a single feed is limited to the full width at half maximum (FWHM) of the primary beam, which is ∼λ/D, where λ is the observing wavelength and D is the aperture diameter of the reflector. The feeds are usually optimized to maximally receive radiation from the reflector while attenuating the ground spillover. The physical size of the feed is determined by this optimization process. Traditionally, the FoV of telescopes is increased by placing multiple such optimized feeds in the focal plane—referred to as a focal plane array (FPA). The physical separation between feeds in an FPA is determined by the size of the feeds. The large physical separation of the feeds results in nonoverlapping beams on the sky. Further, the off-axis beams suffer efficiency degradation, since the feed optimization is usually done for the central beam. Both of these effects result in a relatively poor mapping efficiency improvement.

In the last decade, the use of phased arrays employing a set of smaller focal plane radiating elements—referred to as PAFs—has gained wide interest among the radio astronomy community (Fisher & Bradely 2000; Hay & Bird 2015; Warnick et al. 2016). In such PAF receivers, each element is electrically small and thus does not optimally illuminate the reflector. However, an optimal illumination with low spillover is obtained by the weighted sum of the amplified signal voltages from multiple elements. Multiple beams can be formed by adding signals with different sets of complex weights. The beams formed in this manner can be made to overlap, thus increasing the mapping efficiency. The design and optimization of PAFs are complicated by mutual coupling effects between elements (see, for example, Diao & Warnick 2017). The mutual coupling distorts the element beam pattern and introduces channel-to-channel noise coupling between neighboring low-noise amplifiers (LNAs) that follow these elements. Thus, accurate methods for electromagnetic modeling and beam forming are needed in order to achieve efficient performance.

Currently, PAFs are being developed for both single-dish radio telescopes and radio interferometers. Designing efficient PAFs requires proper accounting of electromagnetic coupling and beam forming, which has led to new theories and techniques in PAF modeling (Woestenburg 2005; Warnick & Jensen 2007; Hay 2010). Further, several leading radio astronomy institutions have made significant progress on developing PAF receivers and systems. The Westerbork Synthesis Radio Telescope (WSRT; Oosterloo et al. 2010) and the Australian Square Kilometer Array Prototype (ASKAP; Hay & O'Sullivan 2008; Chippendale et al. 2015) have both built uncooled, broadband (>800 MHz) PAFs near 1.4 GHz. The elements used by the WSRT for their PAF, called the APERture Tile In Focus (APERTIF), are Vivaldi antennas. The ASKAP Chequerboard PAF is made of a self-complementary connected element array (Hay & O'Sullivan 2008). A phased-array feed demonstrator (PHAD) has been developed by the Dominion Radio Astrophysical Observatory (DRAO) using Vivaldi elements (Veidt et al. 2011). Cryogenic PAF development is being pursued for the Arecibo telescope by Cornell University (Cortes-Medellin et al. 2015) and for the Five hundred meter Aperture Spherical Telescope (FAST; Wu et al. 2016); both have operating frequencies near 1.4 GHz. A higher-frequency (70–95 GHz) PAF is also being developed by the University of Massachusetts (Erickson et al. 2015).

FLAG is a collaborative project between the National Radio Astronomy Observatory (NRAO), the Green Bank Observatory (GBO), Brigham Young University (BYU), and West Virginia University (WVU). During the first phase of the project, a prototype cryogenic "kite dipole array" was built and tested successfully on the GBT (Roshi et al. 2015). In this paper, we present the construction of the next-generation cryogenic PAF and describe the measurement of its performance and comparison with a PAF model. The new PAF is optimized for the GBT optics to provide the required FoV with a diameter of ∼20'. Additionally, all of the instrumentation from the LNA to the back end was upgraded. A brief description of the new system is given in Section 2. For testing and commissioning of the system on the GBT, Nyquist-sampled voltage data were recorded in an instantaneous bandwidth of 300 kHz, and all signal processing was done off-line. The data-processing method is described in Section 3. Before the system was installed on the GBT, the receiver temperature of the PAF was measured at the outdoor test facility at the GBO, as described in Section 4. The test observations made with the GBT are summarized in Section 5, and the results are given in Section 6. We have also observed a pulsar and an extended continuum source using the PAF system on the GBT. The results of these observations are presented in Section 7. The main results are summarized in Section 8. A GPU-based digital signal-processing back-end instrument has been realized for real-time calibration and beam forming by the FLAG collaboration. This system will form the back end for the PAF for science observations with the GBT. The details of the real-time beam former will be published elsewhere.

The PAF consists of a hexagonal array of 19 dual-polarization dipole elements at ambient temperature connected to 19 pairs of cryogenic LNAs located in a vacuum dewar. Optimization of the design for maximum sensitivity over the antenna FoV of angular diameter ∼20' and across a bandwidth of 150 MHz required adjusting the geometric parameters of the dipoles, which had been developed in prior work (Warnick et al. 2011). The optimal design is dependent upon the noise parameters of the LNA and uses maximum S/N beam forming as a parameter. The dipole array is shown in Figure 1(a). The dipoles were fabricated using brass and subsequently plated with copper (with thickness ≈6.35 μm) followed by 1 μm of gold to reduce ohmic loss. An air-filled coaxial conductor transmission line was used to minimize dielectric loss. These vertical transmission lines function as a balun and a means of fixing the correct separation between the radiating elements and the ground plane. Two teflon beads located at either end of the transmission line center the inner conductor. Between the dipoles and the LNAs, which are located in the cryostat, there is a custom low-loss coaxial assembly that also serves as a thermal transition and a vacuum barrier, as shown in Figure 1(b). The LNAs use SiGe transistors selected for their low-noise performance at cryogenic temperatures (Weinreb et al. 2009). The measured average gain of the LNAs is 38 dB over their 1.2–1.7 GHz frequency range, and the median noise temperature is 4.85 K (the peak-to-peak variation in the measured values is 1.5 K) when operated at a physical temperature of 15 K (Groves III & Morgan 2017). A highly integrated, 40-channel electronics assembly encompasses all of the remaining functions of the receiver: calibration signal injection, warm post-amplification, power leveling, local oscillator (LO) distribution, down conversion, analog-to-digital conversion, and serial data transmission through optical fiber, as shown in Figure 2. This post-amplification electronics assembly is the first deployment of a novel integrated unformatted digital link developed at NRAO (Morgan et al. 2013), which allowed the entire analog signal path and digitizers to be located directly behind the phased array. This reduced the power dissipation and minimized the physical footprint. We have confirmed many aspects of this new design, including the methodology for recovering bit and word boundaries in the unformatted received data streams (Morgan & Fisher 2014). The digital link can be scaled in bit rate, bandwidth, and channel count for future PAF applications. The fiber-optic link transports the samples over approximately 2 km to the Jansky Laboratory to terminate in equipment racks containing five ROACH2 FPGA boards,⁹ which perform bit and byte alignment, 512 channel polyphase filter bank, and sideband separation operations. The data from the spectral channels are requantized to 8 bits, packetized, and sent to an Ethernet switch through 10 GbE links. Only 500 spectral channels, selected by removing channels from the band edge, are sent to the switch. The data acquisition system developed for commissioning and testing consists of a Linux computer equipped with a high-speed disk and connected to the switch through a 10 GbE link. The complex voltage samples from one of the spectral channels are recorded to the disk for off-line processing.

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The PAF and the associated receiver box are placed at the prime focus of the GBT. The GBT LO system is used for the first down conversion. The digital down converters and the back-end system are synchronized through a 10 MHz observatory-wide frequency reference, which is also used to lock the GBT LO system. The LO frequencies were set to 1550, 1450, 1350, or 1250 MHz for most observations, since the sideband separation coefficients were previously calibrated for these LO values. For each LO setting, data were collected from a subset of 300 kHz PFB channels. The observing frequency corresponding to this subset of PFB channels was located within the 150 MHz bandwidth centered at the LO value.

For future science observations, a complete GPU-based digital signal-processing back-end instrument has been realized to process all 500 channels from the FPGA boards, covering 150 MHz bandwidth (see Figure 2). It performs phased-array calibration, beam forming, correlation, and pulsar and transient searches. It has several unique capabilities not found on other PAF-equipped telescopes. Array covariance matrices are saved continuously from the correlator as the primary data product. This enables post-correlation beam forming (Hay & Bird 2015) after the fact for spectral-line or continuum observations, so that different beam-forming weights can be applied to improve beam patterns or to compute any desired number of overlapping beams on the sky (within the limits of the FoV accessible to the finite number of PAF elements). Also, we are in the process of developing software for two new operational modes: (a) a commensal mode, where a quick-dump real-time beam-formed spectrometer runs concurrently with the correlator to permit opportunistic transient searches during observations of neutral hydrogen, and (b) a radio frequency interference (RFI) mitigation mode, where the correlator and real-time beam former can be linked to form a tracking RFI-nulling adaptive beam former. This instrument was commissioned separately on the GBT in summer 2017, and the results will be presented elsewhere.

The off-line processing of the recorded data proceeded with first taking a 64-point Fourier transform of the complex voltage time series, which provided a spectral resolution of ∼300/64 = 4.7 kHz. The cross-correlations between signals from all 38 dipole outputs for each spectral channel were then computed, and the correlation matrix ${\boldsymbol{R}}$ was obtained as

$$\begin{eqnarray}&&{\boldsymbol{R}}=\displaystyle \frac{1}{N}\displaystyle \sum _{i=0}^{N-1}{\boldsymbol{V}}[i]{\boldsymbol{V}}{[i]}^{H}.\end{eqnarray} \tag{ 1 }$$

Here ${\boldsymbol{V}}[i]$ is the time series of the complex voltage vector formed from the 38 dipole outputs from a spectral channel. The number of samples N used for the computation typically corresponds to an integration time of 5 s. The high spectral resolution is very useful to excise narrowband RFI. After RFI editing, the cross-correlations were averaged over 300 kHz bandwidth.

An off-line post-correlation beam former is implemented in a MATLAB¹⁰ program (Jeffs et al. 2008; Hay & Bird 2015). For typical observations, the cross-correlations on the source and at a nearby off-source position were measured. In this case,

$$\begin{eqnarray}&&{\rm{S/N}}=\displaystyle \frac{{{\boldsymbol{w}}}^{H}{{\boldsymbol{R}}}_{\mathrm{on}}{\boldsymbol{w}}}{{{\boldsymbol{w}}}^{H}{{\boldsymbol{R}}}_{\mathrm{off}}{\boldsymbol{w}}}-1,\end{eqnarray} \tag{ 2 }$$

where ${{\boldsymbol{R}}}_{\mathrm{on}}$ and ${{\boldsymbol{R}}}_{\mathrm{off}}$ represent the on-source and off-source correlation matrices, respectively, and ${\boldsymbol{w}}$ is the beam-former weight. The beam-former weights are obtained by maximizing the S/N, which will be the eigenvector corresponding to the maximum Rayleigh quotient. For forming beams at different positions in the FoV of the PAF system, the above procedure is repeated by moving the telescope and positioning the source appropriately.

We define the performance metric as the inverse of the maximum S/N when observing a compact astronomical source (Warnick & Jeffs 2008). As shown below, this inverse S/N can be expressed in terms of ${T}_{\mathrm{sys}}/\eta$ if the flux density of the source is known, and it can be directly obtained from the observations of a compact source without making any assumptions. This metric is useful to compare the performance of different PAFs. A nearby off-source position needs to be observed to derive T_sys/η, and hence its value will depend on the diffuse foreground emission temperature at the off-source position. The measured value of ${\rm{S/N}}=\tfrac{{T}_{a}}{{T}_{\mathrm{sys}}}$ for the off-course system temperature T_sys and the excess antenna temperature

$$\begin{eqnarray}&&{T}_{a}=\displaystyle \frac{{SA}\eta }{2\,k}.\end{eqnarray} \tag{ 3 }$$

Here S is the flux density of the source, A is the physical area of the telescope aperture, k is Boltzmann's constant, and η is the product of the aperture efficiency of the telescope and radiation efficiency of the PAF. Substituting in Equation (3), we get

$$\begin{eqnarray}&&\displaystyle \frac{{T}_{\mathrm{sys}}}{\eta }=\displaystyle \frac{{SA}}{2\ k\ {{\rm{S/N}}}_{\max }},\end{eqnarray} \tag{ 4 }$$

where S/N_max is the maximum S/N. We use the flux densities of calibrator sources provided by Perley & Butler (2017). These flux densities are accurate to 3%–5%.

The receiver temperature of the PAF was measured at the outdoor test facility at the GBO. This facility is a small outdoor structure with a retractable roof facilitating hot- and cold-load measurements with the PAF receiver to obtain the receiver noise temperature by the Y-factor method (Warnick et al. 2010). The receiver is mounted with the dipoles facing up toward either an ambient temperature load (hot load) or the cold sky. A large aluminum cone, flaring upward from the edge of the dipole array, is attached to the receiver and functions to shield the dipoles from wide-angle ground radiation. To derive the Y factor, the array output voltage correlation ${{\boldsymbol{R}}}_{\mathrm{hot}}$ was measured with an absorber placed in front of the array, which forms an isotropic hot load at ambient temperature. A second correlation measurement, ${{\boldsymbol{R}}}_{\mathrm{cold}}$, was made by pointing the array to a region of sky away from the galactic plane, and this formed the cold load. In this case, the factor

$$\begin{eqnarray}&&Y=\displaystyle \frac{{{\boldsymbol{w}}}^{H}{{\boldsymbol{R}}}_{\mathrm{hot}}{\boldsymbol{w}}}{{{\boldsymbol{w}}}^{H}{{\boldsymbol{R}}}_{\mathrm{cold}}{\boldsymbol{w}}},\end{eqnarray} \tag{ 5 }$$

and the receiver temperature

$$\begin{eqnarray}&&{T}_{\mathrm{rec}}=\displaystyle \frac{{T}_{\mathrm{hot}}-{{YT}}_{\mathrm{cold}}}{Y-1},\end{eqnarray} \tag{ 6 }$$

where T_hot and T_cold are the temperatures of the hot load and cold sky, respectively, and ${\boldsymbol{w}}$ are the weights. The derived value of the receiver temperature depends on the weights, as seen from Equation (5). The cold-sky temperature is estimated from the sky brightness temperature distribution and typically has a value of ∼8 K (Delahaye et al. 2002). The hot-load temperature is 296.5 K. Despite the use of the conical ground shield, the cold-sky correlations were not devoid of contribution from ground-scattered radiation. From single-feed measurements using the outdoor test facility, it is estimated that a residual of ∼4 K can be present in the receiver temperature values due to this scattered radiation.

Figure 3(a) shows the measured receiver temperature ${T}_{\mathrm{dipole}}$ for each dipole. These temperatures are obtained using the Y factor derived from the output power of each dipole in the array. Thus, for example, T_dipole for dipole 1 is equivalent to using ${{\boldsymbol{w}}}^{T}\,=[1,0,0,\ldots ,0]$ (i.e., weight 1 for dipole one and 0 for all other dipoles) in Equation (5) and then estimating the temperature using Equation (6). This weighting scheme is applied for each dipole to get 38 T_dipole values (see Figure 3(a)). The ${T}_{\mathrm{dipole}}$ values range between 12 and 18 K near 1336 MHz. The missing value at dipole 13 in the Y polarization is due to a bad LNA on that channel. The median value of T_dipole versus frequency is shown in Figure 3(b). The minimum T_dipole is about 13.3 K near 1336 MHz.

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The measured T_dipole has contributions from ground scattering and mutual coupling between array elements. Since both of these contributions produce noise correlations at the output of the array, they can be canceled out to a large extent. This cancellation corresponds to the maximum Rayleigh quotient of Y, which will provide a minimum receiver temperature, T_rec,min. The weight vector that needs to be applied in Equation (5) to get the maximum Y is the eigenvector corresponding to the maximum eigenvalue of the matrix ${{\boldsymbol{R}}}_{\mathrm{cold}}^{-1}{{\boldsymbol{R}}}_{\mathrm{hot}}$. Figure 3(b) shows the T_rec,min obtained from X- and Y-polarization data separately. The measured LNA noise temperature, T_LNA, versus frequency is also shown in Figure 3(b). The minimum difference between the measured LNA noise temperature and T_rec,min is ∼2.5 K near 1350 MHz. We attribute this excess noise temperature to any residual correlated noise and to losses ahead of the LNA, which include (a) loss in the dipoles and balun, (b) loss in the thermal transition, and (c) connection losses. Thus, the measured excess noise temperature provides an upper limit to the losses ahead of the LNA (i.e., the loss in temperature should ≤2.5 K). In this paper, we assume that the losses ahead of the LNA are independent of the beam-former weights.

In 2017 March, the phased-array receiver was installed on the GBT. Extensive observations were made on a set of seven calibrator sources to measure the system performance. A list of observed calibrator sources, their J2000 coordinates, and the flux density at 1350 MHz are given in Table 1. A log summarizing the observations is given in Table 2. The observations can broadly be classified into two categories: (a) to measure the performance over the FoV and (b) to measure the boresight performance. The performance over the FoV was measured by observing on a grid of positions ("grid" observations) centered on the strong radio source Virgo A. The grid observation was made at 1336 MHz (bandwidth ∼300 kHz). The grid positions were separated by 3' in both the elevation and cross-elevation directions. On- and off-source measurements were made toward all calibrators in Table 1 to derive the boresight performance. The observed off-source positions have +1^o offset in R.A. and 0^o offset in decl. from the J2000 source positions. The measurements were made over a set of frequencies ranging from 1200 to 1500 MHz, each with a bandwidth of 300 kHz.

The grid observations are used to check the responses of individual dipoles. Figures 4 and 5 show the distribution of the S/N (as defined in Equation (2)) but for a single dipole) obtained on Virgo A from each of the 19 × 2 dipoles (i.e., without forming beams). The peak S/N for the central dipole was about 2.6. As noted earlier, dipole number 13 in the Y polarization was not functional. Dipole 14 in the Y polarization had a lower peak S/N compared to the central dipole by a factor of 2. This lower S/N is attributed to a faulty digital link. As discussed below, the two faulty dipoles have affected the results obtained from the Y-polarization data set.

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6.1. T_sys/$\eta$ over the FoV

A map of the T_sys/η is obtained from the grid observation data set by maximizing the S/N at each offset position. Figures 6(a) and (b) show the distribution of T_sys/η as a function of elevation and cross-elevation offsets. The distribution is fairly symmetric about the center for the X polarization. The asymmetry seen in the Y polarization toward the southwest side is due to faulty dipoles 13 and 14. The radial distributions (i.e., offset from the boresight) of the normalized T_sys/η for the X and Y polarizations are shown in Figures 7(a) and (b). Only data points for elevations ≳−3' from those shown in Figure 7(b) are used for making the radial distribution of the Y polarization. The half power beamwidth at 1336 MHz is ∼10'. The beam separation required for Nyquist sampling (i.e., λ/(2D), where λ is the wavelength of observation and D = 100 m is the diameter of the GBT aperture plane; Padman 1995) is ∼4'. The degradation in T_sys/η at this offset is ∼1%.

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The grid observations were used to examine the seven formed beam patterns. Figure 8(a) shows the boresight maximum S/N beam measured using Virgo A, and in Figure 8(b), a beam with 5' offset from the boresight is shown. The maximum S/N beams are smooth and approximately Gaussian for levels between 0 and −10 dB. All of the seven formed beams show similar properties.

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6.2. Boresight T_sys/$\eta$

Plots of the measured boresight T_sys/η versus frequency for the two polarizations are shown in Figures 9(a) and (b). The data presented in these plots are from observations toward sources with flux density <50 Jy. The weights for beam forming were derived by maximizing the S/N on the observed source itself. The best median T_sys/η for X polarization is 25.4 K at 1336 MHz, and the peak-to-peak spread in the values is ±2.5 K. The scatter in X-polarization values is due to a combination of (a) uncertainty in the flux densities of the sources, (b) variation in off-source sky contribution, and (c) telescope pointing offset. The 3σ thermal noise uncertainty in all of these measurements is ∼0.3 K. The median T_sys/η increases by ∼5 K near the edge of the 150 MHz bandwidth of interest, centered at 1350 MHz.

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The median T_sys/η of the Y polarization near 1336 MHz is 32.3 ± 5 K (peak-to-peak). To investigate the origin of the higher T_sys/η and the larger scatter of the Y-polarization measurement, we examine the observation toward 3C147 near 1336 MHz. The T_sys/η values derived from this data set are 25 and 36 K for the X and Y polarizations, respectively. The normalized weight distributions obtained from this data set are shown in Figures 10(a) and 10(b). As seen in the figure, the weight distributions are centered near dipole 5, which is due to an uncorrected telescope pointing offset. Since dipoles 13 and 14 in the Y polarization are faulty, the PAF is unable to form an optimum beam, and hence the T_sys/η for the Y polarization is higher. We examined the data sets from all calibrators in the frequency range 1300–1400 MHz and found that a subset of the observations have telescope pointing offsets close to zero, as inferred from the weight distribution (see Figure 11(a)). The derived T_sys/η values for this subset are similar for both polarizations and are between 25 and 28 K. The weight distribution for the subset with T_sys/η  > 30 K for the Y polarization is shown in Figure 11(b). As seen in the figure, the weight distribution is centered at dipole 5 for all of the data in this subset. We conclude that the larger scatter and higher T_sys/η for the Y polarization compared to the X polarization is due to the telescope pointing offset and the presence of the two faulty dipoles. The large telescope pointing offset is because the GBT did not have an accurate pointing model for the PAF receiver system while we were doing the measurements.

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The radio source Virgo A is the strongest calibrator source observed during the commissioning. The flux density of this source is 218.8 Jy at 1350 MHz. The best T_sys/η values measured on this source are 28 and 30 K for the X and Y polarizations, respectively. The 1σ noise is 0.3 K. These values are about 3–5 K higher than the median value obtained from sources with flux density <50 Jy. A possible cause of this higher T_sys/η is the noise contribution due to the source itself (Anantharamaiah et al. 1991), which may be affecting the beam-former weight solutions.

We compare the performance of the PAF with the existing cryogenic optimized single-feed 1.4 GHz receiver on the GBT, which has a T_sys/η ∼ 25.7 K.¹¹ Our measurements show that the performance of the PAF system is comparable to this single-feed receiver. Achieving comparable performance is a major milestone in the development of the PAF. Table 4 lists the T_sys/η values of multibeam receivers in other telescopes for comparison.

6.3. Survey Speed

The intrinsic survey capability per unit bandwidth of an astronomical receiver is found by evaluating the squared sensitivity integral given in (Hay & Bird 2015, Equation (83))

$$\begin{eqnarray}&&{\rm{SSFoM}}=\int {{ \mathcal S }}^{2}({\rm{\Omega }})\,d{\rm{\Omega }},\end{eqnarray} \tag{ 7 }$$

where the sensitivity map ${ \mathcal S }({\rm{\Omega }})$ is the receiver sensitivity as a function of sky angle Ω. By dividing the survey-speed figure of merit (SSFoM) by the peak sensitivity, the survey-speed weighted field of view (SSFoV) of the instrument can be found as

$$\begin{eqnarray}&&{\rm{SSFoV}}=\displaystyle \frac{1}{{{ \mathcal S }}_{\max }^{2}}\int {{ \mathcal S }}^{2}({\rm{\Omega }})\,d{\rm{\Omega }}.\end{eqnarray} \tag{ 8 }$$

The PAF sensitivity map is measured by steering the telescope to place a bright calibrator source at each position on a grid of closely spaced points in the sky, measuring the realized sensitivity of the receiver with the source at that location, and thereby sampling the sensitivity map at many discrete points. The integrals in SSFoM and SSFoV are approximated as sums over the sample points. These figures of merit are quite general and can be used to compare single-pixel receivers, cluster feeds, PAFs, and aperture arrays on an equal footing.

To remove the dependence of the FoV on dish size and obtain a dimensionless number that allows instruments with different aperture sizes to be compared more easily, the SSFoV is commonly expressed as a number of beams. The angular FoV is divided by the area of the sky per beam when fully sampled by independent, formed beams to obtain

$$\begin{eqnarray}&&{N}_{b}=\displaystyle \frac{{\rm{SSFoV}}}{{{\rm{\Omega }}}_{b}}=\displaystyle \frac{{\rm{SSFoM}}}{{{\rm{\Omega }}}_{b}\ {{ \mathcal S }}_{\max }^{2}}.\end{eqnarray} \tag{ 9 }$$

The amount of beam overlap required for full sampling, which determines the value of the area Ω_b per fully sampled beam, is treated in Hay & Bird (2015). While Equation (7) is the primary definition of SSFoM, the number of beams in Equation (9) is quite convenient and widely used in comparing various types of instruments.

6.3.1. Practical Survey Speed with Real-time Beam Forming

The FoV expressed as a number of independent beams N_b as in Equation (9) is generally not equal to the number of beams that are formed in signal processing. The above considerations apply to the intrinsic survey speed of the analog receiver front end. When the digital back end is included in the analysis, the survey speed of an instrument may be limited further in the signal processing when the receiver back end operates in real-time beam-forming mode. To reduce hardware costs, fewer beams than are required to fully sample the FoV may be formed. In this case, the practical survey speed of the instrument is lower than the intrinsic SSFoM in Equation (7).

In other cases, such as array receivers with signal-processing back ends that allow post-correlation beam forming, in certain observing modes, more beams may be formed than are required to fully sample the FoV. In this case, the number of formed beams is greater than N_b in Equation (9). If the formed beams overlap, there is a correlation between the signal and noise from beam to beam, and the information provided by the beams may not be independent.

In view of the complex relationship between the FoV expressed as a number of beams and the number of beams that are formed in digital signal processing, there are differences in the assumptions made in the reported number of beams from one instrument to another. Despite the ambiguity, FoV as number of beams is so convenient a metric, and so generally used in the community, that we accept the disadvantages of this way of parameterizing FoV and provide comparison values, while stating as carefully as possible the assumptions made in the calculation.

To analyze the practical survey speed with a given number of formed beams, we consider three observing cases, which are typical applications of a PAF system on a telescope.

• 1.  
  Survey observations that do not require averaging of data simultaneously obtained from the different beams. Examples for this observing case are searching for pulsars and H i observations of objects with angular size smaller than the FWHM beam size.
• 2.  
  Imaging a region of the sky with the PAF system. H i and continuum imaging of extended sources are examples for the second case. Performing such observations with the PAF in the on-the-fly (OTF) mode has some advantages, for example, to reduce the telescope pointing overhead. Averaging data obtained from different beams in an OTF observation can optimize the survey speed. However, the sky position needs to be aligned before averaging the images from the different beams, which makes the noise in each pixel of the images uncorrelated. This is demonstrated in Figure 12 using a 1D scan toward Virgo A obtained with FLAG.
• 3.  
  Some survey observations that require averaging of data simultaneously obtained from the different beams. An example of such case is imaging of H i emission from an extended source and then smoothing the image to obtain a low angular resolution (>FWHM beamwidth) spectrum. The noise correlation between beams will result in a spatial correlation of noise in the image, and hence the S/N will not improve by the square root of the number of pixels averaged. As discussed below, this class of observations will benefit by keeping the PAF beams at twice the Nyquist separation or more.

Survey-speed metrics for each of these observation cases will be given in the next section.

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6.3.2. Effective Number of Beams

In a PAF system, if a large number of highly overlapping beams were formed in signal processing, the beams would be highly correlated, and little new information could be gleaned from adjacent beams. This manifests as strong signal and noise correlation between beams. Further, the sensitivity of each formed beam will differ because of the correlation of receiver noise between elements in the PAF. Closely following the intrinsic number of beams defined by Equation (9), we develop in this section a figure of merit, in a practical sense, that measures the FoV of the PAF with a given number of formed beams: the effective number of beams.

Survey speed is determined by the time required to integrate an image such that the sensitivity in each pixel is higher than some desired sensitivity. We consider surveying a region of the sky of angular size Ω_s sampled at Ω_b, the independently sampled beam area in Equation (9). The number of pointings that need to be made for such an observation is Ω_s/Ω_b. Imaging speed can be improved with a multibeam system by moving the telescope so that the region of interest is observed in each beam and then averaging the images obtained from different beams. As discussed above, for observing cases 1 and 2, the noise correlation between the beams does not affect the net sensitivity of the averaged image. However, the sensitivities of the beams are different and need to be taken into account in the survey-speed calculation. The effective number of beams for such applications is defined as

$$\begin{eqnarray}&&{N}_{\mathrm{effb}}=\displaystyle \frac{1}{{\left(\tfrac{A\ \eta }{{T}_{\mathrm{sys}}}\right)}_{\max }^{2}}\displaystyle \sum _{n=1}^{{N}_{\mathrm{beam}}}{\left(\displaystyle \frac{A{\eta }_{n}}{{T}_{\mathrm{sys},n}}\right)}^{2},\end{eqnarray} \tag{ 10 }$$

where A is the physical area of the telescope, $\tfrac{A\ {\eta }_{n}}{{T}_{\mathrm{sys},n}}$ is the ratio of the effective area of the telescope to the system temperature for beam n, and ${\left(\tfrac{A\eta }{{T}_{\mathrm{sys}}}\right)}_{\max }$ is the maximum value of $\tfrac{A\ {\eta }_{n}}{{T}_{\mathrm{sys},n}}$. The SSFoM is

$$\begin{eqnarray}&&\mathrm{SSFoM}\approx {N}_{\mathrm{effb}}\ {\left(\displaystyle \frac{A\ \eta }{{T}_{\mathrm{sys}}}\right)}_{\max }^{2}{({\theta }_{b})}^{2},\end{eqnarray} \tag{ 11 }$$

where θ_b is the square root of the independent beam area, which, from the treatment of Hay & Bird (2015), is λ/(2D).

For observing case 3, we must first determine the beam-to-beam noise correlation, as represented in the fluctuations in the estimated power at the output of a formed PAF beam. We estimate the correlation coefficient as

$$\begin{eqnarray}&&{\rho }_{n,m}=\displaystyle \frac{\langle ({P}_{{B}_{n}}-{\overline{P}}_{{B}_{n}})({P}_{{B}_{m}}-{\overline{P}}_{{B}_{m}})\rangle }{\sqrt{\langle {({P}_{{B}_{n}}-{\overline{P}}_{{B}_{n}})}^{2}\rangle \langle {({P}_{{B}_{m}}-{\overline{P}}_{{B}_{m}})}^{2}\rangle }}.\end{eqnarray} \tag{ 12 }$$

Here

$$\begin{eqnarray}&&{P}_{{B}_{n}}={P}_{{B}_{n}}[j]={{\boldsymbol{w}}}_{{\boldsymbol{n}}}^{H}{\boldsymbol{R}}[j]{{\boldsymbol{w}}}_{{\boldsymbol{n}}},\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&{P}_{{B}_{m}}={P}_{{B}_{m}}[j]={{\boldsymbol{w}}}_{{\boldsymbol{m}}}^{H}{\boldsymbol{R}}[j]{{\boldsymbol{w}}}_{{\boldsymbol{m}}},\end{eqnarray} \tag{ 14 }$$

are the time series of the power from beams n and m, respectively, estimated from the time series of the correlation matrices ${\boldsymbol{R}}[j]$ after multiplying it with the beam-former weights ${{\boldsymbol{w}}}_{n}$ and ${{\boldsymbol{w}}}_{m}$ for the two beams. The expectations of ${P}_{{B}_{n}}$ and ${P}_{{B}_{m}}$ are obtained as

$$\begin{eqnarray}&&{\overline{P}}_{{B}_{n}}=\displaystyle \frac{1}{M}\displaystyle \sum _{j=0}^{M-1}{P}_{{B}_{n}}[j],\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&{\overline{P}}_{{B}_{m}}=\displaystyle \frac{1}{M}\displaystyle \sum _{j=0}^{M-1}{P}_{{B}_{m}}[j].\end{eqnarray} \tag{ 16 }$$

The angle brackets in Equation (12) indicate time average over M samples. A plot of the calculated noise correlation between the boresight and off-boresight beams of FLAG as a function of beam separation is shown in Figure 13. The noise correlation is obtained from the off-source data. The correlation drops by about 60% at the Nyquist beam separation (∼4'), and it drops to ∼15% at twice the Nyquist beam separation.

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The beam-to-beam noise correlation will result in a spatial correlation of noise in the image made with a PAF. For a given beam spacing, the spatial correlation coefficient of the noise in the image will be same as that given by Equation (12), even though the correlation coefficient is obtained by time average (the underlying stochastic process is ergodic in nature). A lower angular resolution image needs to be made for the third class of applications, but the S/N of the image will not improve by the square root of the number of pixels averaged during smoothing. The improvement in S/N depends on the angular resolution to which the image is smoothed. For the specific case when the image is smoothed to an angular resolution approximately equal to SSFoV (see Equation (8)), the final noise variance is

$$\begin{eqnarray}&&{\sigma }^{2}=\displaystyle \frac{1}{{N}_{\mathrm{beam}}^{2}}\displaystyle \sum _{m,n=1}^{{N}_{\mathrm{beam}}}{\sigma }_{m}{\sigma }_{n}{\rho }_{n,m},\end{eqnarray} \tag{ 17 }$$

where σ_m and σ_n are the rms noise fluctuations in beams m and n, respectively, and ρ_{n, m} is the correlation coefficient of the noise in beams m and n (see Equation (12)) for the beam spacing used for the survey. The survey speed is inversely proportional to this noise variance. Approximating the sensitivity of the beams as equal and factoring the resulting survey speed as in Equation (9) leads to the effective number of beams,

$$\begin{eqnarray}&&{N}_{\mathrm{effb}}={N}_{\mathrm{beam}}{\left(\displaystyle \frac{1}{{N}_{\mathrm{beam}}}\displaystyle \sum _{m,n=1}^{{N}_{\mathrm{beam}}}{\rho }_{n,m}\right)}^{-1}.\end{eqnarray} \tag{ 18 }$$

If the correlation ρ_n,m vanishes for $n\ne m$ (i.e., the noise is uncorrelated between beams), the number of effective beams is equal to the number of formed beams, as expected. Thus, the third class of observing application will benefit by keeping the beams at twice the Nyquist separation or more, since ρ_n,m is smaller for larger beam spacing (see Figure 13).

6.3.3. Survey-speed Comparisons

The SSFoMs of FLAG, obtained using Equation (11), with seven beams spaced at Nyquist separation (∼4') and twice Nyquist separation (∼8'), are listed in Table 3. A major use of the new PAF system on the GBT will be to observe extended H i emission from nearby galaxies. These observations will be typically done in the OTF mode and fall into the first and second category of observations mentioned above. The T_sys/η of FLAG is optimum near 1350 MHz, and it degrades by a factor of ∼1.1 near 1.42 GHz. Thus, the SSFoMs for H i observations are 2184 and 1640 deg² m⁴ K⁻² for the two beam separations (see Table 3), which are a factor of 5.3 and 4 higher than those of the GBT single-feed receiver. A comparison of the SSFoM of FLAG, the existing GBT single-feed receiver, and our estimated values for multibeam receivers at other telescopes is given in Table 4. We computed the intrinsic SSFoM (see Equation (7)) of FLAG using the data shown in Figure 6(a), which is about 10,690 deg² m⁴ K⁻². The derived SSFoV using Equation (8) shows that about 25 beams need to be formed in the signal-processing back end to obtain the full survey capability of FLAG (see Table 4).

Table 3.  Survey Speed of FLAG^a

Receiver	θbb	Tsys/ηc	Neffbd	SSFoM	Notes
System	(arcmin)	(K)		(deg2 m4 K−2)
FLAG (Nyquist)	4	25.4, 25.7	6.9	2924	1
FLAG (2 × Nyquist)	4	25.4, 30.5	5.2	2195	2
FLAG (Hi, Nyquist)	3.8	28.0, 28.3	6.9	2184	3
FLAG (HI, 2 × Nyquist)	3.8	28.0, 33.5	5.2	1640	4

Notes.

^aThe physical area of the GBT aperture is taken as 7854 m² for the calculation of SSFoM using Equation (11). ^b ${\theta }_{b}=\tfrac{\lambda }{2\ D}$ is taken as the Nyquist beam separation. ^cT_sys/η for the central beam and six outer beams. ^dN_effb is computed using Equation (10).

References. 1. Spectroscopic observations near 1350 MHz with Nyquist (∼4') beam separation. 2. Spectroscopic observations near 1350 MHz with twice Nyquist (∼8') beam separation. 3. H i observations near 1420 MHz with Nyquist (∼4') beam separation. 4. H i observations near 1420 MHz with twice Nyquist (∼8') beam separation.

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Table 4.  Survey-speed Comparison

Receiver	A	Freq.	θba	Tsys/ηb	Neffb	SSFoMc	BWd	SSFoM × BW	Notes/Ref.
System	(m2)	(GHz)	(arcmin)	(K)		(deg2 m4 K−2)	(MHz)	(deg2 m4 K−2 MHz)
FLAG (Nyquist)	7854	1.35	4	25.4, 25.7	6.9	2924	150	3.6 × 105	1e
FLAG	7854	1.35	4	25.4	∼25	10690	150	1.6 × 106	1f
GBT L-band	7854	1.35	4	25.7	1.0	415	400	1.7 × 105	2
Parkes multibeam	3217	1.37	5.9	41.9	13	1010	300	3.0 × 105	3g
Arecibo ALFA	35633	1.37	1.8	35.2, 45.5	4.6	4228	300	1.3 × 106	4h
Effelsberg 7beam	7854	1.41	3.7	45.8	7	782	300	2.3 × 105	5i
Parkes with PAF	3217	1.31	5.9	60.0	∼144	4025	700	2.8 × 106	6j

Notes.

^a ${\theta }_{b}=\tfrac{\lambda }{2\ D}$ is taken as the Nyquist beam separation for all telescopes. ^bT_sys/η values are provided for the central beam and all outer beams for cases where two values are listed. ^cSurvey metric for spectroscopic observations. ^dReal-time signal-processing bandwidth. ^eFLAG with seven formed beams placed at Nyquist (∼4') beam separation. ^fIntrinsic SSFoM (see Equation (7)) of FLAG obtained using the data shown in Figure 6(a). The SSFoV = 0.11 deg²; ${N}_{\mathrm{effb}}\sim \tfrac{\mathrm{SSFoV}}{{\theta }_{b}^{2}}=25$. ^gHere 1.1 Jy K⁻¹ is used for the calculation of SSFoM. ^hThe region illuminated by ALFA is taken as ∼213 m in diameter. Here 11 K Jy⁻¹ for the central beam and 8.5 K Jy⁻¹ for the outer beams are used for the calculation of SSFoM. ⁱAperture efficiency of 48% used for the calculation of SSFoM. ^jThe SSFoM at 1.31 GHz is obtained as SSFoV × ${{ \mathcal S }}_{\max }^{2},$ where SSFoV = 1.4 deg² and ${{ \mathcal S }}_{\max }=3217/60=53.6$ m² K⁻¹. Here ${N}_{\mathrm{effb}}\sim \tfrac{\mathrm{SSFoV}}{{\theta }_{b}^{2}}=144$. The real-time processing bandwidth is assumed to be the same as the front-end bandwidth of ∼700 MHz.

References. 1. This paper. 2. https://science.nrao.edu/facilities/gbt/proposing/GBTpg.pdf. 3. http://www.naic.edu/alfa/gen_info/info_obs.shtml. 4. http://www.naic.edu/alfa/gen_info/info_obs.shtml. 5. https://eff100mwiki.mpifr-bonn.mpg.de/doku.php?id=information_for_astronomers:rx:p217mm. 6. Chippendale et al. (2016).

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For broadband observations (for example, pulsar observations), the survey capability of an instrument scales with the signal-processing bandwidth. The real-time beam-former back end for FLAG will have a bandwidth of about 150 MHz. The mean value of T_sys/η for the seven beams over this bandwidth is about 28 K for Nyquist beam separation. The SSFoM scaled by bandwidth is 3.6 × 10⁵ deg² m⁴ K⁻² MHz. For the GBT single-feed L-band system, the usable bandwidth is about 400 MHz (after removing the RFI-effected bands). Assuming a constant T_sys/η over the 400 MHz bandwidth of the GBT, the survey speed of the single-feed system is 1.7 × 10⁵ deg² m⁴ K⁻² MHz. The SSFoM bandwidth product of FLAG is about 2.1 times larger than that of the GBT single-feed system for pulsar or other broadband applications.

6.4. Comparison with the PAF Model, System Parameters, and FoV

For high-sensitivity receivers, further reductions in system noise become increasingly challenging as system performance improves. This is especially true for phased-array receivers, for which mutual coupling effects require a holistic approach to the design optimization of the array elements and front-end electronics. Extensive modeling efforts were critical to the PAF design optimization and understanding the system performance (Warnick et al. 2011, 2009; Roshi & Fisher 2016). The steps involved in the modeling are the following (Roshi & Fisher 2016). The dipole array was first modeled using a full-wave finite-element solver in the CST microwave studio¹² to obtain the element beam patterns and impedance matrix. The embedded beam patterns are then obtained from the element patterns. The secondary radiation patterns for the GBT optical geometry were obtained using a physical optics approximation. The embedded patterns, along with the GBT geometry, were used to compute the noise covariance matrices due to ground spillover. The secondary patterns were used to compute the signal response due to the source and noise covariances due to the sky background radiation. The impedance matrix of the array combined with a noise model for the cryogenic LNAs (Pospieszalski 2010) provided the receiver noise covariance. The amplifier noise parameters used for the modeling are minimum receiver temperature T_min = 4.2 K, optimum impedance Z_opt = 28.9–j3.5 Ω, and Lange parameter N = 0.007. The noise parameters are considered to be approximately constant over the frequency range 1200–1550 MHz. This LNA noise model is obtained from the amplifier modeling and reproduces the measured LNA noise temperature; however, we note that these parameters cannot be uniquely constrained from noise temperature measurements alone. Accurate noise modeling of the LNA and the measurement of noise parameters are underway; the PAF model results with these new values will be presented elsewhere. The signal response and noise covariances were used to compute the expected S/N. The maximum S/N beam-former algorithm was then used to find beam-former coefficients for each desired beam steering direction. The model was run repeatedly for a set of frequencies ranging from 1200 to 1550 MHz. With the accurate representation of the PAF by input parameters, the model can predict the receiver temperature, antenna temperature, spillover temperature, and full polarization electromagnetic fields in the antenna aperture. Below, we compare the measured system performance with PAF model predictions.

The PAF model prediction for the boresight direction is shown in Figure 14, along with the measured median T_sys/η as a function of frequency.¹³ The median values were computed from the measured data points shown in Figure 9 over a frequency interval of ∼1.5 MHz. The median values for the Y polarization were computed from the subset of measured values that is not severely affected by the pointing offset and faulty dipoles (see Section 6.2). The model results are plotted with an additional noise contribution to T_sys to account for the losses ahead of the LNA. For the LNA noise parameters used here, model results with an additional noise of 2.5 K (see Figure 3(b)) are in qualitative agreement with the measurements at frequencies below 1.45 GHz. The discrepancy between model and measurement at frequencies above 1.45 GHz may be due to a combination of the following factors: inaccuracy in the amplifier noise parameters, error in the electromagnetic simulation, unmodeled ground scattering due to the feed support structure, or manufacturing errors in the dipoles. Ground scattering from the feed support may have additional contributions at higher frequencies where the increase in system temperature is dominated by the presence of array grating lobes. These possibilities are the subject of an ongoing investigation.

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The model prediction for T_sys/η versus offset from the boresight is shown in Figure 7. The model results, obtained with the 2.5 K excess noise due to the losses upstream of the LNA (see Figure 3(b)), tracks closely with the measured variation of T_sys/η as a function of the radial offset very well. The increase in T_sys/η for offsets larger than 5' is due to the finite size of the dipole array. This is evident from Figure 15, where we plot the normalized beam-former weight distribution over the dipole-array geometry for the boresight beam and a beam ∼5' offset from the boresight direction. These weight distributions are obtained from grid observation data toward Virgo A. As seen in the figure, significant amplitudes for the weights are clustered around seven dipole elements, roughly following the Airy pattern due to the compact source. At offsets ≳5', the cluster of seven elements is located at the edge of the array centered on dipole 5 (see Figure 16(b)). Thus, at offsets more than 5' from the boresight, the dipole array does not have enough elements to sample the Airy pattern well. Thus, the FoV limitation of the array indicated by the upward slope of T_sys/η in Figure 7 is caused only by the limited extent of the array, and thus could be extended by the addition of more elements.

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On-telescope measurements do not provide T_sys and η separately, and so we infer these values and other system parameters from the PAF model. The inferred system parameters are summarized in Table 5. The system temperature after forming the beams is about 16 K, with contributions from receiver noise of 7.5 K, spillover of 3.5 K, and sky background plus atmosphere of 5.5 K. The median increase in formed beam S/N on a compact source is about a factor of eight compared to a single dipole near 1336 MHz. This increase in S/N implies a T_sys/η of ∼216 K for the single-dipole case, based on scaling the measured T_sys/η for the formed beam (see Table 5). This high T_sys/η is due to the large spillover contribution when observing with a single dipole. The inferred spillover temperature from the model is ∼100 K for the single-dipole case. The spillover efficiency is increased to about 98% in the process of beam forming, thus reducing the modeled T_sys/η to about 27 K for the formed beam. The high ground suppression achieved for the formed beam results in a somewhat lower aperture efficiency (about 60%) compared to the GBT single-feed system, an inevitable trade-off for the 19-element prime-focus PAF.

Table 5.  System Parameters

Parameter	Value
Measured Parameters
Tsys/η near 1350 MHz	25.4 ± 2.5 K
LNA noise temperature	5 K
Inferred loss ahead of LNAa	2.5 K
Cosmic microwave background temperature	2.7 K
Galactic background temperatureb	0.8 K
Estimated Parameters
Atmospheric temperaturec	2 K
Inferred from Model
Beam-formed receiver temperature	7.5 K
Spillover temperature	3.5 K
Total system temperature	16.5 K
Estimated spillover efficiency	98.8%
Estimated aperture efficiency	60%
Model Tsys/η near 1350 MHz	27.5 Kd

Notes.

^aModel results with an additional noise of 2.5 K to account for losses ahead of the LNA (see Figure 3(b)) are in qualitative agreement with the measurements for the amplifier noise parameters used here. ^bMedian of the off-source sky temperature estimated from the 1.4 GHz survey data of Reich & Reich (1986). ^cDelahaye et al. (2002). ^dThe uncertainty in the model value is up to 20% (see text).

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The uncertainties in the model predictions have several contributions, which include (a) amplifier noise parameters and their frequency dependence, (b) accuracy of the CST simulation results, and (c) the model not accounting for the scattering due to feed support structures. The estimated values of T_sys/η at frequencies below ∼1300 MHz sensitively depend on the amplifier noise parameters due to a higher level of mutual coupling in the array. At frequencies above ∼1450 MHz, the grating lobes become significant; hence, the scattering due to the feed support structure could limit the accuracy of the computation. In the frequency range near 1350 MHz, we estimate that the model predictions are accurate to within 20%. This estimation of accuracy is obtained by considering different amplifier noise parameters that are consistent with the LNA noise temperature measurements and examining the variation of the computed T_sys/η near 1350 MHz.

We have observed the pulsar B0329+54 and the Rosette Nebula with the PAF system on the GBT. The data taken toward these sources were obtained using the experimental setup described in Section 2 and processed as described in Section 3.

7.1. PSR B0329+54

The pulsar B0329+54 was observed with the PAF receiver on 2017 March 16. The observed frequency was 1336.0275 MHz with a bandwidth of  300 kHz. The pulse width of B0329+54 at 10% of the peak average pulsar amplitude is 31.4 ms (Manchester et al. 2005). Therefore, the cross-correlations were integrated for about 10 ms. An on-off observation on the calibrator 3C123 was performed before taking the pulsar data in the same observing setup. The data set on the calibrator was used to obtain the beam-former weights. A time series from the pulsar data was then obtained by estimating the power using the beam-former weights for every 10 ms. This power was converted into flux density units using the calibration factor derived from the 3C123 observations. The calibrated, beam-formed time series from the X-polarization data is shown in Figure 16(a) (bottom line). For comparison, the time series obtained from the central dipole is also shown in Figure 16(a) (top line). The improvement in S/N in the formed beam output is about a factor of 8, similar to what is measured from observations of calibrator sources. This indicates that the transfer of beam-former weights from calibrator observations gives the expected improvement in S/N on the target source.

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7.2. Rosette Nebula

We presented the measured performance of the FLAG front end, a new 1.4 GHz, 19-element, dual-polarization, cryogenic PAF radio astronomy receiver built for the GBT. A brief description of the instrumentation was given, which included a novel method of implementing an unformatted digital link. The performance of the system was measured by placing the PAF at the prime focus of the GBT and observing a set of astronomical calibrators. The performance metric, T_sys/η, had a median value of 25.4 ± 2.5 K near 1350 MHz. This value is comparable to the performance of the single-feed system of the GBT at 1.4 GHz. The median ${T}_{\mathrm{sys}}/\eta$ was higher by about 5 K near the edge of the 150 MHz bandwidth of interest, centered at 1350 MHz. The increase in ${T}_{\mathrm{sys}}/\eta$ at 1336 MHz at ∼4' offset, required for Nyquist sampling, was ∼1%, and at ∼8' offset, it was ∼20%. The distribution of T_sys/η in the elevation and cross-elevation directions was radially symmetric. This symmetry enables the PAF to form seven high-sensitivity beams within the FoV, resulting in an increase in survey speed by a factor between 2.1 and 7, depending on the observing application. The FoV of the PAF system is limited by the size of the array, as there are not enough elements to form a high-sensitivity beam for offset angles ≳5'. The PAF model predictions qualitatively agree with the measured variation of T_sys/η with frequency as well as offset from boresight. The results from the observations of a pulsar and an extended source with the PAF system on the GBT are also presented.

The results presented here were processed by a narrowband off-line processing system. Future observations will use a new real-time 150 MHz bandwidth digital signal-processing system developed by the FLAG collaboration. The PAF and the broadband beam former comprise the complete FLAG instrumentation, which will enable efficient searches for pulsars and FRBs and observations of diffuse extended neutral hydrogen emission in the circumgalactic medium of nearby galaxies.

The authors would like to thank Sivasankaran Srikanth, Marian Pospieszalski, Anthony Kerr, Morgan Mcleod, Bob Dickman, Shing Kuo Pan, Brent Carlson, Bill Randolph, Mike Shannon, Gerry Petencin, Kamaljeet Saini, Greg Morris, and Nicole Thisdell of the National Radio Astronomy Observatory and Karen O'Neil, Joe Brandt, Dennis Egan, Mike Hedrick, Pat Schaffner, Roger Dickenson, Bob Anderson, Ron Maddalena, and Jonah Bauserman of the Green Bank Observatory. Thanks to Lewis Ball and Brian Mason of NRAO for review of a previous version of the text. We thank the anonymous referee for the critical comments on the manuscript, particularly on the noise correlation between the PAF beams and its effect on the survey speed.