Study on Beam Forming and Interference Mitigation in Wide-Field Radio Astronomy, Notas de aula de Engenharia Elétrica

Baixe Study on Beam Forming and Interference Mitigation in Wide-Field Radio Astronomy e outras Notas de aula em PDF para Engenharia Elétrica, somente na Docsity! ar X iv :0 91 2. 02 04 v1 [ as tr o- ph .I M ] 1 D ec 2 00 9 Phased Array Feed Calibration, Beamforming and Imaging Jonathan Landon, Michael Elmer, Jacob Waldron, David Jones, Alan Stemmons, Brian D. Jeffs, Karl F. Warnick Department of Electrical and Computer Engineering Brigham Young University 459 Clyde Building, Provo, UT 84602, USA J. Richard Fisher National Radio Astronomy Observatory1 Charlottesville, VA, USA Roger D. Norrod National Radio Astronomy Observatory1 Green Bank, WV, USA ABSTRACT Phased array feeds (PAFs) for reflector antennas offer the potential for increased reflector field of view and faster survey speeds. To address some of the development challenges that remain for scientifically useful PAFs, including calibration and beamforming algorithms, sensitivity optimization, and demonstra- tion of wide field of view imaging, we report experimental results from a 19 element room temperature L-band PAF mounted on the Green Bank 20-Meter Telescope. Formed beams achieved an aperture ef- ficiency of 69% and system noise temperature of 66 K. Radio camera images of several sky regions are presented. We investigate the noise performance and sensitivity of the system as a function of elevation angle with statistically optimal beamforming and demonstrate cancelation of radio frequency interference sources with adaptive spatial filtering. 1. Introduction The generation of radio astronomy instruments now coming on line will fill much of the observational parameter space—frequency coverage, instantaneous bandwidth, system noise temperature, angular resolu- tion, and time and frequency resolution. The two re- maining open-ended parameters where fundamentally new science will be explored are collecting area and field of view. More collecting area will allow us to ob- serve known phenomena much deeper in the universe, and greater fields of view open the possibility of find- ing new phenomena, such as transient radio sources 1The NRAO is operated for the National Science Foundation (NSF) by Associated Universities, Inc. (AUI) under a cooperative agreement. and rare types of pulsars, by making large-area sky surveys much more efficient. Several major instru- ment development projects are underway worldwide to develop radio cameras, variously referred to as ac- tive, phased, beamforming, or smart arrays to distin- guish them from the more conventional independent- pixel feed-horn arrays which sample less than 1/16th of the available sky area within the array’s field-of- view. These instruments will utilize focal plane phased array feeds (PAF) which can electronically synthe- size multiple, simultaneous far field beams for com- plete coverage of the field of view without loss of sensitivity in each beam. PAFs are in development or in planning stages for single dish instruments in- cluding the Green Bank Telescope (GBT) as well as the Westerbork Synthesis Radio Telescope (WSRT) 1 (Verheijen et al. 2008) and the Australian Square Kilo- meter Array (ASKAP) Pathfinder synthesis imaging array (S. G. Hay et al. 2007). As the cost of signal processing for beam-forming and the correlation of multiple beams in aperture syn- thesis arrays allows, wider fields of view for SKA and its predecessors will open up new science, such as sur- veys of neutral hydrogen at high redshifts to study the evolutionary history of the universe. First science that will be enabled by PAFs with modest signal processing bandwidths include observations of the trajectories and abundance of high-velocity HI clouds interacting with the disk of the Milky Way (Wakker & van Woerden 1997; Putman 2006; Lockman et al. 2008), surveys of gas clouds outside other galaxies covering large ar- eas (D. A. Thilker et al. 2004; Braun & Thilker 2004; M. Grossi et al. 2008), and studies of the kinematics of extended HI clouds contained by galactic groups (S. Borthakur et al. 2008; Braun & Thilker 2004; et al. 2008a). These types of observations are time consum- ing with single-pixel instruments and could be con- ducted more rapidly and to greater depth using a PAF with wide field of view. Demand for use of the GBT to study the inner parts of the Milky Way disk is extremely high. Wider fields of view would enable additional studies of the galac- tic center and objects such as the physical conditions and structure of the recently discovered “far” coun- terpart to the 3-kpc arm (Dame & Thaddeus 2008). A PAF on the GBT would be of immediate use in analyzing the complex chemistry and relationship to dust evolution of the diffuse interstellar medium us- ing 18cm emission from OH, and in understanding the medium to minimize the effect of foreground mat- ter on cosmological investigations (Black & Dalgarno 1977; Gilmon & Shull 2006; Liszt & Lucas 1996; et al. 2008b). As compared to single-pixel instruments, PAF beam formation requires a substantial amount of sig- nal processing for array calibration, operational beam- forming, and image formation. Calibration and beam- forming algorithms and performance criteria for ar- ray feeds were surveyed by Jeffs et al. (2008b). Ra- dio frequency interference (RFI) mitigation using adaptive nulling algorithms was demonstrated by Nagel et al. (2007). Other recent results demonstrat- ing feasibility of PAF-based interference mitigation in astronomical applications include (Jeffs & Warnick 2008, 2007; Jeffs et al. 2008b; Landon et al. 2008a,b; Warnick et al. 2007). Fig. 1.— 19 element single polarized PAF and front end box containing analog downconverters and re- ceiver front ends, mounted on on Green Bank 20- Meter Telescope (October, 2007). In this paper, we present results from an L-band prototype PAF on the Green Bank 20-Meter Tele- scope. Early radio camera images obtained with the PAF were reported by Warnick et al. (2008). A more detailed study of performance metrics including sensi- tivity and system noise are given here. A major con- cern with PAF development has been optimizing the interface between the array and front end receiver elec- tronics (Warnick & Jensen 2007; Ivashina et al. 2008). Due to mutual coupling between array antenna ele- ments, standard impedance matching techniques used for single-port antennas must be extended to multi- port systems using the theory of active impedances (E. E. M. Woestenburg 2005; Warnick et al. 2009b). The performance improvement that could be realized using these methods are explored. PAFs offer the potential for optimizing beam pat- terns to improve sensitivity as the noise environment changes or to maximize system performance for a given type of observation. We study the dependence of sensitivity and efficiency of formed beams on the reflector tipping angle as sky noise increases near the horizon. Results of RFI mitigation experiments are also shown, in order to demonstrate the potential for operational use of RFI nulling algorithms in observa- tions. These results are strong evidence for the feasi- bility of a high sensitivity, wide field of view PAF. 2. Experiment Description The characterization techniques, calibration meth- ods, and beamforming algorithms used in the reported 2 these cases superscript (j) will be dropped for sim- plicity when this does not lead to an ambiguous inter- pretation. 3.2. Calibration Since multiple simultaneous beams are formed with a PAF as shown in Fig. 4, a calibration for the sig- nal array response vector ai must be performed for each direction, Ωi, corresponding to each formed beam’s boresight direction, and any additional direc- tions where point constraints in the beam pattern re- sponse will be placed. Periodic re-calibration may be necessary due to strict beam pattern stability require- ments, to correct for differential electronic phase and gain drift, and to characterize changes in receiver noise temperatures. We proposed a calibration procedure in (Jeffs et al. 2008b), which is improved here with a lower error, noise whitening approach in step 3. Calibration Procedure: 1. Noise covariance, R̆n: Steer the dish to a rela- tively empty patch of sky so x[n] ≈ n[n], and collect a long term (large L, e.g. 10 minutes) sample covariance estimate for the noise field R̆n using (4). 2. Signal-plus-noise covariances, R̆i: While track- ing the brightest available calibration point source, steer the dish to calibration angle Ωi (relative to this source). The observed signal model is x[n] = ais[n] + n[n], where ai is the desired calibration vector at direction Ωi. Cal- culate R̆i using (4) and the same L as in step 1. 3. Array response, ăi: Compute ăi = R̆numax, where umax is the dominant solution to the gen- eralized eigenequation R̆iumax = λmaxR̆numax. This noise-whitening method produces a lower variance estimate with less bias arising from correlated noise in Rn (caused by inter-element mutual coupling) than does the method of Jeffs et al. (2008b). 4. SOI covariance, R̆s,i: Compute R̆s,i = λmaxăiăHi . 5. Form calibration grid: Repeat steps 2–4 in a grid pattern corresponding to the desired dis- tribution of beam centers and constraint points, e.g. for spherical angles {Ωi | 1 ≤ i ≤ K}. 3.3. Beamformer Design In order to form beams with a PAF, a design proce- dure is required to obtain a set of beamformer weight vectors w(j)i , from which the output for the ith beam is computed as yi[n] = w (j) H i x[n], 0 ≤ i ≤ K, j = ⌊ n L ⌋ (5) A distinct beamformer weight vector w(j)i is used for each main lobe steering angle Ωi. For beamformer weights that are fixed during each STI, the dependence on the STI index j can be dropped. In a practical PAF observing scenario the beams are steered in a rectan- gular or hexagonal grid pattern with crossover points at the -1 to -3 dB levels. Proper design of a set of beamformer weights wi allows one to steer the main beams, control beam shape and sidelobe levels, opti- mize sensitivity, and direct placement of nulls towards interferers. A thorough introduction to array signal processing and beamformer design can be found in (Van Veen & Buckley 1988; Van Trees 2002). In general, beamformer weights can be designed us- ing an a priori electrical model for the array, character- ization data measured before installation of the array, or in situ calibration data obtained with a procedure such as that outlined in the previous section. As will be argued below, only the latter of these beamformer design procedures is likely to be viable for astronomi- cal PAFs. Relative to phased arrays for wireless, communi- cations, radar, sonar, and other applications, an im- portant distinguishing characteristic of astronomical PAF beamforming is that given the current state of the art the instrument performance with data independent pre-computed beamformer weights is inadequate. For simulation studies, the conjugate field match beam- former has been commonly used to obtain beamformer weights, but the only demonstrated experimental ra- dio camera images formed to date use statistically optimal, adaptive, data dependent beamforming al- gorithms (Verheijen et al. 2008; Oosterloo et al. 2008; Jeffs et al. 2008a; Warnick et al. 2008; Jeffs et al. 2009). The primary reason for this is that the perturbations in array element patterns, complex receiver gains, and ca- ble phase lengths that occur when the array is mounted on the reflector mean that numerical models or antenna range characterization are not accurate enough to al- low precomputation of beamformer weights for high sensitivity or controlled pattern shapes. 5 In applications with less stringent sensitivity and stability requirements, it is possible to design 2-D array beamformers deterministically to match some fixed array response criterion. A number of classical methods are used, including windowed beamforming and numerical response optimization over a dense grid of far field sample points (Van Veen & Buckley 1988; Van Trees 2002). It has been shown in simulation that using dense calibration response and numerical opti- mization it is possible to design well behaved astro- nomical PAF beam shapes with little coma, distortion, or polarization rotation as beams are steered off-axis (Willis 2009). All such methods require an accurately calibrated array (by antenna range measurements or mathematical modeling) over the entire response field of interest. With astronomical PAF instruments it is not possi- ble a priori to obtain the full-sphere calibration data required to design beamformer weights for a given re- sponse criterion. Antenna range measurements of the bare PAF element response patterns do not account for such effects as interactions with support structures. Numerical modeling of the array and dish combina- tion provides an excellent qualitative match, but our studies of precomputed beamformer weights indicate that modeled results differ sufficiently in fine phase and gain detail over the field of view. Thus beam- former weights designed using numerical electromag- netic simulations lead to on-dish real data beamformer results with lowered sensitivity and beampatterns that deviate significantly from the desired shape. Detailed modeling of the array elements, back- plane, array structure, and dish reflector system can provide excellent qualitative match and prediction of achievable real-world performance when used to compute beampatterns in simulation. The fine detail mismatch though precludes use of these beamformer weight designs directly on the real system. We specu- late that the discrepancies are in subtle fine scale dif- ferences between physical geometry and the model. The simulations can predict how an array and dish of this design will perform, but cannot match the exact phase and gain variation subtleties of a given telescope necessary to design a controlled beampattern. Details of reflector surface roughness, support structure scat- tering, small variations in element position and con- struction, noise temperature variation between LNAs, etc. can only be captured statistically in the models, but the exact unknown values cannot be matched to the real values for a specific dish and array. Since a priori calibration is insufficiently accurate, in situ calibration is required. Even with bright cal- ibrator sources, due to limited SNR and integration time requirements it is not practical to obtain calibra- tion vectors ai with adequate density or coverage be- yond the first one or two sidelobes (although correla- tion of the array outputs with a second high sensitiv- ity antenna could be used to improve coverage). Er- rors introduced in transferring a beamformer design from simulation invariably lead to unacceptable reduc- tion in real-world sensitivity. Further, fine control of beam pattern shape to reduce temporal variation of the beam response (“pattern rumble”) and insure uni- formity across all pixels cannot be attained with pre- computed data independent designs. We have investi- gated these deterministic design methods, but perfor- mance using real experimental data is poor. We are currently studying methods for translating a desirable beamformer design from a detailed numerical simula- tion to the corresponding actual PAF array using avail- able in situ calibrations, but we have found that simply correcting for the per-channel phase and gain calibra- tion is insufficient due to the effects of array mutual coupling. For these reasons, rather than designing the beam pattern shape over a full sphere using classical beam pattern fitting methods, we have proposed using sta- tistically optimal, data-dependent beamforming de- sign methods for PAF array beamforming (Jeffs et al. 2008b). This approach uses calibration grid data over a limited field of view near the reflector boresight to- gether with the measured noise response of the array to design beamformer weight coefficients. In effect, the calibration grid data controls the pattern main lobe for each beam, and the measured array noise response is used to optimize the deep sidelobes to minimize spillover noise. Since receiver noise for a PAF is cor- related, the statistically optimal beamformer design approach also suppresses receiver noise to a degree as well. We have used two of the several well known statis- tically optimal beamforming algorithms: the linearly constrained minimum variance (LCMV) and maxi- mum sensitivity (max SNR) beamformers (Van Veen & Buckley 1988; Van Trees 2002). LCMV minimizes total output power while satisfying a set of linear constraints. The LCMV optimization problem is given by wLCMV,i = arg min w wHRw subject to wHCi = f (6) 6 For example, using Ci = [ai,aj1 , · · · ,ajP ] and f = [1, r1, · · · , rP ] T constrains the beam main lobe to have a response of unity in direction Ωi and rp in P other directions, Ωjp . The single constraint minimum vari- ance distortionless response (MVDR) beamformer is a special case of LCMV obtained when Ci = ai, and f = 1. Using calibration data only, (6) can be solved ap- proximately as wLCMV,i = R̆ −1 n Ci[C H i R̆ −1 n Ci] −1f (7) We refer to this solution as a “fixed–adaptive” beam- former since though it is statistically optimal for the calibration noise environment, it is computed using a noise covariance measured before or after the observa- tion phase and and does not use the current array co- variance during the observation. For noise field track- ing or moving interference canceling we use a fully adaptive mode, replacing R̆n in Eq. (7) with R̂(j) and updating the weight computation for each STI. The maximum sensitivity beamformer is defined as wmSNR,i = argmax w wHRsw wHRnw . (8) The maximization in Eq. (8) invokes the generalized eigenvector problem R̆s,iwmSNR,i = λmaxR̆nwmSNR,i (9) for which the solution using only calibration data yields a practical fixed-adaptive beamformer. Rapid tracking to adapt to noise field evolution can be ac- complished by replacing calibration R̆n in Eq. (8) with periodically updated “off-source-steered” esti- mates R̂off obtained during observation. This method is not well suited to interference mitigation since off-steering changes the spatial structure of Rint in Rn. The maximum sensitivity beamformer has been used for most experimental PAF observations reported to date (Warnick et al. 2008; Verheijen et al. 2008; Oosterloo et al. 2008; Jeffs et al. 2008a, 2009). Some of the PAF science applications described in Section 1 require beams with very low sidelobes. The maximum sensitivity beamformer (8) does not result in lowest possible sidelobes. In principle, the same cali- bration grids used to generate the signal response cor- relation matrices R̆s,i can also be used to design beams with controlled sidelobes. By definition, these beams will result in lower sensitivity than (8), but the over- all instrument performance should be better for obser- vations requiring low sidelobes. We are currently in- vestigating beamformer design procedures that incor- porate beam shape metrics while still maintaining as high a sensitivity as possible. The flexibility to opti- mize beams for different science applications in post- processing represents an advantage of PAFs over fixed feeds. Sidelobe pattern “rumble” or variation between dishes is of particular concern in PAF synthesis imag- ing as is planned for the ASKAP array and PAF up- grade to the WSRT. Stable know sidelobe patterns per- mit high dynamic range imaging. Since calibration grids are only possible (due to SNR limitations) out to the first sidelobe or two, it will not be possible to strictly control deep sidelobe patters with the beam- former weights. On the other hand, outside the first few sidelobe rings, the highly attenuating pattern of the dish aperture itself dominates over anything the array feed can control. This is a positive promising aspect of sidelobe pattern rumble control that needs further study. 4. Performance Metrics and Noise Models 4.1. Sensitivity and Efficiency For a phased array, sensitivity, efficiencies, and sys- tem noise temperature are beam-dependent. The pri- mary figure of merit for a formed beam in the absence of interference is the beam sensitivity Aeff Tsys = 2kb 10−26F s SNR = 2kb 10−26F s wHRsw wHRnw (10) where Aeff is the effective receiving area for the PAF illuminated dish using beamformer weight w, Tsys is the beam equivalent noise temperature, kb is Boltz- mann’s constant, and F s (Jy) is the flux density of a signal source of interest. Sensitivity is related to radia- tion, aperture, and spillover efficiencies (ηrad, ηap, and ηsp respectively) according to Aeff Tsys = ηradηapAp ηrad(Tsp + Tsky) + (1 − ηrad)Tp + Trec (11) where Ap is the physical aperture area; Tsp is the equivalent spillover noise temperature; Tsky = Tcmb+ Tgb + Tatm is the combined non-SOI noise tempera- ture in the beam main lobe due to cosmic microwave background radiation, galactic background, and atmo- spheric noise; Trec is the beam equivalent receiver noise temperature; and Tp is the physical temperature 7 difficult to model or measure accurately. We adopt the approximate diagonal covariance matrix model Rloss = σ 2 loss I (20) For a given value of Tloss, σ2loss = Tloss Tiso wHw wHRisow (21) In the 19 element PAF, the dominant source of loss noise is a short length of coaxial line feeding each ar- ray element. From measurements of the cable loss, we have obtained the estimate Tloss ≃ 5K. 5. Experimental Results 5.1. Noise and Sensitivity Measurements The isotropic noise correlation matrix used to com- pute beam aperture efficiencies and system noise tem- peratures was measured using the ground shield facil- ity shown in Fig. 2 and described in Section 2. The array output correlation matrix R̆cold for an isotropic cold source (sky) and R̆hot with the array aperture covered by microwave absorber at ambient tempera- ture were acquired for the PAF system at 1600 MHz. Using an array generalization of the Y -factor tech- nique, the isotropic noise response of the array can be obtained from Eq. (13) in the form R̆iso = Tiso Thot + Tcold (R̆hot − R̆cold) (22) With the PAF mounted on the reflector, the ar- ray response correlation matrices for on-source, R̆s,i, and off-source pointings, R̆n, were obtained for each beam steering direction Ωi using calibration data as described in Section 3.2. These are combined with R̆iso and the known calibrator flux density F s to com- pute estimates of beam sensitivities, aperture efficien- cies and system temperature using (10), (12), and (13) respectively. To validate the experimental measurements, a finite element method (FEM) numerical model of the array was created using HFSS (Ansoft Corp.). The ground plane and the dipole elements are modeled as perfect electric conductors, and a loss term is added to account for the measured loss of the coaxial cable from the dipoles to the element terminal connectors. Table 1 shows measured and modeled results for the 19 element prototype array for the sensitivity, aper- ture efficiency, and system temperature for the center Table 1: Measured and modeled peak beam sensitivity, system temperature, and aperture efficiency for the 19 element prototype dipole array. Center Element Formed Beam Model Sensitivity 2 m2/K 3.3 m2/K 3.7 m2/K Tsys 101 K 66 K 69 K ηap 64% 69% 81% Table 2: System noise budget. Measured Modeled LNA Tmin 33 K 33 K Mutual coupling 20 K 23 K Spillover 5 K 5 K Tsky 3 K 3 K Tloss 5 K 5 K Tsys 66 K 69 K element beam (i.e., wT = [1 0 . . . 0]) and the full- array formed beam with peak sensitivity. The 12% discrepancy between measured and modeled aperture efficiency is expected, given that blockage and feed support scattering are not modeled and that numerical radiation patterns for any type of feed typically over- estimate efficiency by roughly 10% (Murphy 1989). The system noise temperature for a formed beam was estimated using Eq. (13) expressed in the form Tsys ≃ ηradTiso wHR̂offw wHR̆isow (23) The isotropic noise response essentially provides the available receiver gain wHRisow/(ηradkbTisoB) for the formed beam, allowing the output noise power to be expressed as an equivalent sky temperature. This array characterization technique is particulary conve- nient for phased arrays, but is influenced by nonunifor- mities in the hot and cold noise sources and receiver gain variations when the PAF system is moved from the warm absorber/cold sky facility to the reflector. With a horizon model to determine the sky brightness temperature nonuniformity and comparing measured results to numerical models, the temperatures obtained using this technique appeared to be accurate to within roughly 10%. The system noise budget for a formed beam is shown in Table 2 for the 19 element array. Noise con- 10 tributions due to mutual coupling and spillover were not separately measured, but were estimated by car- rying over the modeled spillover noise and adjusting the mutual coupling contribution to make up the total measured Tsys. The dominant source of loss was the coaxial feed for each dipole. The mutual coupling term in Table 2 is a contribu- tion to the equivalent receiver noise temperature Trec caused by impedance mismatches between the LNAs and the array. The total receiver noise temperature for the formed beam is Trec = 53 K. The optimum source impedances of the front end amplifiers were matched to the isolated input impedances of the array elements, but due to mutual coupling between array elements the effective impedance presented to each front end am- plifier is an active impedance that is different from the element self impedance (E. E. M. Woestenburg 2005). The resulting mismatches between the opti- mum source impedance parameter of the LNAs and the active impedances presented by the array to the ampli- fiers led to an increase in the equivalent receiver noise. The active impedances are beamformer-dependent, which means that the equivalent receiver noise for a phased array varies with respect to the beam scanning angle. Improving the noise match between the front end amplifiers and the array active impedances to reduce the mutual coupling contribution to the system noise is a major focus of current work in PAF development. For communications applications, decoupling net- works have been explored (Warnick & Jensen 2007) but are likely too lossy and narrowband for astronom- ical instruments. More promising approaches include a noise matching condition that is optimal in an aver- age sense over the array field of view (Warnick et al. 2009a,b), and the design of array antennas with ac- tive impedances that remain as close as possible to the LNA optimum source impedance (e.g., 50 Ω) over the array field of view and operating bandwidth. Results on the expected performance improvement with active impedance matching are given in Sec. 6.2. The values given above are for a single beam steered near the reflector boresight direction. All fig- ures of merit, including aperture efficiency and sys- tem temperature as well as sensitivity, vary across the PAF field of view. The antenna figures of merit can be mapped using data acquired for a grid of calibra- tor source pointings. For each beam, an off-source pointing and an on-source pointing with the reflector steered so that the beam is centered on the source were Cross Elevation (HPBW) E le va tio n (H P B W ) −2 −1 0 1 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 (a) −4 −2 0 2 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Beam Steering Angle (HPBW) S en si tiv ity ( m 2 / K ) Experiment Model (b) Fig. 6.— (a) Measured beam sensitivity map (m2/K) for the 19 element dipole array on the 20-Meter Tele- scope (f/D = 0.43). Each pixel in the image cor- responds to the measured sensitivity of one formed beam. (b) Measured and modeled beam sensitivity for an elevation cut through the PAF field of view. Mea- sured sensitivities were obtained using a bright calibra- tor source on a grid of reflector steering directions with 0.1 degree spacing. The model employed HFSS for the array, physical optics for reflector scattering, and a microwave network model for the receiver chains and beamformer. The half-power beamwidth (HPBW) is 0.7 degrees. used to compute SNR, which can be converted to sen- sitivity using the known source flux density. A map of beam sensitivities is shown in Fig. 6(a). In this and all images in Section 5.2 the horizontal axis is given in “cross elevation” rather than azimuth, in order to reduce coordinate system projection distortion on the 11 sky grid. At the image midpoint, cross elevation de- scribes an arc perpendicular to the arc running from horizon to zenith. This provides an undistorted, uni- form pixel size rectilinear grid projection on the sky. Near the horizon, cross elevation is equivalent to az- imuth. For an image centered at zenith, both elevation and cross elevation axes follow arcs from zenith to horizon. Figure 6(b) shows a slice through the sensitivity map with a comparison to the model results. The shape of these sensitivity maps depends on many factors, in- cluding the size of the PAF, the number of elements used to form a beam (in this case, all 19 elements were used for each beam), and the location of the fo- cal spot in relation to the array elements. Based on a 1 dB tolerance for sensitivity loss for steered beams and a raster spacing with beam overlap at the half-power point, the measured field of view is 2.5 HPBW in di- ameter. These results show good performance for the prototype PAF and demonstrate that scientifically use- ful sensitivities and efficiencies can be obtained. 5.2. Radio Camera Imaging The primary motivation for PAF telescope instru- ments is achieving wide fields of view with multi- ple, electronically steered beams forming a radio im- age with a single dish pointing. As part of the July 2008 experimental campaign on the Green Bank 20- Meter Telescope we collected a number of calibration data grids, used these to compute simultaneous beam- former weights using the maximum sensitivity beam- former method of (8), and observed several astronom- ical radio sources with the PAF operating as a radio camera. Calibration grids were either 33 × 33 or 65 × 65 pixels in size, with inter-pixel separation of 0.1◦, where each pixel represents a calibration pointing di- rection as defined in Section 3.2. For diagnostic pur- poses, the calibration grids were larger than the PAF field of view, so a subset of the grids was used to form images. One beam was formed per calibration pixel. When observing a region larger than the PAF field of view, the reflector was physically steered over a grid of pointings with approximately 1.0◦ spacing in order to form a mosaic of PAF images. Receiving patterns for several of the resulting beams are shown in Fig. 7. The peak sidelobe level was better than 10 dB for beams steered up to 0.6◦, which is near the edge of the PAF field of view as defined by a 1 dB sensitivity loss. Boresight −1 0 1 0.8° −1 0 1 −1 0 1 −30 −20 −10 0 0.4° 1.2° −1 0 1 Fig. 7.— Measured beam receiving patterns (dB rela- tive to peak). The 1.2◦ beam is beyond the PAF field of view as defined by a 1 dB sensitivity loss. Figure 8 presents examples of a single pointing im- age and an image mosaic. The observation is over a 450 kHz band centered on the 1612 MHz OH line. The continuum source 3C295 seen in Fig. 8(a) has a flux density of 21 Jy at 1400 MHz. The integration time was 60 seconds. The radio camera grid is 20 × 20 pix- els, consisting of a total of 400 simultaneously formed and electronically steered beams. The 3 × 3 mosaic of Fig. 8(b) shows OH source W49N and the nearby 3C397. Both images were oversampled with more beams than necessary, but they illustrate the fine-scale radio imaging possible. The number of pixels (beams) that can be formed from a data set is limited only by the time required to collect calibrations and the avail- able computational capacity, since additional beams in post-correlation processing do not require more array elements or data samples. A practical radio camera would likely form beams separated by on the order of half of the HPBW crossover distance. Fig. 9 presents a mosaic image of a more complex source distribution, the Cygnus X region, observed at 1600 MHz with a 5 × 5 mosaic for 25 total reflec- tor pointings. The inset circle indicates the HPBW beamwidth for a single pixel beam. As a compari- son, the right image is from the Canadian Galactic Plane Survey image, but blurred by convolution with the equivalent beam pattern of the 20 m telescope to match resolution scales. We expect that the image ar- tifacts caused by discontinuities at mosaic tile bound- aries could be eliminated with more sophisticated pro- cessing. 12 102030405060708090 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 Reflector Elevation Angle (Degrees) η a p (K ) Single Horn Feed Array, adaptive beamformer Array, fixed−adaptive beamformer (a) Aperture efficiency. 102030405060708090 5 5.5 6 6.5 Reflector Elevation Angle (Degrees) S en si tiv ity ( m 2 / K ) Single horn feed 37 element array, adaptive beamformer 19 element array, adaptive beamformer 19 element array, fixed beamformer (b) Sensitivity. Fig. 11.— The 19 element adaptive beamformer pro- vides an improvement in aperture efficiency and sen- sitivity as it responds to changes in the noise field. Higher sensitivity is achieved at mid elevations than for either the fixed PAF beamformer or horn feed. A 37 element PAF would further increase sensitivity. Ac- tive impedance matching is assumed for each array. itive, since the system noise increases as the tipping angle moves away from zenith, as seen in Fig. 10(b). As the reflector boresight moves closer to the horizon, the dominant change in the noise environment is the in- crease in the sky noise temperature in the antenna main beam. Since the beamformer optimizes sensitivity, the increase in sky noise temperature leads to an increase in the beam aperture efficiency. At zenith, the optimal beam corresponds to a reflector illumination pattern with a higher taper at the reflector edge, lower aper- ture efficiency, and higher spillover efficiency. Near the horizon, increased sky noise means that the opti- mal beam corresponds to an illumination pattern with a lower taper and higher aperture efficiency. This ef- fect is apparent in Fig. 11(a). Figures 10(b)–11(b) compare PAF results for a sin- gle horn feed system. The horn is modeled using the standard cosq(φ) illumination pattern model, where φ is the angle, from the perspective of the feed, along the dish surface relative to the boresight axis. The value of q controls illumination taper and aperture efficiency, and is chosen to maximize sensitivity at zenith. This is a realistic approximate model for a typical single-pixel feed. For a 20 m reflector with f/D = 0.43, optimal sensitivity is obtained with q = 4.6, which produces a −14 dB illumination taper at the dish edge. This comparison shows that the 19 element array, steered to boresight, with adaptive beamforming is capable of achieving a sensitivity at least as high as the typical single horn feed system. As noted above, to make a fair comparison to a single feed, for this simulation the LNAs are active impedance matched to the array to re- duce the mutual coupling noise penalty. Figure 11(b) also includes a simulation for a 37 el- ement array to show sensitivity improvements that are possible with a larger feed. The 37 element PAF uses the same element design and inter-element spacing as the 19 element array. The significantly higher sensitiv- ity compared with both the standard horn feed and the 19 element array is due to its larger aperture and the ability to finely control current phase and amplitude distribution across the array to achieve a more nearly optimal illumination pattern. This would be difficult to accomplish with standard horn feed technology, even with an equivalent aperture size. The larger array also permits beams to be steered off-axis with a smaller sensitivity penalty (Waldron 2008). 6.2. Experimental Results The simulated dish tipping scenario of the previous section was applied to a real data acquisition experi- ment with the 19 element PAF test platform on the 20m dish at the NRAO observatory in Green Bank, West Virginia. The following results use data with no bright sources in the array field of view collected during the July 2008 experiment. The observation band was cen- tered at 1612 MHz with a bandwidth of 450 kHz. Ar- ray data was recorded for telescope pointings ranging from zenith to the horizon in 2.5–degree increments. MVDR beamformer weight updates were imple- mented as described in Section 3.3 using R̂(j) to com- pute a new w(j) at each elevation for the adaptive 15 102030405060708090 68 70 72 74 76 78 80 Reflector Elevation Angle (Degrees) T sy s (K ) Simulated adaptive beamformer Measured adaptive beamformer Measured fixed−adaptive beamformer (a) System noise temperature, Tsys. 102030405060708090 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Reflector Elevation Angle (Degrees) S en si tiv ity ( m 2 / K ) Simulated adaptive beamformer Measured adaptive beamformer Measured fixed−adaptive beamformer (b) Sensitivity. Fig. 12.— Real data results for 19 element adap- tive beamforming while tipping the Green Bank 20- Telescope from zenith to the horizon. Simulated sen- sitivity is higher primarily due to scattering and block- age effects neglected in the model. The close curve shape match between simulated and measured results validates the simulation model. The adaptive beam- former exhibits improved sensitivity in the mid ele- vations. The physical array and simulation both used element-wise self impedance matching. beamformer. Calculations for sensitivity, aperture ef- ficiency, and system temperature were formed using elevation independent estimates of R̆s,i and R̆n from calibration data for the boresight beam, and the eleva- tion dependent w(j) in (10), (12) and (13). Experimental results for Tsys and sensitivity are shown in Fig. 12, along with simulations for compar- ison. Simulated curves are based on the full noise model described in Section 4.2. Since our active matched array is still under development, the 19 el- ement test platform array and corresponding sim- ulations reported in this section used element-wise self impedance matching (i.e., the LNAs are noise matched to the element self impedances, not the active impedances). Comparison of Figs. 12(a) and 10(b) illustrates that active impedance matching (see Sec. 5.1) has the potential for this array of reducing Tsys by 23 K. Ohmic losses in Fig. 10(b) are assumed to be negligible, whereas Fig. 12(a) includes 4 K noise due to loss. Figures 12(b) and 11(b) show that ac- tive impedance matching can increase sensitivity by a factor of 1.67 (2.2 dB). There is significant agreement in Fig. 12 between experimental real data and simulated results, which serves as a validation for the proposed noise models. In particular, the increase in Tsys, ηap, and the modest improvement in sensitivity at lower elevations for the adaptive beamformer with respect to the fixed beam- former predicted by the model simulations has been verified with real data. Computed real data aperture ef- ficiency (not shown) also exhibited an excellent match with the model simulations. The good match in this ex- ample application suggests that the model may be used with confidence in a variety of other signal scenarios. In some observing scenarios it may not be practi- cal to obtain an SOI–free R̂(j) estimate to update w(j) continuously with elevation changes. In our example we took pains to find a relatively source-free patch of sky for the elevation scan. Since elevation dependence of sky and spillover noise is based primarily on the geometry and not on transient sources, however, it is possible to pre-compute a set of optimal, elevation in- dexed beamformers from calibration data. These could then be called up at a later time (over several days) from a look-up table to achieve the improved mid- elevation sensitivity shown above. The degradation rate of calibration data due to phase and amplitude drift in the receiver electronics and other effects is currently under study, as are tech- niques to refresh calibration data using a small num- ber of bright source observations or external electronic calibration sources. 7. RFI Mitigation As contemporary science goals increasingly require observing sources outside the traditional protected spectrum bands, a critical need is developing to deal with ubiquitous man-made interfering signals such as satellite downlink transmissions (S.W. Ellingson 2001; 16 Poulsen et al. 2005; Combrinck et al. 1994), radar systems (Dong et al. 2005; Jeffs et al. 2006; Fisher 2001; Ellingson & Hampson 2003; Zhang et al. 2003), air navigation aids (Zhang et al. 2005; Fisher et al. 2005), wireless communications (Leshem et al. 1999; Boonstra et al. 2000), and digital television broad- casts. Even locating instruments in undeveloped ar- eas with regulatory protection does not avoid many man-made sources such as satellite downlinks. The PAF, as illustrated in Fig. 4, offers a promising new approach that exploits the spatial structure of the interfering signal to track and remove it without having to discard data (Jeffs et al. 2008b). With spatial can- celing, even interferers that entirely overlap the signal of interest (SOI) spectrum may be mitigated. It is an- ticipated that using this technique, data collection may now be possible where previously interference was too dominant to permit serious scientific observations. To demonstrate feasibility of adaptive RFI miti- gation with the 19 element array on the 20m dish, a local, moving, man-made interference source was introduced. This involved an RF function generator and hand-held antenna, while walking a circuit located about one kilometer from the telescope. The interfer- ing signal was FM-modulated with a 200 kHz band- width overlapping and masking the W3OH spectral line seen at the array at 1665 MHz. RFI was removed using the subspace projection algorithm (Leshem et al. 2000; Jeffs et al. 2008b). This method adapts the beamformer weights to the changing interference envi- ronment, so as to place a spatial null in the interference direction. Beamformer weights are updated every STI according to w (j) sp,i = P ⊥wi P⊥ = I − UintU H int, R̂(j)[Uint |Un] = [Uint |Un]Λ (24) where j is the STI index, sample covariance R̂(j) is computed as in (4), and wj is the nominal determinis- tic (non adaptive canceling) beamformer weight vector for the beam steered in the ith direction. Equation (24) is an eigenvector decomposition of R̂(j) with eigen- values in diagonal Λ ordered in descending magnitude such that the dominant eigenvectors in the partition Uint span the interference subspace. The full eigen- vector matrix U = [Uint |Un] is unitary. Images of the source with and without RFI miti- gation are shown in Fig. 13. Some small distortion due to residual RFI is apparent in Fig. 13(c) after sub- Cross Elevation (Degrees) E le va tio n (D eg re es ) −1 −0.5 0 0.5 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −10 −5 0 5 10 15 20 25 30 (a) No RFI. Cross Elevation (Degrees) E le va tio n (D eg re es ) −1 −0.5 0 0.5 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 50 100 150 (b) With RFI. Cross Elevation (Degrees) E le va tio n (D eg re es ) −1 −0.5 0 0.5 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −10 −5 0 5 10 15 20 25 30 (c) RFI canceled. Fig. 13.— W3OH image with and without RFI. The color scale is equivalent antenna temperature (K). space projection adaptive cancelation processing, but the source which was completely obscured by interfer- ence is now clearly visible. 8. Conclusions We have reported experimental results for a proto- type L-band PAF and have demonstrated radio camera imaging using in situ calibrated maximum sensitivity beamforming. Experimental results agree with simu- lations for a complete electrical and noise model for the PAF and reflector system. Measured beam sen- sitivities, aperture efficiencies and system noise tem- peratures achieve expectations for the 19 element, un- cooled array. The potential of PAFs for adaptive RFI mitigation was explored. These results indicate that there is a clear path forward to a high sensitivity, wide 17