Dual Polarization Measurements of MWA Beampatterns at 137 MHz

The MWA is an aperture array telescope, with 128 receiving elements or tiles, each constructed from a grid of $4\times 4$ dual polarization bow-tie dipoles, mounted on a $5\times 5$ m reflective metal mesh (Tingay et al., 2013). The two orthogonal linear polarizations of the MWA tiles are labled XX and YY, with dipoles aligned along the East-West and North-South directions respectively. MWA tiles have a wide field of view, with a full-width half-maximum $\sim 25^{\circ}$ at 150 MHz, which can be steered using an analogue delay-line beamformer. The beamformers have a set of quantised delays available, which results in a set of 197 discrete pointings to which the beamformer can point the phase-center of the MWA beam. The phased array design of MWA tiles improves the collecting area of tiles, at the expense of additional complexity introduced to the beam shapes.

The experimental setup used in this work is based on Line et al. (2018) and expanded to accommodate our new science goals which differ from previous methods in a few key ways.

We measure the all-sky beam response of 14 MWA tiles, over a 6 month period, at both instrumental polarizations (XX, YY) and at multiple pointings using ORBCOMM⁹⁹9https://www.orbcomm.com/en/networks/satellite communication, METEOR¹⁰¹⁰10http://www.russianspaceweb.com/meteor-m.html and NOAA¹¹¹¹11https://www.noaa.gov/satellites weather satellites. This work is the first demonstration of parallel, in-situ beam measurements without disruption to the telescope’s observational schedule. The 14 MWA tiles are a part of the inner core of the compact configuration of the MWA array, located within the “Southern Hex” as shown in Figure 1. The names of the tiles can be found in Table 1. In addition to the Zenith pointing of the telescope, measurements of the beam response are carried out at two off-zenith pointings (see Table 2).

Radio frequency (RF) signals are simultaneously recorded from 14 MWA tiles and two reference antennas, in both XX and YY polarizations. The reference antennas are constructed using a single dual polarization MWA dipole, centered on a $5\times 5\,$m conductive ground mesh. Custom-built RFI shielded circuits are used to power the Low Noise Amplifiers (LNAs) within the dipole, and retrieve data via coaxial cables. These field boxes contain secondary LNAs, to further amplify RF signals, and Bias-Ts which facilitate data and power transfer through coaxial cables. These field boxes are placed near the reference antennas and are connected with long coaxial cables, to RF Explorers¹²¹²12http://rfexplorer.com located within a RFI shielded hut approximately 50 m away. RF signals from the tiles are acquired inside the MWA receivers (see Tingay et al.,, 2013), using beam splitters, after amplification and filtering by the Analogue Signal Conditioning unit. These are passed to RF Explorers installed within the receivers.

The RF Explorers are set to have a spectral resolution of 12.5 kHz, sampling 112 frequency channels between 137.150 MHz and 138.550 MHz. This frequency window was chosen to observe Meteor and NOAA weather satellites and the ORBCOMM constellation of communication satellites, which provide excellent sky coverage. The signal is acquired at a rate between 6 - 9 samples per second, limited by the hardware in the RF Explorers. A set of five Raspberry Pi¹³¹³13https://www.raspberrypi.org single-board computers are used to control and retrieve data from the 32 RF explorers connected to 14 MWA tiles and 2 reference antennas. The positions of the antennas can be seen in Figure 1. USB hubs are used to power and facilitate the control of multiple RF Explorers by a single Raspberri Pi. An outline of our experimental setup can be found in Figure 2.

The Raspberri Pi’s are connected to the MWA network via ethernet cables, enabling remote control over the experiment. Network access allows the synchronisation of the Raspberri Pi’s by syncing them to the same NTP server. The Raspberri Pi’s control the RF Explorers using a custom python script and the pySerial¹⁴¹⁴14https://pythonhosted.org/pyserial module. Every 24 hours, a scheduled cron job¹⁵¹⁵15http://man7.org/linux/man-pages/man8/cron.8.html transfers the recorded RF data to an external server and, using the at¹⁶¹⁶16http://man7.org/linux/man-pages/man1/at.1p.html command, schedules a day of 30 minute observations across all the RF Explorers.

The beam splitters allowed the experiment to run concurrently with normal MWA operations, meaning the pointing of the telescope was dictated by the regular observational schedule. A large amount of data was recorded using this setup, invariably including a significant portion irrelevant to this project. Though the experiment was plagued by technical failures of the RF Explorers, USB hubs and a rare lightning strike, between 12^th September 2019 and 16^th March 2020, over 4000 hours of raw data were collected.

Before the analysis of our data can proceed, it must be pre-processed to ensure that sensible comparisons can be drawn between the tiles and references. A complication we encountered was that different RF Explorers recorded the data at different temporal rates, ranging between 6 and 9 Hz. We attribute this issue to two distinct batches of RF Explorers used. The first batch of 8 were purchased in 2017, and recorded data at a rate between 6-7 samples per second, while the remaining 24 RF Explorers were purchased in 2019 and recorded data at a rate between 8-9 samples per second. Though the model numbers of the RF Explorers and their configuration settings were identical, we infer that there must have been hardware improvements in the more recently manufactured modules.

An optimal balance between the RF Explorers sampling rate, Signal-to-Noise and the sky coverage of our selected satellites, determines the N-side of our HEALPix (Gorski et al., 2005) maps. We use a N-side of 32, corresponding to an angular resolution of 110 arcmins. An important consideration at this stage was that Satellites in Low Earth Orbit typically transit the visible sky in 5-15 minutes, depending on their orbital altitudes (Cakaj et al., 2009). Typical transit periods of satellites used in this experiment were observed to be in the 15 minute range, at which satellites took $\sim$9 seconds to transit across one 110 arcmin HEALPix pixel.

The calculation above indicates that the raw data is highly oversampled, providing a certain leeway to get around the issue of varied temporal sampling. An iterative Savitzky–Golay (SavGol) filter is selected to smooth the raw noisy data, while preserving it’s high dynamic range. Initially, a SavGol filter with a small window is used to preserve the depth of the null in the beam response, followed by a second SavGol filter with a larger window to smooth short time-scale noise present in the data. We then interpolate our data down to a 1 Hz frequency, while retaining multiple data points per HEALPix pixel. This enables us to compare our tile and reference data accurately. Figure 4 shows the concurrence between the raw data and the SavGol smoothed, interpolated data.

A noise threshold is defined at this stage, allowing further analysis to be limited to RF satellite signals above the noise floor. In a 30 minute observation, typically 3-7 of the 112 frequency channels contain satellite signals. These channels are identified to first order by having peak signals above a single standard deviation ($\sigma_{\mathrm{raw}}$) of the data. Excluding these occupied channels, the Median Absolute Deviation (MAD¹⁹¹⁹19MAD - robust statistic more resilient to outliers than standard deviation) $\sigma_{\mathrm{noise}}$ and the median $\mu_{\mathrm{noise}}$ of the remaining noisy channels are used to define a noise threshold shown in Equation 2. The noise threshold for both $P_{\mathrm{AUT}}$ and $P_{\mathrm{ref}}$ is computed for every time-step with

As observations were carried out in parallel to the regular observational schedule of the MWA, satellite RF data is recorded at all pointings the telescope visited over the course of the experiment, accumulating over 4000 hours of raw data. The total integrated data at most pointings fell far short of the $\sim 400$ hours required to make maps with a N-side of 32. The Zenith and two EoR 2, 4 pointings met this criteria, resulting in $\sim 1600$ hours of usable data. The data is sorted based on pointing, and separate maps are created for each. See Table 2 for details about the pointings and the amount of usable data collected at each.

Satellites transmit data to Earth on their allocated “downlink” frequency, the exact location of which are often proprietary. Reliable sources of data regarding spectrum allocations in the 137-138 MHz band are scarce and often outdated. Our initial estimate of $\sim 70$ active satellites within our window was optimistic, with a total of 18 satellites being regularly observed in our data. Some of our initial satellite candidates were no longer actively transmitting, while others presumably transmitting marginally outside our frequency window. Table 3 contains information on the satellites we used. The orbital parameters (ephemeris) of most satellites are recorded multiple times a day by USSPACECOM and are published by Space-Track.org. The ephemerides of our satellites are downloaded in the form of Two Line Elements²⁰²⁰20http://www.satobs.org/element.html (TLEs). A custom python script reads these TLEs and accurately (within $\sim$10 arcsec at epoch) computes when the satellites are above the horizon and their trajectories in the sky, at the MWA telescope . The Skyfield²¹²¹21https://rhodesmill.org/skyfield(Rhodes, 2019) software package was instrumental to these calculations.

The sheer quantity of data made it infeasible to manually determine transmission frequencies of our satellites. Instead, we developed a method to automatically cross match satellite ephemerides and raw RF data, identifying the transmission frequency of every satellite in each 30 minute observation. Using the ephemerides of each satellite, a temporal window within the RF data is identified, within which transmissions are expected to be found. We define a set of criteria to identify the correct frequency channel.

Window Occupancy:

$W_{\mathrm{RF}}$ is the percentage of RF signal above the noise threshold $P_{\mathrm{noise}}$ (Eq. 2), within the temporal window. Identified satellites were required to have an occupancy in the range $80\%\leqslant W_{\mathrm{RF}}<100\%$. The lower limit accounts for satellite passes close to the horizon, where long noise-like tails are observed on either end of the satellite data.

Power Threshold:

$P_{\mathrm{peak}}$ is introduced to set a minimum peak satellite power. It was observed that channels adjacent to a bright satellite pass were often observed to be contaminated with lower power, noise-like, RF signals. This probably occur due to transmission bandwidth marginally exceeding the 12.5 kHz channel width of the RF Explorers, leading to spectral leakage. Such channels typically have peak power in the range of 10-15 dB, compared to the 20-40 dB peak powers. To eliminate these contaminated channels, we require identified channels to have $P_{\mathrm{peak}}\geqslant 15\mathrm{dB}$.

Triplets:

It is common to observe pairs or triplets of almost identical signal, as seen in labels A, B of Figure 3, which often pass both filters described above. In such cases, the channel with the higher window occupancy is selected, indicative of a superior match between RF data and satellite ephemerides.

While this method has been highly effective, it is not foolproof. At later stages in the analysis, described in Section 4.3, obvious errors in this method are eliminated by implementing a goodness of fit test between measured beam profile and the FEE simulated model.

FEKO simulations were run to create simulated beam models of the reference antennas $B_{\mathrm{ref}}$, using on-site measurements of the ground screen and dipole positions, identical to those used to generate the FEE models of the MWA beam. These models are used to make maps of the tile responses by computing $P_{\mathrm{AUT}}/P_{\mathrm{ref}}\times B_{\mathrm{ref}}$ (Eq. 1) for each satellite pass, for every pair of AUT and Reference. The different amplifications that the RF signals undergo along the two distinct signal paths – through the field box for the reference data, and via the beamformer and the Analogue Signal Conditioning unit for the AUTs – have not been considered (see Figure 2). Since we are interested in the profile of the signal, rather than the absolute power, a least-squares method is used to assign each satellite pass, a single multiplicative gain factor $G_{\mathrm{FEE}}$, effectively fitting it to power level of a corresponding slice of the FEE model.

This slice of the beam response is now projected onto a HEALPix map with a N-side of 32, using the satellite ephemerides, resulting in a map with an angular resolution of 110 arcmins, a good balance between integration per pixel and resolution. Each pixel of the map now contains a distribution of values from multiple satellite passes, the median of which gives us a good estimate of the beam response, without being influenced by outliers.

Two reference antennas ref₀ and ref₁, seen in Figure 5, were used in this experiment. This provides the ability to perform a null test to characterize the differences between the beam patterns of the references, and their FEKO simulated models. The ratio of the beam powers, for a set of perfect reference antennas, should ideally be unity and $P_{\mathrm{ref0}}/P_{\mathrm{ref1}}=1$ should hold true for all satellite passes. Deviations from this expression are indicative of systematics such as alignment errors and imperfections in the ground screen, soil, dipole or the surrounding environment.

The results of the null test are shown in Figure 6. The first row (subplots (i)-(iv)) shows slices of the ref₀ HEALPix map along both East-West (EW) and North-South (NS) directions for XX and YY polarizations, respectively. The median of the distribution of values in each pixel is power P_ref0, while an estimate of the errors is determined from the Median Absolute Deviation $\sigma_{\mathrm{MAD}}$ of the distribution. These are compared to corresponding slices of the reference FEKO model B_ref, and the residuals $\Delta$ref${}_{0}=$P${}_{\mathrm{ref_{0}}}-$B_ref are fit with a third order polynomial. The second row (subplots (v)-(viii)) is an identical analysis carried out for the ref₁ HEALPix map. The null test is performed in the third row (subplots (ix)-(xii)), where corresponding slices of ref₀ and ref₁ HEALPix maps are compared. The green data represents a pixel to pixel comparison between of ref₀ and ref₁, with error bars propagated in quadrature from the $\sigma_{\mathrm{MAD}}$ of each references. We also compare the fits to the residual power $\Delta$ref (orange curve), seen in the lower panels of the first two rows of Figure. 6.

An interesting pattern emerges in the residuals between the map slices and FEKO model $\Delta$ref (Figure 6 (i)-(viii) lower panels). For zenith angles between $30^{\circ}-60^{\circ}$, a systematic deficit of power is observed with residual power structure observed with deviations up to $\pm 2$ dB from the FEKO reference models. This feature is investigated by summing the residuals of all four reference HEALPix maps and averaging the results in $2^{\circ}$ radial bins. By classifying the data according to the progenitor satellite type, an illuminating pattern emerges, shown in Figure 7. We achieve a good fit of the radial residuals using a 8${}^{\textrm{th}}$ order polynomial. Each satellite has a distinct and well defined residual structure. These residuals represent a profile measurement of the beam shapes of satellite transmitting antennas. This can be understood by considering that satellites primarily focus on transmitting data downwards, normal to the surface of Earth. As satellites rise, the reference antennas observe RF transmitted power convolved with the sidelobes of the satellite beam shapes, which is attenuated away from its primary beam (pointed to the surface).

The amplitude and structure of these residuals may appear significant to our analysis, but are in-fact accounted for by our primary Equation 1. This can be illustrated by considering the concurrent measurement of satellite data by both MWA and reference tiles. Any modulation encoded in the data transmitted by the satellites will be identically recorded by all antennas, convolved with individual tile beam shapes. The ratio of observed powers in Eq. 1 ($P_{\mathrm{AUT}}/P_{\mathrm{ref}}$) will neatly divide out any satellite beam structure or modulation encoded within the incoming RF data.

We note the slightly exaggerated slope in the null test of the EW slice of the YY reference maps, as seen in the last column of Figure. 6 (subplots (iv), (viii), (xii)). On further inspection of subplot (viii), we note that the East edge of the ref₁ receives $\sim 2$ dB less, and the West edge receives $\sim 2$ dB more power that the corresponding slice of ref₀. We suggest that this discrepancy probably results from a slight EW gradient in ground screen or the dipoles of the tile, which points the bore-sight of the dipole marginally off-zenith.

The agreement between the fits to the residuals (orange curve in subplots (ix)-(xii) of Figure. 6) and the expected null (red lines) represent a good validation of our experimental procedure described in section 2. We observe less than a $\sim$0.5 dB error in the central 25^∘ of the reference model, corresponding to the primary lobe of the MWA beam at 137 MHz. These errors do increase as we move towards the horizon, reaching a maximum of $\sim$2 dB, in our most inaccurate reference. This validates the efficacy of our null test, in characterising systematic effects from the references, which propagate into the beam maps created in the following sections (see grey errorbars in Figure 12).

The null tests display a marginally better performance of reference tile 0 (ref₀). Despite this, we have chosen to use reference tile 1 (ref₁) in proceeding sections as hardware failures on ref₀ resulted in more data and better sky coverage for ref₁.

During the last stages of the experiment, we noticed that the very brightest satellite signals exceeded the maximum recommended power of the RF explorers, resulting in the internal amplifiers entering a non-linear regime. Unfortunately, the limited dynamic range of the RF Explorers coupled with the high dynamic range of satellite observations resulted in almost no leeway for errors in this regard. This effect was only present in RF Explorers recording data from MWA tiles, via the MWA receivers and is apparent in Figure 8, where the light blue raw tile data is $\sim 6$ dB lower than a corresponding slice of the FEE model (yellow curve). This deficit of measured power in the primary lobe was unexpected as the primary lobe has been well characterized (Line et al., 2018) and validated by scientific studies which primarily use the primary lobe (e.g. Hurley-Walker et al., 2017) . The effort to recover the “missing” power led to the creation of a global gain calibration scheme.

It was observed that RF Explorers begin to leave their linear amplification zone at around -45 dBm²²²²22dBm - physical units of power, measured with respect to 1 milliwatt and were definitely non-linear by -35dBm, where slices of the FEE model had visibly diverged from raw tile data (see Fig. 8). We begin by considering deformed AUT power P_def, non deformed reference power P_ref and slices of the FEKO reference B_ref and FEE MWA beam B_FEE models for a satellite pass. Once Equation 1 is computed, information regarding absolute power recorded by the RF explorers is lost in favour of a normalized beam profile (see Section 3.4). Thus, gain calibration of the RF explorers must take place at the tile power level, before scaling or normalization processes distort the original power levels. A mask M_def is created using the region where the deformed tile power P_def exceeds -35dBm. This mask prevents the distorted sections of the measured primary beam from biasing the results of the multiple least-squares gain fits described below.

Equation 1 is used to compute the deformed beam slice B_def using P_def, P_ref and B_ref. To maintain the initial power level, we mask the deformed section of B_def using the mask M_def and use a least-squared method to determine a single multiplicative gain factor which will scale B_def down to the initial power level of P_def. A similar method is used to scale the slice of the FEE beam B_FEE down to the initial power level of P_def. The result of the scaling can be seen in Figure 8 where B_FEE (yellow) and B_def (light blue) have been successfully scaled to match at low powers while clearly displaying a deficit of power at the peak of the primary beam.

We can now empirically determine a gain calibration solution by looking at the residual power (B_FEE - B_def) of all satellite passes. The 2D histogram of all residual power is shown in Figure 9, with the horizontal axis representing power observed by the AUT RF explorers, and the vertical axis representing residual power. The figure displays a bridged bimodal distribution, which can be explained by considering the profile shape of cross sectional slices of the MWA beam models. The nodes at the edges of the primary beam are sharply peaked and extremely narrow, leading to a dearth of observational data points in such regions as satellites pass over them relatively quickly. The cluster of points at lower observed power is the result of satellites passing over the relatively broad secondary lobes of the MWA beam while the cluster at higher observed power comes from satellite passes transiting through the primary beam. For linear gain internal to the RF Explorer, one would expect the residuals to be $\sim$ zero, while positive residuals result from non linear gains. The white curve and associated black squares are a 3${}^{\textrm{rd}}$ order polynomial fit to the median values (red crosses) of the data binned in $\sim$ 4dBm intervals. This clearly demonstrates that the RF explorers gradually enter the non-linear regime at $\sim-40$dBm and exhibit residuals of $\sim 6$dB at observed powers of –30 dBm.

The result of applying the calibration solution developed above to a single satellite pass are seen in Figure 8 where B_def (light blue) is scaled up to B_cali (navy blue) and represents a much better fit to a slice of the fee model B_FEE (yellow).

The RF Explorer gain calibration technique presented in this section has been shown to be necessary but comes with a minor drawbacks. Primarily, the global nature of our method could result in the loss of potentially interesting structure present at the center of the primary lobe. The accuracy of the primary lobe has been validated by multiple studies (e.g. Line et al., 2018; Hurley-Walker et al., 2017) and deviations are not expected. The gain correction was essential as the absolute scale of fluctuations in the more uncertain side-lobes, were determined by fitting satellite signals to the well characterized primary lobe. These corrections also enable us to regenerate all-sky beam maps which may be utilized in further studies. Future iterations of this experiment, which could be scaled to passively monitor the full MWA array or SKA-Low, will have to extensively characterize off-the-shelf components such as RF Explorers. Our characterization of the gain profile revealed that the accuracy of factory specification may not be sufficient for experiments of such sensitivity and scale.

We now create MWA beam maps using the method described in Section 3 with the caveat that the RF explorers gain calibration solution described in Section 4.2 are applied to all data from the AUT RF explorers. A single multiplicative gain factor, determined by least-squares minimization, is used to scale measurements to the level of the zenith-normalized FEE beam model. Before B_AUT can be projected onto a HEALPix map, it must pass a final goodness-of-fit test. The frequency mapping method described in Section 3.3 has been highly successful at dealing with the massive volume of data produced over the course of this experiment, but does exhibit an $\sim 2\%$ failure rate, where the transmission frequency of satellites is misidentified. To catch these final outliers, a chi-squared p-value goodness-of-fit test between the scaled measured beam B_AUT and the FEE model B_FEE is implemented, with a threshold tuned to ensure that only the beam profiles with obviously wrong null positions are rejected. Successful satellite passes are projected onto a HEALPix map representative of an accurate all-sky MWA beam response.

A set of tile maps at multiple pointings and polarisations are shown in Figure 10, created with data from tile S08 and Ref₁. The residual maps shown in the second and fourth row of Figure 10 display large gradients in power at the Southern and Eastern edges of their primary lobes. This effect is attributed to gradients in the ground screen of the MWA tiles. Such gradient can lead to systematic angular offsets from the intended pointing of the MWA tiles specified by the beamformers. This effect is most pronounced at the steep nulls surrounding the primary lobe where systematic displacements in null positions occur. The mismatch in the measured position of the nulls as compared to the FEE model manifest as the gradients observed in the residual maps of Figure 10.

We further investigate this effect to determine the gradient of the ground screens of our MWA tiles. This is achieved by displacing our measured beam maps and minimizing the residual power at the edge of the primary lobe. The gradient in the ground screens were determined to $\sim 15$ arcmin resolution by interpolating our HEALPix maps to a higher resolution with NSIDE=256. Figure 11 shows the measured angular offset of our 14 tiles from the zenith pointing. Local surveys of the tiles in the Southern Hex have identified a gradual half degree gradient in the soil, from the North-West to the South-East which would result in all beams being offset by $\sim 0.5^{\circ}$ towards the South-East, displayed as the black cross in Figure 11. This analysis shows a significant scatter in angular beam offsets, indicative of tile gradients ranging up to 1.4^∘, and vertical displacements exceeding 10 cm over a 5 m ground screen.

In Figure 12, NS and EW slices of the tile maps are compared to the corresponding FEE models. The first row (subplots (i)-(iii)) represent NS slices of the XX beam map of tile S08. The lower panels of these subplots explore residual power between measurements and the FEE model. The orange curve represents a 3${}^{\textrm{rd}}$ order polynomial fit to the residual power, while the cyan shaded regions account for errors which can be attributed to the reference tiles, as seen from the null tests (See §4.1 and Fig. 6). The second row (subplots (iv)-(vi)) represents an identical analysis for the EW slice of the beam maps. The last two rows (subplots (vii)-(xii)) complete the analysis described above, for the YY beam maps. The three columns represent the zenith and the 2 and 4 off-zenith pointings.

The distribution of beam shapes of our 14 tiles can been seen in Figure 13, displayed as cross-sections of the beam maps along the cardinal axes. The marginally larger scatter observed of data points around the primary lobes can be attributed the global RF Explorer gain calibration described in 4.2.

A subtle but interesting pattern emerges from Figures 12 and 13. Consider the first row of subplots, representing NS slices of XX beams. There is a slight excess of measured power ($\sim$2dB) at the outer edge of the secondary lobes. XX dipoles are EW oriented and are most sensitive perpendicular to their physical orientation. Thus our measurements indicate a greater than expected sensitivity along the most sensitive axis of the XX dipole. Similarly, the YY beam oriented along the NS, measures an excess of power along its most sensitive axis (EW) as seen in the fourth rows of Figures 12 and 13. Conversely, the power measured by the dipoles along their least sensitive axis, parallel to their physical orientation, is less than expected. This is seen in the second and third rows of Figures 12 and 13.

This effect was investigated by computing median residual power for all 14 tiles along EW and NS slices. The results shown in Figure 14 (i) have been fit with a 2${}^{\textrm{nd}}$ order polynomial which shows systematic, radially dependent offsets. This residual structure could potentially be attributed to a rotation of the reference antenna. This scenario was explored using the simulated FEKO models of the reference, as shown in Figure 14 (ii). The solid lines represent the residual power which would be measured along a NS slice of the XX MWA beam if the reference tile was rotated by a range of angles, while the dashed lines represent the EW slices. As observed in Figures 12 and 13, the excess measured power along the most sensitive axis of the dipole and the deficit of power along the least sensitive axis of the dipoles seem to have similar shapes to the simulated residuals of reference antenna rotations. Unfortunately, the degeneracy inherent to the symmetric reference FEKO models prevents the identification of the direction of this rotation.

The measurements of the western sidelobe of tile S08 show a significant deficit in power of order $\sim$4 dB, seen in the second row of Figure 10. Pictures of the in-situ condition of the tile reveal potential environmental factors which could potentially be responsible. In Figure 15, we observe a number of large rocks on the ground screen of the tile. Additionally, the harsh weather conditions on site seem to have swept some loose soil onto the ground screen, partially obscuring the metal mesh. Both these effects are most prominent along the western edge of the tile and could plausibly explain the measured deficit of power.