{"id":4136,"date":"2022-10-28T09:30:38","date_gmt":"2022-10-28T16:30:38","guid":{"rendered":"https:\/\/www.cloudacm.com\/?p=4136"},"modified":"2025-03-09T09:46:30","modified_gmt":"2025-03-09T16:46:30","slug":"radio-frequency-visualization","status":"publish","type":"post","link":"https:\/\/www.cloudacm.com\/?p=4136","title":{"rendered":"Radio Frequency Visualization"},"content":{"rendered":"

This post will revisit a topic which has been covered in earlier posts, but with some enhancements.\u00a0 This earlier post used python to visualize a radio sweep, https:\/\/www.cloudacm.com\/?p=3209<\/a>. The method was specific to the SDR hardware and the rtl_power command to generate a dataset that was then processed with python to generate a plot.\u00a0 This post will expand on the visualization by using python to generate varied plot types to help in understanding the radio signals observed.\u00a0 The previous post was limited to the SDR hardware.\u00a0 In this post, the processed datasets will be the focus with an unfixed approach to the data sources.<\/p>\n

This link provided some footing on the python method, https:\/\/docs.astropy.org\/en\/stable\/convolution\/index.html<\/a>.\u00a0 What is interesting about the method is its ability to fill in the blanks of a sparse dataset and the results closely matching the higher resolution control.<\/p>\n

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This was applied to RSSI readings taken in an area to generate a heat map of the signal coverage.\u00a0 Here is the python code used.<\/p>\n

import matplotlib.pyplot as plt\r\nimport numpy as np\r\nfrom scipy.interpolate import Rbf  # radial basis functions\r\n\r\n# x y arrays\r\nx = [1, 3, 4, 4, 5, 6, 8, 9, 10, 10, 11, 12, 15, 16, 17, 19, 19, 20]\r\ny = [5, 15, 10, 18, 3, 16, 8, 10, 5, 18, 15, 9, 8, 16, 18, 4, 14, 9]\r\nz = [-42, -53, -44, -58, -28, -48, -62, -62, -44, -69, -66, -64, -49, -67, -72, -36, -55, -40]\r\n# this made it click\r\n# https:\/\/stackoverflow.com\/questions\/65652769\/interpolation-scatter-plot\r\n# z = [1]*len(x)\r\n\r\n#RBF Func\r\nrbf_fun = Rbf(x, y, z, function='linear')\r\n\r\nx_new = np.linspace(0, 20, 81)\r\ny_new = np.linspace(0, 18, 82)\r\n\r\nx_grid, y_grid = np.meshgrid(x_new, y_new)\r\nz_new = rbf_fun(x_grid.ravel(), y_grid.ravel()).reshape(x_grid.shape)\r\n\r\nplt.pcolor(x_new, y_new, z_new);\r\nplt.plot(x, y, 'o');\r\nplt.xlabel('x'); plt.ylabel('y');\r\nplt.title('RBF Linear interpolation');\r\nplt.show();\r\n<\/pre>\n
The x and y values were points derived from a floor plan, while the z values were RSSI signal readings made using the AirPort Utility on an iPhone.\u00a0 The AirPort Utility can be set to measure signal strength and display the values by enabling the Wi-Fi Scanner option in the app settings.\u00a0 This process requires manual data point entry, which can be tedious and prone to error on a large and repetitive scale.\u00a0 However, for the purposes of a demonstration it can prove to be valuable.\u00a0 Here are the results of the plot compared to the sparse readings.<\/p>\n
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The interpolated plot fills in the blanks to give a smoother appearance of the radio coverage.\u00a0 These heatmaps can be generated using commercial software.\u00a0 However, the licensing costs often keep it out of the reach of those that may have casual or occasional use for it.<\/p>\n
Another use case would be radio location.\u00a0 In this example, an area was surveyed with the ESP32-Cam data logger that was discussed in this post, https:\/\/www.cloudacm.com\/?p=3681<\/a>.\u00a0 The data logger captured the x and y values as GPS coordinates, while the z values are the RSSI values.\u00a0 These RSSI values were captured from another ESP32-Cam module acting as a beacon, it was originally a time lapse camera from this post, https:\/\/www.cloudacm.com\/?p=4036<\/a>.\u00a0 The beacon was encircled by the data logger with the data logger always facing in the same direction towards the beacon.\u00a0 The plot closely matches a typical radio pattern along its horizontal axis.<\/p>\n
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Here is the python code used with the included datasets.<\/p>\n
from scipy.interpolate.rbf import Rbf  # radial basis functions\r\nimport matplotlib.pyplot as plt\r\nimport numpy as np\r\n\r\nfig = plt.figure(facecolor='silver')\r\n\r\n# Longitude values \r\ny = [30.48, 31.47, 32.26, 32.65, 30.93, 29.70, 29.89, 28.12, 26.99, 27.33, 28.56, 30.48, 33.64, 35.51, 36.64, 36.00, 34.18, 31.91, 29.45, 26.64, 24.13, 22.36, 22.31, 23.39, 25.51, 27.82, 30.63, 33.93, 36.98, 39.45, 41.56, 43.63, 44.52, 42.55, 39.40, 35.95, 32.21, 27.23, 22.75, 18.86, 16.60, 16.05, 17.38, 20.04, 23.64, 27.68, 32.50, 34.23, 35.26, 40.38, 43.24, 45.36, 44.91, 42.40, 38.95, 34.96, 30.78, 26.59, 22.21, 19.70, 16.05, 13.20, 12.46, 13.94, 16.40, 19.65, 23.69, 28.27, 32.90, 36.79, 40.48, 44.08, 47.18, 50.97, 52.40, 51.76, 50.23, 47.47, 43.09, 38.22, 33.64, 28.96, 24.23, 19.50, 15.32, 11.67, 8.82, 6.70, 5.71, 5.32, 6.21, 7.73, 10.34, 13.84, 17.58, 21.87, 26.54, 30.98, 35.75, 41.17, 44.08, 47.67, 51.41, 54.12, 56.14, 57.57, 58.11, 58.41, 57.96, 56.53, 54.22, 51.07, 47.67, 42.94, 38.26, 32.40, 27.63, 22.60, 17.97, 13.49, 9.50, 6.45, 4.83, 2.56, 0.98, 0.64, 0.15, 0.00, 0.34, 1.63, 3.79, 6.55, 9.65, 13.30, 17.58, 21.82, 26.45, 30.29, 30.93, 31.17, 31.27, 31.52, 31.71, 31.52, 31.86]\r\n\r\n# Latitude Values\r\nx = [39.48, 40.19, 41.42, 43.57, 46.74, 47.97, 47.86, 47.97, 46.13, 42.95, 39.48, 37.53, 38.35, 39.58, 43.26, 47.15, 50.22, 51.65, 51.75, 51.95, 47.86, 43.87, 39.07, 35.39, 32.52, 29.56, 27.82, 28.23, 28.94, 30.78, 34.36, 40.30, 45.92, 51.14, 55.43, 57.89, 58.40, 57.17, 54.31, 49.70, 44.59, 40.70, 36.20, 30.78, 27.20, 24.03, 24.24, 24.85, 26.08, 30.37, 37.02, 45.41, 52.67, 59.42, 63.92, 68.11, 69.44, 67.91, 64.84, 60.34, 57.27, 50.42, 44.59, 38.25, 30.78, 25.36, 21.89, 18.61, 17.08, 17.39, 19.84, 23.32, 28.23, 34.36, 42.03, 49.70, 56.86, 63.92, 69.55, 74.15, 76.19, 76.50, 75.17, 72.92, 70.26, 65.25, 60.14, 54.10, 47.97, 41.11, 34.26, 28.23, 23.11, 17.69, 13.19, 9.82, 7.26, 5.42, 5.42, 6.55, 8.18, 10.84, 15.65, 21.37, 27.31, 33.75, 40.50, 48.27, 56.15, 64.23, 70.36, 75.78, 81.00, 84.78, 88.26, 90.00, 89.80, 88.26, 86.11, 83.35, 79.77, 75.27, 71.59, 65.97, 59.73, 53.39, 48.17, 42.14, 35.28, 28.43, 22.50, 16.87, 12.27, 8.49, 4.70, 2.05, 0.00, 0.31, 6.55, 13.40, 20.45, 27.31, 34.06, 41.22, 44.49]\r\n\r\n# Sensor Readings \r\nz = [-38, -37, -43, -50, -49, -49, -48, -51, -55, -54, -48, -49, -49, -51, -53, -61, -59, -53, -51, -53, -54, -56, -57, -59, -62, -52, -55, -55, -61, -58, -60, -61, -60, -56, -57, -55, -57, -55, -59, -60, -63, -61, -58, -55, -53, -52, -53, -52, -54, -56, -59, -63, -63, -66, -66, -66, -70, -81, -71, -75, -81, -76, -76, -70, -70, -81, -70, -74, -69, -65, -67, -64, -75, -74, -71, -73, -76, -74, -70, -70, -64, -63, -64, -63, -69, -70, -70, -76, -68, -66, -68, -64, -66, -64, -60, -58, -58, -57, -59, -62, -62, -59, -61, -62, -63, -65, -67, -68, -68, -68, -68, -66, -66, -63, -62, -65, -64, -65, -63, -64, -66, -67, -66, -66, -70, -71, -66, -65, -67, -65, -64, -68, -61, -63, -61, -59, -58, -58, -59, -64, -65, -51, -49, -38, -29]\r\n\r\nrbf_adj = Rbf(x, y, z, function='linear')\r\n\r\n# horizontal range\r\ny_fine = np.linspace(-5, 66, 82)\r\n# vertical range\r\nx_fine = np.linspace(-5, 95, 81)\r\n\r\n\r\nx_grid, y_grid = np.meshgrid(x_fine, y_fine)\r\n\r\nz_grid = rbf_adj(x_grid.ravel(), y_grid.ravel()).reshape(x_grid.shape)\r\n\r\n# https:\/\/matplotlib.org\/stable\/tutorials\/colors\/colormaps.html\r\n# plt.pcolor(x_fine, y_fine, z_grid);\r\n# plt.pcolor(x_fine, y_fine, z_grid, cmap=plt.cm.autumn);\r\nplt.pcolor(x_fine, y_fine, z_grid, cmap=plt.cm.inferno);\r\n# plt.pcolor(x_fine, y_fine, z_grid, cmap=plt.cm.hot);\r\n\r\n\r\nplt.plot(x, y, '.k');\r\nplt.xlabel('meters'); plt.ylabel('meters'); plt.colorbar();\r\nplt.title('ESP32-Cam RF Radiation Patern');\r\n\r\n# plt.show()\r\nfig.savefig('Plot_RF-Pattern_Meters1.png', facecolor=fig.get_facecolor()) \r\n<\/pre>\n
The next plot contains z values that were detected networks in the area.\u00a0 It should be noted that the orientation of the ESP32-Cam module that was taking the readings was maintained toward the beacon.\u00a0 This is an important factor, as seen in this plot, because the direction of the networks detected becomes visible.<\/p>\n
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The bright yellow and dark purple areas establish the linear path toward the network sources.\u00a0 The following illustration shows the direction in green.<\/p>\n
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The original intention was to plot the beacon’s radiation pattern.\u00a0 It was a welcomed surprise to be able to plot the direction of these networks.\u00a0 However, it should be noted that the interpolation method requires readings to be well spaced.\u00a0 The following plots demonstrate the limitations inherent to interpolation.<\/p>\n
\"\"<\/a>The resulting interpolated data is incorrect, so be aware of the context when using this method.<\/p>\n
The following were some useful resources found during the research of this topic.\u00a0 RF Line of Sight, https:\/\/www.scadacore.com\/tools\/rf-path\/rf-line-of-sight\/<\/a>.<\/p>\n
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DragonOS LTS an out-of-the-box Lubuntu 20.04 based x86_64 operating system for anyone interested in software defined radios but were too scared to ask, https:\/\/sourceforge.net\/projects\/dragonos-lts\/<\/a>.<\/p>\n