The Design of Widespread Spectrum Monitoring Systems

Widespread radio-frequency (RF) spectrum monitoring could enable data-driven modeling of spectrum usage, enhance spectral utilization, and strengthen policy enforcement. Natural questions arise about the number and capabilities of RF sensors to deploy and relevant data to capture. Several previous works in wireless sensor networks (WSN) offer insights related to these questions, but they assume emitters that radiate isotropically. In the RF domain, directional emitters are increasingly common, especially with the advent of multiple input, multiple output (MIMO) and millimeter wave (mmWave) technologies. Consequently, this dissertation develops a new framework to consider directional sensors and emitters, which generalizes the isotropic models. Although the framework extends to general dimensions, we focus in this dissertation on two-dimensional and three-dimensional scenarios. Specifically, we determine the probability that a single emitter is detected by a randomly deployed sensor network, and we quantify the increase in the average number of sensors required as a function of emitter directivity. In the case of multiple emitters, we develop other metrics, including a lower bound on the probability of multi-emitter detection and the average number of undetected emitters, and draw similar conclusions.

For example, in two-dimensions our results suggest that with a path loss exponent of 4 and all other things equal, quartering the emitter half-power beamwidth doubles the average number of sensors needed for detection. We also conclude that omni-directional sensors are optimal in terms of emitter detection probability, regardless of emitter directivity. Additionally, assuming higher sensor quality results in higher sensor cost, we consider a fixed-budget deployment and observe that sensor quantity is more important than sensor quality for emitter detection. In particular, from a survey of current software-defined radios, for a given total cost, we observe that decreasing the individual sensor cost by a factor of 10 increases the system probability of detection by about a factor of 10.

In three-dimensions, we derive expressions for half-power beamwidths (HPBWs) that optimize the emitter detection probability. With the optimal HPBWs, we observe that if the path loss exponent is below 3.22, directional sensors result in a higher emitter detection probability. Otherwise, omni-directional sensors perform better.

Returning to two dimensions, we estimate the RF power field over space from sensor measurements of power, a data product we call an RF ``power map.'' We explore multiple estimation techniques, including planar interpolation, ordinary kriging, a radial basis function network, and an approximation to the maximum a posteriori (MAP) estimate. We observe that increasing sensor density generally improves the accuracy of each method, and we also compare the computational complexities of the methods. Simulated and experimental results indicate that ordinary kriging achieves the lowest normalized root mean square error (NRMSE). Nonetheless, planar interpolation is a close second with a much lower algorithmic complexity. Consequently, planar interpolation is recommended for computationally-limited applications, such as viewing real-time power maps.

Finally, future directions are suggested. To generalize the model framework further, we discuss extensions to the RF channel model and deployment model. Additionally, we remark on analyzing other data products of spectrum monitoring, such as emitter localization and power estimation.