Understanding spectrum activity is challenging when attempted at scale. The wireless community has recently risen to this challenge in designing spectrum monitoring systems that utilize many low-cost spectrum sensors to gather large volumes of sampled data across space, time, and frequencies. These crowdsensing systems are limited by the uplink bandwidth available to backhaul the raw in-phase and quadrature (IQ) samples and power spectrum density (PSD) data needed to run various applications. This paper presents, a framework based on the Walsh-Hadamard transform to compress spectrum data collected from distributed and low-cost sensors for real-time applications. This transformation allows sensors to significantly save uplink bandwidth thanks to its inherent properties both when it is applied to IQ and PSD data. Additionally, by leveraging a feedback loop between the sensor and the edge device it connects to, carefully adapts the compression ratio over time to changes in the spectrum and different applications, jointly considering data size, application performance, and spectrum variations. We experimentally evaluate in several applications. Our results show that is particularly suitable for IoT transmissions and signals close to the noise floor. Compared with prior work, provides up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7\times$</tex-math> </inline-formula> more reduction of uplink data size for signal detection based on PSD data, and reduces up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\times$</tex-math> </inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times$</tex-math> </inline-formula> the number of undecodable messages for IQ sample decoding.
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