A LoRa device for communicating sensor signals in a low power wide area network (LPWAN) includes a physical layer using Hamming encoding and Gray indexing with chirp spread signal (CSS) modulation to encode and modulate the sensor signals and a medium access layer (MAC) including a compressive sensing sub-layer which reduces encoded, modulated signals to sparse vectors. A transmission packet is formed by combining the sparse vectors with a selected set of sparse vectors representing past measurements and the incoming velocity of the sensor signals. A receiver decompresses the transmission packet by reconstructing, at a sparse recovery sub-layer of a receiver MAC layer, the encoded, modulated sensor signals. A decoder path removes the CSS modulation and Gray indexing, and Hamming decodes the sensors signals.