Internet of things method for class-A end device communication

An internet of things (IoT) method for compressive sensing based communications of low range (LoRa) Class A end devices in a low power wide area network (LPWAN) with differential phase shift keying mapping, comprising:

• receiving, by a physical layer of a Class A LoRa end device including a temperature sensor, a bit stream of sensor measurements at an incoming velocity, wherein the Class A LoRa end device is connected to a gateway;
• encoding the bit stream to generate an encoded bit stream;
• modulating the encoded bit stream by chirp spread spectrum modulation to generate a chirp modulated encoded bit stream;
• forming a first transmission packet including at least a preamble, the chirp modulated encoded bit stream and a cyclic redundancy check (CRC);
• receiving the first transmission packet by a multiple access layer (MAC) of the LoRa device;
• compressing the chirp modulated encoded bit stream of the first transmission packet into sparse vectors;
• combining the sparse vectors with a linear combination of a randomly selected set of sparse vectors representing past measurements and the in-coming velocity of the bit stream to generate a payload;
• forming a second transmission packet including the preamble, the payload and the cyclic redundancy check;
• mapping the second transmission packet to in-phase and quadrature transmission paths with a differential phase shift keying (DQPSK) mapper;
• and
• transmitting the second transmission packet through the antenna according to the mapping to the network via the gateway at a randomly selected time.