Compressive sensing-aided LPWAN MAC layer

1. A system for communicating in a low power wide area network (LPWAN), comprising:

a long range (LoRa) sensing device having circuitry including:

at least one sensor configured to generate a bit stream of sensor signals;

a first physical layer (PHY);

a first medium access (MAC) layer;

a compressive sensing-aided transmission sub-layer embedded within the first medium access layer;

a first computer processing unit including a computer-readable medium comprising program instructions, executable by a first processing circuitry, to cause the first processing unit to:

receive, at the first physical layer of a LoRa device, the bit stream of sensor signals at an incoming velocity;

encode the bit stream to generate an encoded bit stream;

modulate the encoded bit stream by chirp spread spectrum modulation to generate a chirp modulated encoded bit stream;

form a first transmission packet including at least a preamble, the chirp modulated encoded bit stream and a cyclic redundancy check (CRC);

receive the first transmission packet by the first multiple access layer (MAC) of the LoRa device;

compress the chirp modulated encoded bit stream of the first transmission packet into sparse vectors;

combine 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;

form a second transmission packet including the preamble, the payload and the cyclic redundancy check;

transmit, by the first physical layer, the second transmission packet at a randomly selected time;

a receiver having circuitry including:

a second physical layer (PHY);

a second medium access (MAC) layer;

a sparse recovery sub-layer embedded within the second MAC layer;

a second computer processing unit including a computer-readable medium comprising program instructions, executable by a second processing circuitry, to cause the second processing unit to:

receive, at the second physical layer, the second transmission packet;

de-map the transmission packet to recover a compressed, encoded bit stream;

reconstruct, by the sparse recovery sub-layer, the compressed, encoded bit stream by recovering sparse vectors to generate a chirp spread spectrum encoded bit stream;

demodulate the chirp spread spectrum encoded bit stream by chirp spread spectrum demodulation to generate an encoded bit stream;

decode the encoded bit stream to remove indexing and generate an interleaved bit stream;

de-interleave the interleaved bit stream; and

decode the interleaved bit stream to recover the bit stream of sensor signals.

2. The system of claim 1 , further comprising:

a Hamming encoder;

a Gray indexer:

wherein the first processing circuitry is further configured to:

encode the bit stream, with the Hamming encoder, by using Hamming forward error correction to form a first coded bit sequence;

interleave the first coded bit sequence to form a second coded bit sequence; and

apply Gray indexing to the second coded bit sequence to prevent off-by-one errors when resolving symbols to generate the encoded bit stream.

3. The system of claim 2 , further comprising:

a local oscillator configured to generate a base chirp signal; and

wherein the first processing circuitry is further configured to modulate the encoded bit stream by combining the encoded bit stream with the base chirp signal at a chirp rate.

4. The system of claim 3 , wherein the first processing circuitry is further configured to:

select a channel bandwidth from the group consisting of 125 kHz, 250 kHz and 500 kHz;

match a coding rate to a channel coding rate, wherein the coding rate is selected from R c =4/4+n where n={1,2,3,4}; and

encode the signal bits by using Hamming forward error correction at the coding rate.

5. The system of claim 4 , wherein the first processing circuitry is further configured to compress the chirp modulated encoded bit stream of the first transmission packet into sparse vectors by retaining only non-zero values of the sparse vectors.

6. The system of claim 5 , wherein the first processing circuitry is further configured to:

map the second transmission packet to in-phase and quadrature transmission paths; and

transmit the second transmission packet on the in-phase and quadrature transmission paths.

7. The system of claim 6 , wherein the first processing circuitry is further configured to transmit the second transmission packet according to a Class A protocol, in which the LoRa device sleeps until it wakes for transmission at the randomly selected time.

8. The system of claim 7 , wherein the second processing circuitry is further configured to demodulate the chirp spread spectrum encoded bit stream by subtracting a base chirp signal generated by a local oscillator at a chirp rate from the chirp spread spectrum encoded bit stream.

9. The system of claim 8 , further comprising:

a Gray decoder configured to decode the encoded bit stream; and

a Hamming decoder configured to decode the interleaved bit stream.

10. A method for compressive sensing based communications of low range (LoRa) devices in a low power wide area network (LPWAN), comprising:

receiving, by a physical layer of a LoRa device, a bit stream of sensor measurements at an incoming velocity;

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;

transmitting the second transmission packet at a randomly selected time.

11. The method of claim 10 , further comprising:

encoding the bit stream by:

encoding the bits with a Hamming encoder, by using Hamming forward error correction to form a first coded bit sequence;

interleaving the first coded bit sequence to form a second coded bit sequence; and

applying Gray indexing to the second coded bit sequence to prevent off-by-one errors when resolving symbols to generate a third coded bit sequence.

12. The method of claim 11 , further comprising:

modulating the encoded bit stream by combining the third coded bit sequence with a base chirp signal generated by a local oscillator at a chirp rate.

13. The method of claim 12 , further comprising:

selecting a channel bandwidth from the group consisting of 125 kHz, 250 kHz and 500 kHz;

matching a coding rate to a channel coding rate, wherein the coding rate is selected from R c =4/4+n where n={1,2,3,4}; and

encoding the signal bits by using Hamming forward error correction at the coding rate.

14. The method of claim 13 , further comprising:

compressing the chirp modulated encoded bit stream of the first transmission packet into sparse vectors by retaining only non-zero values of the sparse vectors.

15. The method of claim 14 , further comprising:

mapping the second transmission packet to in-phase and quadrature transmission paths; and

transmitting the second transmission packet according to the mapping.

16. The method of claim 15 , further comprising:

transmitting the second transmission packet according to a Class A protocol, in which the LoRa device sleeps until it wakes for transmission at the randomly selected time.

17. A method for decoding compressive sensing based communications of low range (LoRa) devices in a low power wide area network (LPWAN), comprising:

receiving, at a receiver physical layer, a compressed, encoded transmission packet from a LoRa device;

de-mapping the transmission packet to recover a compressed, encoded bit stream;

reconstructing, by a sparse recovery sub-layer of a receiver multiple access layer (MAC) layer, the encoded transmission by recovering sparse vectors to generate a chirp spread spectrum encoded bit stream;

demodulating the chirp spread spectrum encoded bit stream by chirp spread spectrum demodulation to generate an encoded bit stream;

decoding the encoded bit stream to remove indexing and generate an interleaved bit stream;

de-interleaving the interleaved bit stream; and

decoding the interleaved bit stream to recover the bit stream of the communications.

18. The method of claim 17 , further comprising:

decoding the encoded bit stream, with a Gray decoder, and

decoding the interleaved bit stream with a Hamming decoder.

19. The method of claim 18 , further comprising:

demodulating the chirp spread spectrum encoded bit stream by subtracting a base chirp signal generated by a local oscillator at a chirp rate from the chirp spread spectrum encoded bit stream.

20. The method of claim 19 , further comprising:

waking the receiver physical layer periodically to listen for messages from a LoRa transmitter in a Class A communication.