Low-power wide area networks

1. A method comprising:

receiving, at a low-power wide-area network base receiver, two or more signals from two or more transmitters, each of the two or more signals encoding information as initial frequencies of two or more up-chirps;

separating the up-chirps of the two or more signals to two or more frequency domain peaks;

identifying a frequency offset corresponding to the each of the two or more frequency domain peaks; and

subtracting each of the frequency offsets from their corresponding frequency domain peaks to retrieve data encoded in the initial frequency of each up-chirp.

2. The method of claim 1 wherein the frequency offsets are identified in a first up-chirp receive in each signal, further comprising:

determining that subsequent chirps having a same frequency offset as the first up-chirp originated from a same transmitter as the first up-chirp.

3. The method of claim 2 wherein the separating step further comprises:

multiplying each up-chirp by a corresponding down-chirp, resulting in two tones at separate frequencies; and

applying a Fourier transform to the two resulting tones.

4. The method of claim 3 wherein a size of the Fourier transform is a multiple of 2 n , where n is the number of up-chirps in the received signals.

5. The method of claim 1 wherein identifying the frequency offset for each transmitter further comprises:

estimating the frequency offset for said transmitter;

estimating a wireless channel for said transmitter based on the estimate of the frequency offset for said transmitter;

re-constructing the received signal from said transmitter using the estimated wireless channel and the estimated frequency offset for said transmitter;

subtracting the re-constructed signal from the received signal, resulting in a residual signal; and

adjusting the estimated frequency offset and repeating the above steps until power of the residual signal is minimized.

6. The method of claim 5 further comprising:

identifying strong transmitters as transmitters having simultaneously discernable peak frequencies;

subtracting signals of the strong transmitters from the received signal; and

identifying any remaining signal as originating from one or more weak transmitters.

7. The method of claim 1 further comprising:

transmitting a beacon signal requesting a response from multiple transmitters at a pre-agreed time after the multiple transmitters have received the beacon signal;

receiving concurrent signals from one or more of the multiple transmitters at the pre-agreed time;

averaging power of the Fourier representation over a plurality of observed symbols from a preamble chirp of each of the received concurrent signals;

identifying frequency offsets for the concurrent signals based on the average power;

reconstructing different possible collisions of the concurrent signals based on the frequency offsets for each possible sequence of data bits in the observed symbols from each of the received concurrent signals; and

identifying a collision of the possible collisions that best fits the observed symbols.

8. A non-transitory, computer-readable storage medium storing software that, when executed by a processor, performs the functions of:

receiving two or more signals from two or more transmitters, each of the two or more signals encoding information as initial frequencies of two or more up-chirps;

separating the up-chirps of the two or more signals to two or more frequency domain peaks;

identifying a frequency offset corresponding to the each of the two or more frequency domain peaks; and

subtracting each of the frequency offsets from their corresponding frequency domain peaks to retrieve data encoded in the initial frequency of each up-chirp.

9. The medium of claim 8 wherein the frequency offsets are identified in a first up-chirp receive in each signal, the software performing the further function of:

determining that subsequent chirps having a same frequency offset as the first up-chirp originated from a same transmitter as the first up-chirp.

10. The medium of claim 9 wherein the software performs the separating step by performing the further functions of:

multiplying each up-chirp by a corresponding down-chirp, resulting in two tones at separate frequencies; and

applying a Fourier transform to the two resulting tones.

11. The medium of claim 10 wherein a size of the Fourier transform is a multiple of 2 n , where n is the number of up-chirps in the received signals.

12. The medium of claim 8 wherein identifying the frequency offset for each transmitter further comprises:

estimating the frequency offset for said transmitter;

estimating a wireless channel for said transmitter based on the estimate of the frequency offset for said transmitter;

re-constructing the received signal from said transmitter using the estimated wireless channel and the estimated frequency offset for said transmitter;

subtracting the re-constructed signal from the received signal, resulting in a residual signal; and

adjusting the estimated frequency offset and repeating the above steps until power of the residual signal is minimized.

13. The medium of claim 12 , the software performing the further function of:

identifying strong transmitters as transmitters having simultaneously discernable peak frequencies;

subtracting signals of the strong transmitters from the received signal; and

identifying any remaining signal as originating from one or more weak transmitters.

14. The medium of claim 8 , the software performing the further function of:

transmitting a beacon signal requesting a response from multiple transmitters at a pre-agreed time after the multiple transmitters have received the beacon signal;

receiving concurrent signals from one or more of the multiple transmitters at the pre-agreed time;

averaging power of the Fourier representation over a plurality of observed symbols from a preamble chirp of each of the received concurrent signals;

identifying frequency offsets for the concurrent signals based on the average power;

reconstructing different possible collisions of the concurrent signals based on the frequency offsets for each possible sequence of data bits in the observed symbols from each of the received concurrent signals; and

identifying a collision of the possible collisions that best fits the observed symbols.

15. An apparatus comprising:

a processor;

a radio transceiver; and

a non-transitory memory storing software that causes the processor to:

receive, via the radio transceiver, two or more signals from two or more transmitters, each of the two or more signals encoding information as initial frequencies of two or more up-chirps;

separate the up-chirps of the two or more signals to two or more frequency domain peaks;

identify a frequency offset corresponding to the each of the two or more frequency domain peaks; and

subtract each of the frequency offsets from their corresponding frequency domain peaks to retrieve data encoded in the initial frequency of each up-chirp.

16. The apparatus of claim 15 wherein the frequency offsets are identified in a first up-chirp receive in each signal, the software further causing the processor to:

determine that subsequent chirps having a same frequency offset as the first up-chirp originated from a same transmitter as the first up-chirp.

17. The apparatus of claim 16 wherein the software causes the processor to perform the separating step by further causing the processor to:

multiply each up-chirp by a corresponding down-chirp, resulting in two tones at separate frequencies; and

apply a Fourier transform to the two resulting tones, wherein a size of the Fourier transform is a multiple of 2 n , where n is the number of up-chirps in the received signals.

18. The apparatus of claim 15 wherein the software causes the processor to perform the identifying step by further causing the processor to:

estimate the frequency offset for said transmitter;

estimate a wireless channel for said transmitter based on the estimate of the frequency offset for said transmitter;

re-construct the received signal from said transmitter using the estimated wireless channel and the estimated frequency offset for said transmitter;

subtract the re-constructed signal from the received signal, resulting in a residual signal; and

adjust the estimated frequency offset and repeating the above steps until power of the residual signal is minimized.

19. The apparatus of claim 15 , further comprising:

identifying strong transmitters as transmitters having simultaneously discernable peak frequencies;

subtracting signals of the strong transmitters from the received signal; and

identifying any remaining signal as originating from one or more weak transmitters.

20. The method of claim 15 , the software further causing the processor to:

transmit a beacon signal requesting a response from multiple transmitters at a pre-agreed time after the multiple transmitters have received the beacon signal;

receive concurrent signals from one or more of the multiple transmitters at the pre-agreed time;

average power of the Fourier representation over a plurality of observed symbols from a preamble chirp of each of the received concurrent signals;

identify frequency offsets for the concurrent signals based on the average power;

reconstruct different possible collisions of the concurrent signals based on the frequency offsets for each possible sequence of data bits in the observed symbols from each of the received concurrent signals; and

identify a collision of the possible collisions that best fits the observed symbols.