Filtering channel responses for motion detection

1. A method, comprising:

obtaining a set of frequency-domain channel responses based on a set of wireless signals transmitted through a space, each of the frequency-domain channel responses corresponding to a respective wireless signal of the set of wireless signals;

for each frequency-domain channel response:

generating a time-domain channel response based on the frequency-domain channel response;

generating a filtered time-domain channel response based on a constraint applied to the time-domain channel response;

generating a reconstructed frequency-domain channel response based on the filtered time-domain channel response;

generating an error signal indicative of a difference between the frequency-domain channel response and the reconstructed frequency-domain channel response; and

determining whether the error signal satisfies a criterion; and

detecting, in response to each of the error signals satisfying the criterion, motion of an object in the space based on the set of frequency-domain channel responses.

2. The method of claim 1 , comprising:

for at least one of the frequency-domain channel responses and in response to the error signal not satisfying the criterion:

generating an updated time-domain channel response based on the filtered time-domain channel response, the error signal, and the constraint;

generating an updated reconstructed frequency-domain channel response based on the updated time-domain channel response;

regenerating the error signal based on a difference between the frequency-domain channel response and the updated reconstructed frequency-domain channel response; and

repeating generation of the updated time-domain channel response, the updated reconstructed frequency-domain channel response, and the error signal until the error signal satisfies the criterion.

3. The method of claim 1 , wherein the constraint comprises a constraint on a time duration of the time-domain channel response.

4. The method of claim 1 , wherein the constraint comprises a constraint on amplitudes of the time-domain channel response.

5. The method of claim 1 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion based on the reconstructed frequency-domain channel responses.

6. The method of claim 1 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion of the object based on the set of frequency-domain channel responses and a set of quality metrics, each of the frequency-domain channel responses corresponding to a respective quality metric of the set of quality metrics.

7. The method of claim 6 , comprising determining, for each frequency-domain channel response, the respective quality metric based on the error signal.

8. The method of claim 6 , wherein the respective quality metric comprises a ratio of a power of the frequency-domain channel response to a power of the error signal.

9. The method of claim 1 , wherein the set of wireless signals comprises a set of orthogonal frequency division multiplexing (OFDM) signals, and each of the frequency-domain channel responses is based on one or more training fields in a PHY frame of a corresponding OFDM signal of the set of OFDM signals.

10. The method of claim 1 , wherein the set of wireless signals is formatted according to a wireless communication standard.

11. A non-transitory computer-readable medium comprising instructions that are operable, when executed by data processing apparatus, to perform operations comprising:

obtaining a set of frequency-domain channel responses based on a set of wireless signals transmitted through a space, each of the frequency-domain channel responses corresponding to a respective wireless signal of the set of wireless signals;

for each frequency-domain channel response:

generating a time-domain channel response based on the frequency-domain channel response;

generating a filtered time-domain channel response based on a constraint applied to the time-domain channel response;

generating a reconstructed frequency-domain channel response based on the filtered time-domain channel response;

generating an error signal indicative of a difference between the frequency-domain channel response and the reconstructed frequency-domain channel response; and

determining whether the error signal satisfies a criterion; and

detecting, in response to each of the error signals satisfying the criterion, motion of an object in the space based on the set of frequency-domain channel responses.

12. The non-transitory computer-readable medium of claim 11 , the operations comprising:

for at least one of the frequency-domain channel responses and in response to the error signal not satisfying the criterion:

generating an updated time-domain channel response based on the filtered time-domain channel response, the error signal, and the constraint;

generating an updated reconstructed frequency-domain channel response based on the updated time-domain channel response;

regenerating the error signal based on a difference between the frequency-domain channel response and the updated reconstructed frequency-domain channel response; and

repeating generation of the updated time-domain channel response, the updated reconstructed frequency-domain channel response, and the error signal until the error signal satisfies the criterion.

13. The non-transitory computer-readable medium of claim 11 , wherein the constraint comprises a constraint on a time duration of the time-domain channel response.

14. The non-transitory computer-readable medium of claim 11 , wherein the constraint comprises a constraint on amplitudes of the time-domain channel response.

15. The non-transitory computer-readable medium of claim 11 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion based on the reconstructed frequency-domain channel responses.

16. The non-transitory computer-readable medium of claim 11 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion of the object based on the set of frequency-domain channel responses and a set of quality metrics, each of the frequency-domain channel responses corresponding to a respective quality metric of the set of quality metrics.

17. The non-transitory computer-readable medium of claim 16 , the operations comprising determining, for each frequency-domain channel response, the respective quality metric based on the error signal.

18. The non-transitory computer-readable medium of claim 16 , wherein the respective quality metric comprises a ratio of a power of the frequency-domain channel response to a power of the error signal.

19. The non-transitory computer-readable medium of claim 11 , wherein the set of wireless signals comprises a set of orthogonal frequency division multiplexing (OFDM) signals, and each of the frequency-domain channel responses is based on one or more training fields in a PHY frame of a corresponding OFDM signal of the set of OFDM signals.

20. The non-transitory computer-readable medium of claim 11 , wherein the set of wireless signals is formatted according to a wireless communication standard.

21. A system, comprising:

a plurality of wireless communication devices in a wireless communication network, the plurality of wireless communication devices configured to transmit a set of wireless signals through a space;

a computer device comprising one or more processors configured to perform operations comprising:

obtaining a set of frequency-domain channel responses based on the set of wireless signals, each of the frequency-domain channel responses corresponding to a respective wireless signal of the set of wireless signals;

for each frequency-domain channel response:

generating a time-domain channel response based on the frequency-domain channel response;

generating a filtered time-domain channel response based on a constraint applied to the time-domain channel response;

generating a reconstructed frequency-domain channel response based on the filtered time-domain channel response;

generating an error signal indicative of a difference between the frequency-domain channel response and the reconstructed frequency-domain channel response; and

determining whether the error signal satisfies a criterion; and

detecting, in response to each of the error signals satisfying the criterion, motion of an object in the space based on the set of frequency-domain channel responses.

22. The system of claim 21 , the operations comprising:

for at least one of the frequency-domain channel responses and in response to the error signal not satisfying the criterion:

generating an updated time-domain channel response based on the filtered time-domain channel response, the error signal, and the constraint;

generating an updated reconstructed frequency-domain channel response based on the updated time-domain channel response;

regenerating the error signal based on a difference between the frequency-domain channel response and the updated reconstructed frequency-domain channel response; and

repeating generation of the updated time-domain channel response, the updated reconstructed frequency-domain channel response, and the error signal until the error signal satisfies the criterion.

23. The system of claim 21 , wherein the constraint comprises a constraint on a time duration of the time-domain channel response.

24. The system of claim 21 , wherein the constraint comprises a constraint on amplitudes of the time-domain channel response.

25. The system of claim 21 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion based on the reconstructed frequency-domain channel responses.

26. The system of claim 21 , wherein detecting, in response to each of the error signals satisfying the criterion, the motion of the object in the space based on the set of frequency-domain channel responses comprises detecting the motion of the object based on the set of frequency-domain channel responses and a set of quality metrics, each of the frequency-domain channel responses corresponding to a respective quality metric of the set of quality metrics.

27. The system of claim 26 , the operations comprising determining, for each frequency-domain channel response, the respective quality metric based on the error signal.

28. The system of claim 26 , wherein the respective quality metric comprises a ratio of a power of the frequency-domain channel response to a power of the error signal.

29. The system of claim 21 , wherein the computer device comprises one of the wireless communication devices.

30. The system of claim 21 , wherein the computer device is remote from the wireless communication devices.