1. January 2006
doc.: IEEE /0006r0
Impact of limited signal bandwidth on echo location and resolution using the Vernier process
Authors:
Abstract
Verification of the impact of the signal bandwidth on echo location and resolution for a given WRAN signal bandwidth: 5.63 MHz. Confirmation of the Nyquist limit.
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Gerald Chouinard, CRC
Gerald Chouinard, CRC

2. The 802.22 Vernier process doc.: IEEE 802.22-06/0006r0 January 2006
Gerald Chouinard, CRC
Gerald Chouinard, CRC

3. The 802.22 Vernier process doc.: IEEE 802.22-06/0006r0 January 2006
Gerald Chouinard, CRC
Gerald Chouinard, CRC

4. Impact of signal bandwidth limitation on resolving closely spaced echoes
(The curse of Nyquist!)
Echo 1: 0 dB, Echo 2: 0 dB
Echo 2 brought progressively closer to echo 1
Gerald Chouinard, CRC

5. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

6. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

7. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

8. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

9. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

10. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

11. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

12. Impact of limited BW on echo location and resolution
Nyquist limit
Gerald Chouinard, CRC

13. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

14. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

15. Impact of signal bandwidth limitation on resolving closely spaced echoes
Echo delay (m)
(The curse of Nyquist!)
100
200
300
400
500
Nyquist= 1/BW 20
Echo 1: 0 dB, Echo 2: 0 dB
Echo 2 brought progressively closer to echo 1
Figure shows the drift in delay between the echoes 1 and 2 considered separately and the combination of the two echoes as they are brought closer together. 10
Distance error (m)
-10
-20
Gerald Chouinard, CRC

16. Impact of signal bandwidth limitation on resolving closely spaced echoes
(The curse of Nyquist!)
Echo 1: -7 dB, Echo 2: 0 dB
Echo 2 brought progressively closer to echo 1
Gerald Chouinard, CRC

17. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

18. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

19. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

20. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

21. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

22. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

23. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

24. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

25. Impact of limited BW on echo location and resolution
Nyquist limit
Gerald Chouinard, CRC

26. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

27. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

28. Impact of limited BW on echo location and resolution
Gerald Chouinard, CRC

29. Impact of signal bandwidth limitation on resolving closely spaced echoes
Echo delay (m)
(The curse of Nyquist!)
100
200
300
400
500
Nyquist= 1/BW 20
Echo 1: -7 dB, Echo 2: 0 dB
Echo 2 brought progressively closer to echo 1
Figure shows the drift in delay between the echoes 1 and 2 considered separately and the combination of the two echoes as they are brought closer together. 10
Distance error (m)
-10
-20
Gerald Chouinard, CRC

30. January 2006
doc.: IEEE /0006r0
Conclusion
The Nyquist limit for defining the maximum resolution of a system to distinguish between closely spaced specular echoes has been confirmed by the simulation exercise reported in this presentation.
For the 6 MHz version of the WRAN systems, the Nyquist limit is:
Resolution limit= 1/BW = 1/5.63 MHz = ns = m
This Nyquist limit is found to be somewhat optimistic since it is not sure that echoes can be resolve reliably slightly above that limit, especially if the two echoes are not of the same amplitude.
Echoes tend to try to stay apart as much as possible until they get too close and then they quickly collapse into one undistinguishable echo.
The drift of these echoes apart from each other can be found deterministically for simple specular echoes for given amplitude differences and can be used to correct for the timing drift to come up with the right echo timing location relative to the receiver time reference to carry out fine ranging, until the two echoes get too close and collapse into only one echo where fine ranging is no longer possible.
Gerald Chouinard, CRC
Gerald Chouinard, CRC

31. January 2006
doc.: IEEE /0006r0
References
IEEE Std TM, Standard for Wireless Regional Area Networks— Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Policies and procedures for operation in the TV Bands, July 2011
_OFDM-based Terrestrial Geolocation.ppt
Multicarrier ranging.ppt
Echo resolution simulation results
Gerald Chouinard, CRC
Gerald Chouinard, CRC