Smart antenna arrays - a geometrical explanation of how they work

1. Smart antenna arrays - a geometrical explanation ofhow they work Peter F. Driessen Electrical and Computer Engineering University of Victoria Victoria B.C. Canada www.driessen.ca

2. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

3. Introduction • With multiple antennas at both ends of a radio link, • Channel capacity grows linearly with number of antennas by • sending different messages on each antenna on the same carrier frequency, and • Separating the messages using the multiple antennas at the receiver • 8 antennas yield 8 times the capacity • Generalized “polarity”

4. Introduction (2) • If send same message on each antenna • Then we get only the power gain of the antenna array, and • Capacity grows only logarithmically with the number of antennas • 8 antennas yield 3 times the capacity

5. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

6. Channel capacity nT transmit antennas, nR receive antennas Channel transfer function is a matrix nT x nR of complex scalars

7. Channel capacity Generalized Shannon capacity for matrix channel

8. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

9. Ricean channels

12. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

13. Line of sight • Close antenna spacing • Wide antenna spacing • 3 examples • Narrow-wide spacing • Narrow spacing (constrained to practical size) at one end, • wide spacing at the other end

14. LOS - close antenna spacing (1) All elements have same amplitude and phase (e.g. all equal to 1)

15. LOS - close antenna spacing (2)

16. LOS - wide antenna spacing

18. T1 R1 R2 T2

20. T1 R2 T2 R1

21. Example 3

24. Narrow-wide spacing

27. For large number of array elements , arc = 126 degrees

29. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

30. Street canyon View from above buildings street buildings

31. Capacity in street canyon

33. Ricean channels

35. Capacity calculation H is a combination of LOS matrix of rank depending on geometry plus Rayleigh matrix

36. Minimum capacity, high correlation Large k, and close-spaced antennas Small k, independent Rayleigh, antennas spaced sufficiently for small correlation Maximum capacity, no correlation Large k, and wide-spaced antennas to a specific calculated spacing

40. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

41. System design options Mobile cellular

43. System design options • Fixed wireless • Antennas spaced equally at both ends of link

44. Outline • Introduction • Capacity expressions • Ricean channels • Line-of-sight channels • Specified environments • System design • Summary

45. Summary • Geometric interpretation of multiple antenna systems • Transmitter antenna pattern has nulls on all but one receiver antenna • Thus can have independent channels on the same carrier frequency