Smart antenna arrays a geometrical explanation of how

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

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

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”

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

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

Channel capacity n. T transmit antennas, n. R receive antennas Channel transfer function is a matrix n. T x n. R of complex scalars

Channel capacity Generalized Shannon capacity for matrix channel

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

Ricean channels

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

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

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

LOS - close antenna spacing (2)

LOS - wide antenna spacing

T 1 R 1 T 2 R 2

T 1 R 2 T 2 R 1

Example 3

Narrow-wide spacing

For large number of array elements , arc = 126 degrees

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

Street canyon View from above buildings street buildings

Capacity in street canyon

Ricean channels

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

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

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

System design options Mobile cellular

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

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

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