1. MIMO capacity basics

Transcription

1 Introduction to MIMO: Antennas & Propagation aspects Björn Lindmark. MIMO capacity basics. Physical interpretation of the channel matrix Example x in free space 3. Free space vs. multipath: when is scattering beneficial? 4. Measurements of a hallway channel at S3 5. Summary. MIMO capacity basics

2 Capacity: Multiple antennas TX h h h RX n T h n R 3. cont.: MIMO introduction 4

3 5 Graphic representation of MIMO for n T = n R = M M transmitters, total power P Channel matrix H Average SNR at each receiver is equal to ρ ideally H has full rank representing the maximum number of signal paths or channels! power P Alt. Beamforming on RX with M elements array gain M power P /M power P /M Alt. : MIMO array gain M array gain M array gain M array gain M M number of parallel single channels with /M of the SNR! 3

4 . Example: x antennas in free space TX h h RX d h h R 7 x in free space () 4

5 x in free space (3) 9. cont.: Free space with angular separation h d TX φ h h RX R h 5

6 Free space... () 7.5 x MIMO, SNR = db for SISO i.e. abs(h ij )= no csi at TX perfect csi at TX Phase of h = h [degrees] 3. Free space vs. multipath Free space: we have low path loss but also low rank (~) Multi-path: higher rank but also increased path loss. Where is the point of break-even? We will consider a 4 x 4 antenna case and compare: SISO link in free space (Line Of Sight) SISO with array gain MIMO in LOS MIMO with optimal multipath environment: identical independent (complex Gaussian) distribution (i.i.d.)

7 Free space vs. multipath () x4 MIMO, P TX normalized for given SNR in SISO SISO LOS SISO and RX array gain SISO, RX and TX array gain MIMO LOS no CSI at TX MIMO LOS, perfect CSI at TX MIMO i.i.d., no CSI at TX MIMO i.i.d., perfect CSI at TX Receiver SNR ρ [db] MIMO in free space equivalent to SISO with array gain. If we consider e.g. C= bits/s/hz, we can allow db lower SNR for the same capacity compared to SISO If we compare to RX combining, the gain is 5 db 3 3. cont.: MIMO vs. SISO x system, no CSI at TX Gaussian channel (Rayleigh) in both cases A single channel vs. a x ideal MIMO system with no channel knowledge at the transmittter. The TX power in the MIMO system is divided equally over the transmitters If we consider a SNR of db in the MIMO case, a SISO link would need more than 3 db higher power to achieve the same capacity. A considerable path loss is thus acceptable for such a large system! Capacity [bits/hz] Single channel x MIMO element receive array Average SNR at the receivers [db] 4 7

8 4. Measurements of a hallway at S3 Indoor measurements at S3 part of ACE WP.3 Task 5 Thanks to Laura Garcia and Niklas Jaldén for measurement setup and analysis!!! frequency = 7 MHz TX: slant +/-45 polarized antennas RX: 4 monopole antennas, λ/ spacing Distance: 4-4 m 5 Measurement equipment and hallway RX cart, calibrating researcher, and TX cart! View from TX position heading west along hallway

9 Measurement route, 4th floor north hallway 4 TX south hallway 4 7 Propagation in the north hallway: Path loss & capacity -3 channel coeff. h, h,.. and mean power (solid black) Capacity for mean(snr) = db h,..., h 44 [db] no CSI at TX perfect CSI at TX (w.f.) The received signal from TX-4 shows uncorrelated fading Capacity very correlated to the path loss as expected! Note the diversity effect on capacity; almost no effect of fading. 9

10 North hallway: Channel rank & capacity normalized singular values of H 3 Capacity at SNR = σ /σ σ /σ σ 3 /σ σ 3 /σ 9 7 no CSI at TX perfect CSI (w.f.) no CSI i.i.d Judging from singular values, capacity seems to increase at ~3s (hallway junction) but in reality it decreases (previous slide) due to lower RX power! 9 South hallway: Channel coefficients -3 channel coeff. h, h,.. and mean power -4 TX h,..., h 44 [db] south hallway

11 South hallway: Channel rank & capacity.9. normalized singular values of H 3 Capacity at SNR = no CSI at TX perfect CSI at TX σ /σ σ /σ σ 3 /σ 9 7. σ 4 /σ Hallway MIMO vs. Free Space Consider the north hallway with ~LOS along the whole route. We normalize h,..., h 44 to at the minimum distance x = 4 m. We also define a normalized free space coefficient h. Question: Is MIMO in the hallway better than free space? Normalized channel coefficients in north hallway TX coeeficient [db] h h h 3 h 4 h (free space) Distance [m]

12 Hallway MIMO vs. Free Space () Hallway MIMO vs. free space (LOS), SNR = db at x = 4 m MIMO in hallway MIMO in free space MIMO with CSI in hallway MIMO with CSI in free space SISO in free space 4 4 Hallway MIMO vs. free space (LOS), SNR = 3 db at x = 4 m MIMO in hallway MIMO in free space MIMO with CSI in hallway MIMO with CSI in free space SISO in free space Distance [m] Distance [m] MIMO in the hallway typically outperforms SISO and RX combing (no CSI) in free space! 3 Summary MIMO can be interpreted physically only for very simple cases In general, both the power and the singular values of the channel matrix determines the capacity A 4 x 4 MIMO system may with SNR = is in theory equivalent to a SISO system with SNR = 3 db. Measured data in the S3 department confirm that MIMO in a suitable environment is equivalent to SISO or RX combining in free space. 4