Lindmark - Antennas Propagation and MIMO

7/30/2019 Lindmark - Antennas Propagation and MIMO

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Introduction to MIMO: Antennas &Propagation aspects

Bjrn Lindmark

1. MIMO capacity basics

2. Physical interpretation of the channel matrix

Example 2 x 2 in free space

3. Free space vs. multipath: when is scattering

beneficial?

4. Measurements of a hallway channel at S3

5. Summary

2

1. MIMO capacity basics


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Capacity: Multiple antennas

h11

h22

h12

h2111

nRnT

TX RX

4

1. cont.: MIMO introduction


3/12

5

6

Graphic representation of MIMOfor n

T= n

R= M

Channel

matrix H

array gainM

array gainM

Mtransmitters,

total powerP0

array gainM

array gainMpowerP0/M

powerP0/M

Alt. 2: MIMOAlt.1 Beamforming on RX

withMelements

array gainMpowerP0

ideally H has full rank representing the

maximum number of signal paths or

channels!

Average SNR at

each receiver is

equal to

Mnumber of parallel single channels with 1/M

of the SNR!


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2. Example: 2 x 2 antennas infree space

h11

h22

h12

h21

11

22

RXTX

R

d

8

2 x 2 in free space (2)


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2 x 2 in free space (3)

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2. cont.: Free space with angularseparation

h11

h22

h12

h21

1

1

2

2

RX

TX

R

d

2


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Free space... (2)

0 20 40 60 80 100 120 140 160 1804

4.5

5

5.5

6

6.5

7

Phase of h12

=h21

[degrees]

MutualinformationC

[bits/Hz/s]

2x2 MIMO, SNR =10 dB for SISO i.e. abs(hij)=1

no csi at TX

perfect csi at TX

12

3. Free space vs. multipath Free space: we have low path loss but also low rank (~1)

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.)


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Free space vs. multipath (2)

MIMO in free space equivalent to SISO with array gain. If we consider e.g. C=10 bits/s/Hz, we can allow 20 dB lower SNR

for the same capacity compared to SISO

If we compare to RX combining, the gain is 15 dB

0 5 10 15 20 25 300

5

10

15

20

25

30

35

Receiver SNR [dB]

MutualinformationC

[bits/Hz/s]

4x4 MIMO, PTX

normalized for given SNR in SISO

SISO LOS

SISO and RX array gain

SISO, RX and TX array gainMIMO 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

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3. cont.: MIMO vs. SISO6 x 6 system, no CSI at TX

Gaussian channel (Rayleigh) in

both cases

A single channel vs. a 6 x 6 ideal

MIMO system with no channel

knowledge at the transmittter. The

TX power in the MIMO system is

divided equally over the 6

transmitters

If we consider a SNR of 10dB inthe MIMO case, a SISO link

would need more than 30 dB

higher power to achieve the same

capacity.

A considerable path loss is thus

acceptable for such a large

system!

-20 -10 0 10 20 30 400

10

20

30

40

50

60

70

80

90

100

Average SNR at the receivers [dB]

Capacity

[bits/Hz] Single channel

6 x 6 MIMO

6 element receive array


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4. Measurements of a hallwayat S3

Indoor measurements at S3

part of ACE WP 2.3 Task 5

Thanks to Laura Garcia and

Niklas Jaldn for

measurement setup and

analysis!!!

frequency = 1766 MHz

TX: 2 slant +/-45 polarized

antennas

RX: 4 monopole antennas,

/2 spacing

Distance: 4 - 48 m

16

Measurement equipment and

hallway

RX cart, calibrating

researcher, and TX cart!

View from TX

position heading

west along hallway


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Measurement route, 4th floor

north hallway 41

south hallway 48

TX

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Propagation in the northhallway: Path loss & capacity

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

18Capacity for mean(SNR) =10 dB

time [s]

M

utua

linforma

tion

C

[bits

/Hz

/s]

no CSI at TX

perfect CSI at TX (w.f.)

0 10 20 30 40 50 60-100

-90

-80

-70

-60

-50

-40

-30

channel coeff. h11

, h12

,.. and mean power (solid black)

time [s]

h11,...,

h44

[dB]

The received signal from TX1-4 shows uncorrelated fading

Capacity very correlated to the path loss as expected!

Note the diversity effect on capacity; almost no effect of fading.


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North hallway: Channel rank &capacity

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1normalized singular values of H

time [s]

1/1

2/1

3/1

3/1

0 10 20 30 40 50 605

6

7

8

9

10

11

12

13Capacity at SNR = 10

time [s]

Mu

tua

linforma

tion

C

[bits

/Hz

/s]

no CSI at TX

perfect CSI (w.f.)

no CSI i.i.d

Judging from singular values, capacity seems to increase at~32s (hallway junction) but in reality it decreases (previousslide) due to lower RX power!

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South hallway:Channel coefficients

0 10 20 30 40 50 60-100

-90

-80

-70

-60

-50

-40

-30

channel coeff. h11

, h12

,.. and mean power

time [s]

h11,...,

h44

[dB]

south

hallway

48

TX


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South hallway: Channel rank& capacity

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1normalized singular values of H

time [s]

1/1

2/1

3/1

4/1

0 10 20 30 40 50 605

6

7

8

9

10

11

12

13Capacity at SNR = 10

Mu

tua

linforma

tion

C

[bits

/Hz

/s]

time [s]

no CSI at TX

perfect CSI at TX

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Hallway MIMO vs. Free Space Consider the north hallway with ~LOS along the whole route.

We normalize |h11|, ..., |h44| to 1 at the minimum distancex = 4 m.

We also define a normalized free space coefficient h0.

Question: Is MIMO in the hallway better than free space?

0 5 10 15 20 25 30 35 40 45 50 55-50

-40

-30

-20

-10

0

10

Distance [m]

coee

ficien

t[dB]

Normalized channel coefficients in north hallway

h11

h21

h31

h41

h0

(free space)

TX


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Hallway MIMO vs. Free Space (2)

MIMO in the hallway typically outperforms SISO and RX combing

(no CSI) in free space!

0 10 20 30 40 50 60

0

1

2

3

4

5

6

7

8

9Hallway MIMO vs. free space (LOS), SNR =10 dB at x =4 m

Distance [m]

Mu

tua

linforma

tion

C

[bits

/Hz

/s]

MIMO in hallway

MIMO in free spaceMIMO with CSI in hallway

MIMO with CSI in free space

SISO in free space

0 10 20 30 40 50 60

0

2

4

6

8

10

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Distance [m]

Mu

tua

linforma

tion

C

[bits

/Hz

/s]

Hallway MIMO vs. free space (LOS), SNR =30 dB at x =4 m

MIMO in hallway

MIMO in free space

MIMO with CSI in hallwayMIMO with CSI in free space

SISO in free space

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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 = 10 is in theory

equivalent to a SISO system with SNR = 30 dB.

Measured data in the S3 department confirm that

MIMO in a suitable environment is equivalent to SISOor RX combining in free space.

Documents

Lindmark - Antennas Propagation and MIMO