Upload
mete-torun
View
247
Download
0
Embed Size (px)
Citation preview
7/30/2019 Lindmark - Antennas Propagation and MIMO
1/12
1
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
7/30/2019 Lindmark - Antennas Propagation and MIMO
2/12
3
Capacity: Multiple antennas
h11
h22
h12
h2111
nRnT
TX RX
4
1. cont.: MIMO introduction
7/30/2019 Lindmark - Antennas Propagation and MIMO
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!
7/30/2019 Lindmark - Antennas Propagation and MIMO
4/12
7
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)
7/30/2019 Lindmark - Antennas Propagation and MIMO
5/12
9
2 x 2 in free space (3)
10
2. cont.: Free space with angularseparation
h11
h22
h12
h21
1
1
2
2
RX
TX
R
d
2
7/30/2019 Lindmark - Antennas Propagation and MIMO
6/12
11
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.)
7/30/2019 Lindmark - Antennas Propagation and MIMO
7/12
13
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
14
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
7/30/2019 Lindmark - Antennas Propagation and MIMO
8/12
15
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
7/30/2019 Lindmark - Antennas Propagation and MIMO
9/12
17
Measurement route, 4th floor
north hallway 41
south hallway 48
TX
18
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.
7/30/2019 Lindmark - Antennas Propagation and MIMO
10/12
19
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!
20
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
7/30/2019 Lindmark - Antennas Propagation and MIMO
11/12
21
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
22
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
7/30/2019 Lindmark - Antennas Propagation and MIMO
12/12
23
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
12
14
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
24
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.