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Topic: Massive MIMO
Prof. Dr. Wolfgang Utschick
Technische Universität München
MOOC @ TU9
Week 3
Digital Engineering: From Advanced Physical Layer
Technologies in 5G to Secure Services
Mon 03 Nov 2014
Chair of Signal Processing Methods Technische Universität München
Today’s Agenda
◮ Wireless communications suffers from attenuation and
interference
◮ Multiple antenna systems (MIMO) are a well-known
solution against
◮ Massive MIMO promises additional advantages over
standard solutions
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 2
Chair of Signal Processing Methods Technische Universität München
Physical Wireless Communication Link: SISO
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 3
Chair of Signal Processing Methods Technische Universität München
Physical Wireless Communication Link: SISO
sig
nal
str
en
gth
-80dB
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 3
Chair of Signal Processing Methods Technische Universität München
MISO
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 4
Chair of Signal Processing Methods Technische Universität München
MISO
x1
h1
x2h2
x3h3
x4 h4
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 4
Chair of Signal Processing Methods Technische Universität München
MISO
x1
h1
x2h2
x3h3
x4 h4
Transmission Model (baseband representation)
y =
4∑
m=1
hmxm + n = hTx+ n, hm ∈ C
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 4
Chair of Signal Processing Methods Technische Universität München
Beamforming
x1w1
h1
x2w2
h2
x3w3
h3
x4w4
h4
s
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 5
Chair of Signal Processing Methods Technische Universität München
Beamforming
x1w1
x2w2
x3w3
x4w4
s
Received Signal (baseband rep.)
y =hTh∗
‖h‖s+ n = ‖h‖s+ n
Matched Filter
w =h∗
‖h‖
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 5
Chair of Signal Processing Methods Technische Universität München
Array Gain
Matched filter
w =h∗
‖h‖
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 6
Chair of Signal Processing Methods Technische Universität München
Array Gain
Matched filter
w =h∗
‖h‖
Received Signal (baseband rep.)
y =hTh∗
‖h‖s+ n = ‖h‖s+ n
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 6
Chair of Signal Processing Methods Technische Universität München
Array Gain
Matched filter
w =h∗
‖h‖
Received Signal (baseband rep.)
y =hTh∗
‖h‖s+ n = ‖h‖s+ n
SNR =‖h‖2σ2
s
σ2n
∝ M
M ≡ number of antenna elements
σ2s (σ2
n) ≡ signal (noise) variance
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 6
Chair of Signal Processing Methods Technische Universität München
Multi-User MISO (−→ MIMO)
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 7
Chair of Signal Processing Methods Technische Universität München
Multi-User MISO (−→ MIMO)
h1
h2
h3
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 7
Chair of Signal Processing Methods Technische Universität München
Multi-User MISO (−→ MIMO)
h1
h2
h3
Received Signal (baseband rep.)
yi = hT
i x+ ni, x =
K∑
i=1
h∗i
‖hi‖si
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 7
Chair of Signal Processing Methods Technische Universität München
Multi-User Transmission
Beamforming
yi = ‖hi‖si +
K∑
j=1
j 6=i
hTi h
∗j
‖hj‖sj + ni
useful signal interference
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 8
Chair of Signal Processing Methods Technische Universität München
Multi-User Transmission
Beamforming
yi = ‖hi‖si +
K∑
j=1
j 6=i
hTi h
∗j
‖hj‖sj + ni
useful signal interference
Received Signal (baseband rep.)
SNRi =‖hi‖
2σ2si
σ2
ni
→ SINRi =‖hi‖
2σ2si
K∑
j=1
j 6=i
|hTi h
∗j |2
‖hj‖2σ2
sj+ σ2
ni
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 8
Chair of Signal Processing Methods Technische Universität München
Massive MIMO
◮ Large number of base station antennas
◮ M ≫ K
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 9
Chair of Signal Processing Methods Technische Universität München
Benefits
Array Gain
M
SNR
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 10
Chair of Signal Processing Methods Technische Universität München
Benefits
Array Gain
M
SNR
Asymptotic Orthogonality
hH
i hj
M→ 0 ⇒ SINR → SNR
◮ Robust and simple signal processing methods
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 10
Chair of Signal Processing Methods Technische Universität München
Task of the Week
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Chair of Signal Processing Methods Technische Universität München
Channel State Information (CSI) Acquisition
Uplink Training
h = h + n
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 12
Chair of Signal Processing Methods Technische Universität München
Channel State Information (CSI) Acquisition
Uplink Training
h = h+hI + n
Pilot-Contamination
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 12
Chair of Signal Processing Methods Technische Universität München
Questions
◮ What is the impact of Pilot Contamination (PC) on the
downlink communication mode?
◮ What kind of Countermeasures (against PC) could be
thought of?
◮ Hint: Compute the SINR at the i-th receiver based on the
erroneous channel vector estimates
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 13
Chair of Signal Processing Methods Technische Universität München
Appendix
◮ SISO stands for Single-Input Single-Output and – in the
context of wireless communications – refers to a single
antenna element at the transmitter and a single antenna
element at the receiver side of a communication link
◮ MISO stands for Multiple-Input Single-Output
◮ MIMO stands for Multiple-Input Multiple-Output where
the multiple antenna elements at the receiver side are
either deployed at a single receiver or distributed among
multiple receivers
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 14
Chair of Signal Processing Methods Technische Universität München
Appendix (cont’d)
◮ M is the number of antenna elements at the transmitter◮ K is the number of receivers◮ si is the dedicated signal for the i-th receiver◮ wi is the weight at the i-th antenna element of the
transmitter (in case K = 1)◮ wi is the weight vector (beamformer) at the transmitter
dedicated to the i-th receiver (in case K > 1)◮ wi consists of the weights wi,1, wi,2, . . . , wi,M where wi,m is
the m-th weight of the i-th beamformer◮ xi is the transmitted signal from the i-th antenna element at
the transmitter◮ x is the transmitted signal vector◮ ni is the noise at the i-th receiver◮ yi is the received signal at the i-th receiver
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 15
Chair of Signal Processing Methods Technische Universität München
Appendix (cont’d)
◮ hi is the channel coefficient from the i-th antenna element
at the transmitter to the single receiver (in case K = 1)◮ hi is the channel vector from the transmitter unit to the i-th
receiver (in case K > 1)◮ hi consists of the channel coefficients hi,1, hi,2, . . . , hi,M
where hi,m is the channel coefficient between the m-th
antenna element at the transmitter and the i-th receiver◮ hi is an estimate of the channel vector hi
◮ hI,i is the distortion of the estimated channel vector due to
pilot contamination◮ σ2
siand σ2
niare the variances of signal si and noise ni
◮ SNR is the Signal-to-Noise Ratio◮ SINR is the Signal-to-Interference-and-Noise Ratio◮ h
T is the transposed vector h, ‖h‖ is the norm (length) of
h, and h∗ is the conjugate complex vector h
Technische Universität München – Chair of Signal Processing MethodsTechnische Universität München 16