topic: massive mimo - [email protected]/.../uploads/2014/11/slides_task_massive_mimo.pdf ·...

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


Physical Wireless Communication Link: SISO



Physical Wireless Communication Link: SISO

sig

nal

str

en

gth

-80dB



MISO



MISO

x1

h1

x2h2

x3h3

x4 h4



MISO

x1

h1

x2h2

x3h3

x4 h4

Transmission Model (baseband representation)

y =

4∑

m=1

hmxm + n = hTx+ n, hm ∈ C



Beamforming

x1w1

h1

x2w2

h2

x3w3

h3

x4w4

h4

s



Beamforming

x1w1

x2w2

x3w3

x4w4

s

Received Signal (baseband rep.)

y =hTh∗

‖h‖s+ n = ‖h‖s+ n

Matched Filter

w =h∗

‖h‖



Array Gain

Matched filter

w =h∗

‖h‖



Array Gain

Matched filter

w =h∗

‖h‖


y =hTh∗

‖h‖s+ n = ‖h‖s+ n



Array Gain

Matched filter

w =h∗

‖h‖


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



Multi-User MISO (−→ MIMO)




h1

h2

h3




h1

h2

h3


yi = hT

i x+ ni, x =

K∑

i=1

h∗i

‖hi‖si



Multi-User Transmission

Beamforming

yi = ‖hi‖si +

K∑

j=1

j 6=i

hTi h

∗j

‖hj‖sj + ni

useful signal interference



Multi-User Transmission

Beamforming

yi = ‖hi‖si +

K∑

j=1

j 6=i

hTi h

∗j

‖hj‖sj + ni

useful signal interference


SNRi =‖hi‖

2σ2si

σ2

ni

→ SINRi =‖hi‖

2σ2si

K∑

j=1

j 6=i

|hTi h

∗j |2

‖hj‖2σ2

sj+ σ2

ni



Massive MIMO

◮ Large number of base station antennas

◮ M ≫ K



Benefits

Array Gain

M

SNR



Benefits

Array Gain

M

SNR

Asymptotic Orthogonality

hH

i hj

M→ 0 ⇒ SINR → SNR

◮ Robust and simple signal processing methods



Task of the Week



Channel State Information (CSI) Acquisition

Uplink Training

h = h + n



Channel State Information (CSI) Acquisition

Uplink Training

h = h+hI + n

Pilot-Contamination



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



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



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



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


topic: massive mimo - [email protected]/.../uploads/2014/11/slides_task_massive_mimo.pdf ·...

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