Cybersecurity Electronic and Communication Systems MIMO

Dip. Ingegneria dell’Informazione, Univ. Pisa, Pisa, Italy

MIMO & 5G Cellular Communications

Marco [email protected]

Cybersecurity

Electronic and Communication Systems

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Marco LuiseMIMO & 5G Cellular Communications

2

Dip. Ingegneria dell’Informazione

University of Pisa, Pisa, Italy

Multiantenna Systems 1: Reception Diversity

TX RX

• 1 transmitting antenna• 2 receiving antennas with

combining• No increase in bit-rate•DIVERSITY Gain = 3 dB

( ) ( ) ( )

1 1

m m mr s n= +

( ) ( ) ( )

2 2

m m mr s n= +

( )ks

( ) ( ) ( ) ( )( ) ( ) ( ) ( )1 2 1 2

2 2

+ += = + = +

m m m mm m m mr r n n

z s s n

At time mT…

( )mz

The noise variance is reduced by a factor 2

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Multiantenna Systems 2: Independent Channels

TX RX

• 2 transmittingantennas

• 2 receiving antennas• No mutual interference• No diversity gain•MULTIPLEXING GAIN x 2

The bit-rate is DOUBLED

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4



MIMO Channel Modeling

TX RX

2 x 2 simple example with narrowband signals on a

frequency-flat channel at time mT, neglecting noise

(1)

ms

(2)

ms

(1)

mr

(2)

mr

11h

22h

21h

12h

The terms hij are just complex coefficients that modify the amplitude/phase of the transmitted symbols because the channel is non-frequency-selective !

( ) ( ) ( )

1 11 1 12 2

( ) ( ) ( )

2 21 1 22 2

m m m

m m m

r h s h s

r h s h s

= +

= +

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MIMO-OFDM 1/2

How can we possibly havea narrowband channel at the high signaling rates of modern communications?

( ) ( ) ( )

1 11 1 12 2

( ) ( ) ( )

2 21 1 22 2

m m m

m m m

r h s h s

r h s h s

= +

= +

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MIMO-OFDM 2/2

The flat MIMO channel isactually experienced on each single frequency

k/TMC of the subcarriersraster in OFDM

communications !

( ) ( ) ( )

1, 11 1, 12 2,

( ) ( ) ( )

2, 21 1, 22 2,

0,..., 1

= +

= −

= +

m m m

k k k

MC MC

m m m

k k k

MC MC

k kr H s H s

T Tk N

k kr H s H s

T T

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General MIMO (Multiantenna) System

TX RX

H• NT transmitting antennas• NR receiving antennas• low-rate channels with

flat-fading• NR x NT channel matrix H

NTNR

The channels are “different” in SPACE

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The complex-valued MIMO channel at time m

m m m= +r Hs w

( )

1

( )

2

( )

R

m

m

m

m

N

r

r

r

=

r

( )

1

( )

2

( )

T

m

m

m

m

N

s

s

s

=

s

Transmitted symbols vector Received (soft) symbols vector

( )

1

( )

2

( )

R

m

m

m

m

N

w

w

w

=

w

White noise vector

11 1

1

T

R R T

N

N N N

h h

h h

=

H

ChannelMatrix

• Independent (equi-power Rayleigh) Channels

• Spatially White equi-power noise

• Stationary channel(long coherencetime)

TX RX

H

NTNR

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Simple Examples

• Diagonal matrix (NR=NT): independent channels, max. multiplexing gain, no diversity gain

• NR x 1 matrix: conventional diversity reception, max. diversity gain, no multiplexing gain

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MIMO Reception (spatial MUX)

m m m= +r Hs w

( )

1

( )

2

( )

R

k

k

k

k

N

r

r

r

=

r

( )

1

( )

2

( )

T

k

k

k

k

N

s

s

s

=

s

TX RX

H

NTNR

( )1 1 1ˆ ˆ ˆ− − − = = + = + = +m m m m m m m mz H r H Hs w s H w s w

•Need to know the channel matrix H

• H has to be non-singular•Possible noise enhancement→need to reduce constellation size

T RN N=

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The MIMO Channel

• DIVERSITY gain by combination of multiple RX copies of the same signal with independent noise components(improves SNR)

• MULTIPLEXING gain by using multiple independentchannels with multiple TX/RX antennas (improves rate) but increases noise and increases bit-rate less thanexpected

SNR/Rate relation through capacity theorem

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MIMO Capacity – Perfect CSI and Feedback Info 1/4

Compute the SVD of H:†=H UDV

=NR

NT

0

0

NT

Unitary Matrix

Unitary

Matrix

are the NT and the channels are DECOUPLED †eigen( )HH

†

RN=UU I

NR >NT

NR

†

TN=VV I

, uplink-like

H D

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† † )(m m m m m m m m m= + = + = + = +U U UV VD D Dr Hs w s w s w s w

I am left with an equivalent set of NT independent (parallel) channels whose capacity is evaluated via the Shannon formula for

the AWGN channel

( )† †

m m m m m m = = + = +r r s Dw sDU U wU

and also

( ) ( ) ( ) , 1,..., = + =m m m

i i i i Tr d s w i N

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S/P P/SV †U

1 0

0TN

d

D

d

=

If we want to actually “exploit” such parallel channels, we have to pre-code sm by V

before transmitting, and then post-process rm by U disregarding the excess NR-NT

useless channels

†=H UDV

sm

rm

†

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2 2

2 2 21

log 1 , .

=

= + + =

TN

k kk

k k

d PC P const

d

Now, if the TX has knowledge of D then it can i) allocate different power on the different “virtual channels”, and ii) allocate it in an optimal fashion by WATER FILLING !

(independent channels)

S/P

sm

1P

TNP

1

TN

k TOT

k

P P=

=

Constraint:

V

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MIMO Capacity – Perfect RX CSI & no TX Feedback

2 2

2 22 21 1

log 1 log 1 = =

= + = +

TT NN

k TOT k TOT

k kT T

d P d PC

N N

Cannot do water-filling – I just distribute power evenly, Pk=PTOT/NT:

22 † †

2 2eigen ( ) 1 eigen

= + = +

T

k TOT TOTk k k N

T T

d P Pd

N NHH I HH

BUT

† †

2 22 21

log eigen log det =

= + = +

T

T T

N

TOT TOTk N N

k T T

P PC

N NI HH I HH

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Ergodic MIMO Capacity (Telatar)

The entries hij of channel matrix are actually

ZERO-MEAN GAUSSIAN (Rayleigh Fading) independent of each other

What we have computed up to now has to be averaged over the channel realizations:

†

2 min( , ) 2E log det

= +

R TE N N

T

PC

NH I HH

†

2 2log det

= +

T

TOTN

T

PC

NI HH

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An Example (Schlegel)

•vmobile = 50 km/h - mobile

receiver speed

•Ts = 1 ms – sampling

time

•R = 50 m - radius of

circle containing the

scatterers

•L = 2 km – separation

of TX and RX

•d = 5l - separation of

antenna elements

•f0 = 2.4GHz - carrier

frequency

•Es/N0 = 10dB - symbol

signal to noise ratio

2 x 2

8 x 8

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Time-, Space-, and Space-Time coding

COD/MOD

DEM/DEC

S/P P/SH

TX RX

Redundant (parity-check symbols) can be added in time (interleaved with information symbols), in space, by multiplexing them on the TX antennas with

information symbols, or BOTH: space-time codes.

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Space-Time Block Codes

ST

EncoderST

DecoderS/P P/S

H

= +R HS W

( ) 2 ( ) 2 2| | 1 , | | 2m m

i iE s E w = = =

(1) (2) ( )

1 1 1

(1) (2) ( )

2 2 2

(1) (2) ( )

T T T

M

M

M

N N N

s s s

s s s

s s s

=

S

TIME

SP

AC

E

Space-TimeCodeword

ksnd kr nz

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(1) (1)*

(1) (2) 1 2

1 2 1 2(1) (1)*

2 12

− = = +

Sd dP

r r h h w wd d

R

The mother-of-all ST Block Codes (Alamouti)

*(1) (1) (2) (1)

1 1 1 2

*(1) (1) (2) (1)

2 2 2 1

s d s d

s d s d

= = − = = =

S

Designed for a NR=1 x NT=2 MIMO system (single RX antenna !!!)Coding rate: 1 in space, ½ in time, overall ½

BUT no bandwdith increase wrt 1 x 1 system with no coding

TX RX

1h

2h2 2

1 2| | | | 2+ =h h

Ps is the TOTAL transmitted power from the two antennas

Variance of noise terms: 2 2 2 2

1 2 02 / = = + =I Q sN T

Unit-power Constellation

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The mother-of-all ST Block Codes (Alamouti)

*(1) (1) (2) (1)

1 1 1 2

*(1) (1) (2) (1)

2 2 2 1

s d s d

s d s d

= = − = = =

S

Received code block:

( ) ( )

(1) (1)*

(1) (2) 1 2

1 2 1 2(1) (1)*

2 1

(1) (1) (1)* (1)*

1 1 2 2 1 1 2 2 1 2

2

2 2

− = = +

= + + − + +

S

S S

d dPr r h h w w

d d

P Ph d h d w h d h d w

R

TX RX

1h

2h

2 2

1 2| | | | 2+ =h h

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Decoding the Alamouti code

The decoder needs (perfect) CSI to compute the sufficient statistics(soft symbols) Z for data detection

( ) ( )

(1) (1(1) (1) * (1)*

1 1 1 2

* *

(1) (1)* 1 2

1 2

2 2 (1)

1 2

) * (1)

2

2 1

*

2 1 2 1 2

2 2 (1)

1 2 21 1 2| | | | | |2

| |2

= = − = −

=

+

+ + +

−

+S S

z r hz r h h r

Ph h d

h r

Ph h d ww

h hr r

h hZ

where

* *

1 1 1 2 2w w h w h = + * *

2 1 2 2 1w w h w h = −

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Decoding the Alamouti code

The decoder needs (perfect) CSI to compute the sufficient statistics(soft symbols) for data detection

(1) (1) * (1)*

1 1

* *

(1) (1)* 1 2(1) (1) * (1)*

2 1 2 1 2

(1)

2 2

1 2 2

(

1 2

2 1

1)

1 122

22

+

= = − = −

=

−

+ + SS

z r h h rz r h h r

P

h hr r

h h

Pwd w d

Z

Where the new noise variances are

( )2 2 2 2 2

1 2 1 2 1 0| | | | 2 2 / = = + = sh h N T

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Where is the gain ?

• The signal power increases by

• The noise power increases by

•There are no CROSS TERMS between channels !

•TWO-FOLD GAIN DIVERSITY (3dB gain) as in a

conventional receive-diversity 2 x 1 system (requires

CSI !)

( )2

2 2

1 2| | | | 4+ =h h

2 2

1 2| | | | 2+ =h h

Can we GENERALIZE?

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With two RX antennas (2 x 2 code)

* * * *

(1) (1) (1) (2)* (1) (2)*11 12 21 22

1 2 1 1 2 2

12 11 22 21

= = − + − − −

Zh h h h

z z r r r rh h h h

(1) (2) (1) (1)*1 1 11 12 1 2

(1) (1)*(1) (2)21 22 2 12 2

2

− = = +

Sr r h h d dP

h h d dr rR W

TIMETIME

SP

AC

ES

PA

CE

Show that we have FOUR-FOLD

diversity gain (but no mux gain)

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MU MIMO / Space-Division Multiple Access (SDMA)

When the number of antennas is much larger than the number of users in the cell, we can also implement Multiple Access/Multiplexing by «synthesizing» multiple beams directed to spatially separated users: Multi-User MIMO (MU-MIMO)

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Massive MIMO

Lead to MASSIVE MIMO (very many antennas at the BTS or AP)

†

2 2E log det

= +

T

TOTE N R T

T

PC N N

NH I H H

†

2 2E log det

= +

R

TOTE N R T

T

PC N N

NH I HH

NT→ (Downlink): MUX gain only

NR→ (Uplink): MUX and DIV gain

† →RT NNHH I

† →TR NNHH I

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Massive MIMO

Lead to MASSIVE MIMO (very many antennas at the BTS or AP)

NT→ (Downlink): MUX gain only

NR→ (Uplink): MUX and DIV gain

2 2log 1

= +

TOTE R

PC N

2 2log 1

/ ( / )

= +

TOTE T

R T

PC N

N N

†

2 2E log det

= +

T

TOTE N R T

T

PC N N

NH I H H

†

2 2E log det

= +

R

TOTE N R T

T

PC N N

NH I HH

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30



Beyond-4G technologies (1/3)

Basics of beyond-4G technologies

Do we really need 5G?

o over 50%/year growth in data traffic

o at least, a 1000× increase every decade

o in 2018, global traffic will reach more

than 1/100 of a zettabyte (1 ZB=1021 B)10

×in

cre

ase

in f

ive

ye

ars

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According to CISCO, mobile data traffic will reach the following milestones within

the next five years:

o monthly global mobile data traffic will

surpass 15 exabytes by 2018

o the number of mobile-connected devices

will exceed the world’s population by 2014

o the average mobile connection speed will surpass 2 Mb/s by 2016

o due to increased usage on smartphones, smartphones will reach 66% of

mobile data traffic by 2018

o tablets will exceed 15% of global mobile data traffic by 2016

o 4G traffic will be more than half of the total mobile traffic by 2018

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33



Technology drivers


o network densitification

o massive MIMO

o mm-wave technology

and many more: full-duplex antennas, spectrum sharing, advanced PHY and

interference management, device-to-device (D2D) communications, etc.

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Network densification (1/3)


Cooper’s “law”: the wireless capacity has doubled every

30 months over the last century in the last fifty years,

capacity has increased about a million times!

5× 5× 25×

1600×

The right path to pursue is

network densification: very

dense deployment of BTSs

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Shannon’s law:

number of antennas

bandwidth

adaptive coding and modulation, interference

management

With extreme network densification, we can reuse Shannon’s law

everywhere, thus increasing the area spectral efficiency (in b/s/Hz/m2)

heterogeneous, multi-tier

dense networks: small cells,

relays, etc.

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Open challenges include:

o self-organization, exacerbated by

random/unplanned deployment of small cells

o coverage and performance predicition:

stochastic geometry and random matrix

theory could serve as powerful tools

o interference management and resource

allocation, also considering the presence of

multiple tiers

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37



Massive MIMO (1/2)


Massive MIMO (a.k.a. as multiuser MIMO) technology:

antennas

(hundreds)

single-

antenna terminals

The massive MIMO concept relies on the law of large numbers, to average

out frequency selectivity and thermal noise:

o spatial multiplexing gain

o array gain

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38



Massive MIMO (2/2)


In the uplink, the BTS:

o acquires CSI from pilot symbols

o detects the information symbols

o since , adopts linear

processing techniques (MRC, ZF,

MMSE), which are nearly optimal

In the downlink, the BTS:

o uses CSI obtained in the uplink

o applies multiuser MIMO precoding,

using low-complexity precoders

o Thanks to the unused degrees of freedom, massive MIMO can obtain:

• hardware-friendly waveform shaping

• PAPR reduction due to multiuser precoding

o The major challenge is getting accurate CSI estimation

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mm-wave technology (1/2)


Increasing the carrier frequency increases the path loss

However, network densification includes small cells with coverage radius

path loss becomes acceptable

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mm-wave technology (2/2)


o mm-waves can provide a brand-new, very wide frequency band, with

very high-gain steerable antennas at both the MS and the BTS sides

o we can augment the currently saturated 700 MHz – 2.5 GHz radio

spectrum, moving to 60 GHz

o due to very low wavelengths, we can

accommodate the antennas required

by massive MIMO

Wireless channel modeling is not valid anymore: research challenges

include new propagation models for mm-wave communications

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MMIMO Antennas

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Structure of the LTE-A frame

4G systems

15=scf kHz

2048 , 847= =vN N

1201 15 18= =RFB MHz

Nominal Channel BW: 20 MHz

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Summary of LTE PHY Parametrs

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New Radio: the Radio Interface of 5G

• CP-OFDM format, both UL and DL, plus SC-FDMA for UL

• QAM constellations up to 256-QAM

• Multiple carrier spacing: Df=2m x 15 kHz, where m=0,1,2,3,4 is the so-callednumerology

• 1 slot=14 OFDM symbols (twice as many as in LTE)

• (I)FFT size 2048 or 4096

Documents

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