MIMO Communications Lecture1

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Forschungszentrum Telekommunikation Wien[Telecommunications Research Center Vienna]

MIMO Communications (389.094)

Lecture 1

Maxime Guillaud, Erwin Riegler

October 9, 2008



MIMO Communications

Lecturers

Maxime Guillaud {[email protected]}Erwin Riegler {[email protected]}

from FTW (Telecommunications Research Center Vienna)http://www.ftw.at/

Webpagehttp://userver.ftw.at/˜guillaud/MIMO_course/mimo_course.html

Grading - Written exam at the end of the winter term

Lecture notes: Hardcopy of the slides handed out at thebeginning of each lecture

Time: Thursdays 17:00h-18:30h, Room CG 0118..

October 9, 2008 Maxime Guillaud, Erwin Riegler 2

http://www.ftw.at/

http://userver.ftw.at/~guillaud/MIMO_course/mimo_course.html

http://userver.ftw.at/~guillaud/MIMO_course/mimo_course.html

http://www.ftw.at/



Reference Books

Fundamentals of Wireless Communications , D. Tse and P.Visvanath, Cambridge University Press, 2005. Available onlineat http://www.eecs.berkeley.edu/˜dtse/book.html

MIMO Wireless Communications , E. Biglieri, R. Calderbank, A.Constantinides, A. Goldsmith, A. Paulraj, H.V. Poor, CambridgeUniversity Press, 2007.

MIMO Wireless Communications , C. Oestges, B. Clerckx,

Academic Press, 2007.


http://www.eecs.berkeley.edu/~dtse/book.html

http://www.eecs.berkeley.edu/~dtse/book.html



Outline (1)

Fundamentals

Electromagnetic wave propagation and channel models

MIMO channel and signal models

Tools from information theory

Coding theory, capacityImportance of channel knowledge

Channel fading

Frequency-selective channels, time-variant channels

Space-time codingDiversity and multiplexing

Receiver architecture and algorithms

Multi-user systems




Outline (2)

Applications

UMTS with MIMO enhancements in Release 7 andLong-Term Evolution

Wireless LAN according to IEEE 802.11n

WiMAX 802.16




A General Point-to-Point

Communication System

Transmitter ReceiverChannel(Tx) (Rx)

- --

Message

Message ?

The engineer seek to design the Tx and Rx so that themessage is transmitted with a prescribed reliability

We have no control over the behaviour of the channel – but

it is a good idea to know it well and to adapt Tx and Rx to it




Multiple-Input Multiple-Output (MIMO)

Communications

RxTx H

.

.

.

.

.

.




Benefits of Multiple Antennas

Energy efficiency (array gain): Signal to thermal noise ratio is

improved. Increased coverage.

Error rate reduction (diversity gain): Mitigates fading throughspatial diversity.

Spectral efficiency (multiplexing gain): Increased bits/channel

access (bpca) rate.

6

-Spectral

Error rate

Energy

reduction

efficiency

efficiency

Interference reduction: Improve the reuse factor in multi-userscenarios.




Obstacles to MIMO Implementations

Hardware costs: Multiple antennas mean multiple RF chains.

Hardware costs: More involved signal processing requiresmore computing power (and energy).

Portable consumer devices are especially sensitive to costarguments.




General Model of the Wireless

Propagation Channel

TxRx

-

3z

-

kpath 1 (LOS)

path 2

path 3

scatterers

U

Received signal contains multiple copies of the transmittedsignals, at different delays (τ l ) and attenuations (ηl ),correponding to different paths of the electromagnetic waves.

The straightest path (when it is not obstructed) is called

Line-of-Sight (LOS)October 9, 2008 Maxime Guillaud, Erwin Riegler 10



Some figures...

Absolute delay due to the propagation between Tx and Rx isrelated to the speed of light c = 2.9979× 108m.s−1 (in theair:2.9970× 108m.s−1)

Current-generation telephone systems (UMTS) transmit3.84 × 106 symbols per second

The symbol duration T s = 13.84×106 is equivalent to the time that

the electromagnetic waves propagates for T s c ≈ 78m

In general, this means that the various copies of the transmitted

signal will overlap with the next symbols

Classically modeled by a tapped delay line




SISO Channel Representation

Transmitted signal: baseband complex signal s b (t ) is modulating

a carrier of frequency f c

s (t ) = Re[s b (t )e j2πf c t ] .

Example for UMTS: s b has 5 MHz bandwidth,f c = 1.8GHz, 1.9GHz, 2.1GHz

Received signal is the superposition of L paths and noise(thermal noise and interference from other transmitters)

x (t ) = Re[L−1=0

ηs b (t − τ ) r b (t )

e j2πf c t ] + n (t )

r b (t ): baseband complex received signal




SISO Tapped Delay Line Model

The previous expressions can be simplified by using anequivalent baseband model

Introduce the impulse response function

h (τ ) =L−1

=0

ηδ(τ − τ

)

At the baseband level, the effect of the channel is a convolutionof s b (t ) with a time-variant filter h (τ ):

r b (t ) = +∞τ =−∞

s b (t − τ )h (τ )dτ + n b (t ) =L−

1=0

ηs b (t − τ ) + n b (t )

n b (t ) is the bandlimited version of the noise term n (t )




Some remarks

The previous model is missing the following features

Time dependency: h (t , τ ) instead of h (τ ) (τ and η changewhen the relative position of Tx, scatterer , and Rx changes)

r b (t ) =

+∞τ =−∞

s b (t − τ )h (t , τ )dτ + n b (t )

Multiple antennas at the transmitter and/or receiver !




Convolution with Time-Variant Channel

6

-τ

h (

t , ·)

6

-

τ

h (t + T s , ·)

6

-τ

h (t + 2T s , ·)

s (t )·

+s (t + T s )·

+s (t + 2T s )·

-

6

t




Several effects at work (I)

Frequency Selectivity

h (t , τ ) is an impulse response in the “lag” domain (τ ) (there areτ 1, τ 2 . . . for which h (t , τ 1) = 0 and h (t , τ 2) = 0 . . .)

The maximum delay between paths (τ max − τ min ) is the delay spread .

Equivalently, the representation of h (t , ·) in the frequency

domain h̃ (t , f ) is not constant for all f .

The width (in f ) over which it can be assumed constant is thecoherence bandwidth.




Several effects at work (II)

Temporal Variation

h (t , τ ) depends on t

The maximum time ∆t over which the channel can be assumedconstant (h (t , τ ) ≈ h (t + ∆t , τ )) is the coherence time.

Equivalently, the representation of h (·, τ ) in the (Doppler)

frequency domain h̃ (f d , τ ) has energy in non-zero frequencies

(h̃

(f 1, τ ) = 0 for f 1 = 0).




Time-Selective Fading - Doppler Effect

A stationary EM field of frequency f c

is periodic in space (in thedirection of propagation), of period λc = c

f c .

Sampling it at a different point in space introduces a phaserotation (1λc in space = 2π phase rotation).

t

t + ∆t ~ v

θ-∆d

- d ∆d = v ∆t cosθ

Phase rotation over time ∆t : e j 2π∆d λc = e j 2π

v cosθλc

∆t

Doppler shift ν caused by a rectilinear uniform movement ofspeed v of the Tx or Rx: ν = v

λc cos(θ) [Hz ]




Time-Selective Fading - Doppler Effect

(II)

Movement of a scatterer can create a Doppler frequencymultiple of ν

Non rectilinear uniform movement, or superposition of manypaths leads to Doppler spread.

For UMTS with carrier frequency 2GHz and users moving with

v = 100km/h, Doppler is ν = 185Hz.




Multiple Antennas System

MIMO systems are useful when the various Tx-Rx antenna pairsexperience different channels

This can be achieved through

Spatial separationPolarization separationDirection separation (directive antennas)




MIMO Channel

scattering

environment

y 1x 1

x M T y M R

U

R

1

Tx Rx M T Number oftransmit antennas

M R Number ofreceive antennas

Tx antenna n and Rx antenna m are linked by the lineartime-varying filter h m ,n (t , τ ).




Time-Variant MIMO Channel: Tx-Rx

relationship

Channel matrix: H(t , τ ) =

h 1,1(t , τ ) . . . h 1,M T

(t , τ )...

...h M R ,1(t , τ ) . . . h M R ,M T

(t , τ )

Tx-Rx relationship

y(t ) =

H(t , τ )s(t − τ )dτ + n(t )

between the M T -dimensional transmitted signal s(t ) andM R -dimensional transmitted signal y(t )




Directional Discrimination Capability of

Antenna Arrays (I)

d

q

Tz

z(t)

y (t)1

y (t)2

Single Planar Wavefront modulated by has bandwidth B

Wavefront z (t ) = β (t )e j2πf c t

Two antenna array with inter-element spacing d , angle θ w.r.t.wavefront


Di i l Di i i i C bili f




Antenna Arrays (II)

d

q

Tz

z(t)

y (t)1

y (t)2

Narrowband assumption: B 1/T z ⇒ β (t − T z ) ≈ β (t )

y 1(t ) = z (t ) y 2(t ) = z (t )e j2π sin(θ) d

λ

Define the array response vector a (θ) = [1, e j2π sin(θ) d λ ]T. Then

y(t ) =

y 1(t )y 2(t )

= a (θ)z (t )


Di ti l Di i i ti C bilit f




Antenna Arrays: Beamforming

This effect has been exploited for a long time in radarapplications

The effect is reversible: one can transmit using the conjugateresponse vector as a ”precoder”

x(t ) =

x 1(t )x 2(t )

= a ∗(θ)s (t )

This technique favours one transmission direction given by θ:beamforming


S tt i F ti



Scattering Function

Scattering functions represent the channel gains between two

antenna arrays as a function of directionsExample using only one angle parameter at each side:S (φi , τ i , θi ) is the scattering amplitude of scatterer i located atangles φi and θi . The propagation delay for this path is τ i .

Tx

Rx

~̂

U

N

φ1

φ2

θ1

-+

-

θ2

S (φ2, θ2, τ 2) = g 2S (φ1, θ1, τ 1) = g 1


S tt i F ti (II)



Scattering Function (II)

If the transmitter is sending x(t ) = a (φ)s b (t ) and the receiver isapplying the Rx beamformer r b (t ) = a H (θ)T y(t ) we have theequivalent channel

r b (t ) = τ a

H

(θ)H(t , τ )a (φ)s b (t − τ ) + n (t )

Scattering function: S (φ,θ,τ ) = a H (θ)H(t , τ )a (φ).In the previous example, the scattering function has only twodiscrete scatterers:

S (φ,θ,τ ) = g 1δ(φ−φ1)δ(θ−θ1)δ(τ −τ 1)+g 2δ(φ−φ2)δ(θ−θ2)δ(τ −τ 2)


Scattering Function (III)



Scattering Function (III)

Channel experienced by the communications system is a

combination of the characteristics of the electromagneticchannel (S (φ,θ,τ )) and the antenna patterns (P T (φ) at thetransmitter and P R (θ) at the receiver.

h(t , τ ) = θ φ P R (θ)S (φ,θ,τ )P T (φ)

In our example, with isotropic antennas(P T (φ) = 1, P R (θ) = 1∀φ, θ) the equivalent channel is

h(t , τ ) = g 1δ(τ − τ 1) + g 2δ(τ − τ 2)

With a directional Rx antenna (e.g. P T (φ) = 1, P R (θ1) = α andP R (θ2) = 0), it becomes

h(t , τ ) = αg 1δ(τ − τ 1)


On The Importance of Channel



On The Importance of Channel

Statistics

So far, we assumed that we know perfectly the parameters of thechannel (τ , η, for each path and for each Tx-Rx antenna pair(n , m ))

It is possible to realistically evaluate those parameters throughray-tracing or other methods – however this is very complex anda very good knowledge of the antennas design and thescatterers (position, refractive index...) is required

In practical design and evaluation of communication systems,channels are stochastic, and some distribution must beassumed.


MIMO Communications Lecture1

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