mimo communications lecture1
Post on 06-Jul-2015
42 Views
Preview:
TRANSCRIPT
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 1/29
Forschungszentrum Telekommunikation Wien[Telecommunications Research Center Vienna]
MIMO Communications (389.094)
Lecture 1
Maxime Guillaud, Erwin Riegler
October 9, 2008
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 2/29
MIMO Communications
Lecturers
Maxime Guillaud {guillaud@ftw.at}Erwin Riegler {riegler@ftw.at}
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
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 3/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 3
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 4/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 4
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 5/29
Outline (2)
Applications
UMTS with MIMO enhancements in Release 7 andLong-Term Evolution
Wireless LAN according to IEEE 802.11n
WiMAX 802.16
October 9, 2008 Maxime Guillaud, Erwin Riegler 5
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 6/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 6
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 7/29
Multiple-Input Multiple-Output (MIMO)
Communications
RxTx H
.
.
.
.
.
.
October 9, 2008 Maxime Guillaud, Erwin Riegler 7
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 8/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 8
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 9/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 9
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 10/29
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
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 11/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 11
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 12/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 12
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 13/29
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 )
October 9, 2008 Maxime Guillaud, Erwin Riegler 13
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 14/29
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 !
October 9, 2008 Maxime Guillaud, Erwin Riegler 14
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 15/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 15
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 16/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 16
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 17/29
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).
October 9, 2008 Maxime Guillaud, Erwin Riegler 17
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 18/29
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 ]
October 9, 2008 Maxime Guillaud, Erwin Riegler 18
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 19/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 19
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 20/29
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)
October 9, 2008 Maxime Guillaud, Erwin Riegler 20
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 21/29
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 ).
October 9, 2008 Maxime Guillaud, Erwin Riegler 21
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 22/29
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 )
October 9, 2008 Maxime Guillaud, Erwin Riegler 22
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 23/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 23
Di i l Di i i i C bili f
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 24/29
Directional Discrimination Capability of
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 )
October 9, 2008 Maxime Guillaud, Erwin Riegler 24
Di ti l Di i i ti C bilit f
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 25/29
Directional Discrimination Capability of
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 25
S tt i F ti
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 26/29
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
October 9, 2008 Maxime Guillaud, Erwin Riegler 26
S tt i F ti (II)
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 27/29
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)
October 9, 2008 Maxime Guillaud, Erwin Riegler 27
Scattering Function (III)
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 28/29
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)
October 9, 2008 Maxime Guillaud, Erwin Riegler 28
On The Importance of Channel
5/7/2018 MIMO Communications Lecture1 - slidepdf.com
http://slidepdf.com/reader/full/mimo-communications-lecture1 29/29
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.
October 9, 2008 Maxime Guillaud, Erwin Riegler 29
top related