wireless access systems: introduction and course outline
TRANSCRIPT
Wireless Access Systems:Introduction and Course Outline
2Communication Technology LaboratoryWireless Communication Group
Some Wireless Access Systems
• Wireless Access Systems provide short to medium range tetherless access to a backhaul network, a central unit or peer nodes
• Examples include
– Bluetooth– WLAN– Vehicular Networks– WiMax– RFID– WBAN– WPAN
3Communication Technology LaboratoryWireless Communication Group
Wireless Access Systems are Ubiquitous
Internet
4Communication Technology LaboratoryWireless Communication Group
Some More Applications
intelligent homeambient intelligencesecurity wearable computing
shopping
defencesurveillance
supply chain management
logisticsindustrial
information exchangepervasive computingvirtual reality
health carehome care
communicationsinstant messagingenterprise communication
environment
trafficsecuritysurveillanceaccess control
Internet
5Communication Technology LaboratoryWireless Communication Group
Characteristics of Wireless Access Systems
Heterogeneous standards• IEEE 802.11 WLAN• IEEE 802.15 WPAN• IEEE 802.16 WMAN• (Hiperlan)• Bluetooth• DECT• various RFID standards
• RFID tags, readers• sensors, actors• communication appliances• information access• information processing• backhaul access points
Heterogeneous nodes
Lots of spectrum (approx.)• [email protected] (ISM)• [email protected] (ISM)• [email protected] (ISM)• [email protected] (ISM)• >3GHz@5GHz (UWB)
WLAN
Internetbackhaul
Sensornetwork
RFID
cellular:GSMUMTS
BluetoothWPAN
WMAN
Pervasive wirelessaccess
6Communication Technology LaboratoryWireless Communication Group
The Throughput - Range Tradeoff
RFID
Bo
dy A
rea Netw
orks
100M
10M
1M
100k
10k
1k
1 3 10 30 100 range [m]
link throughput[bps]
11b
11a 11g
15.4
15.3
15.1
Sensor Netw
orks
15.3a
WLAN
WPAN
UWB
Bluetooth
ZigBee
UWB region(conceptional)
7Communication Technology LaboratoryWireless Communication Group
Outline of Course
Fundamentals
1. Fundamentals of short/medium range wireless communication 1
– digital transmission systems– equivalent baseband model– digital modulation and ML-detection
2. Fundamentals of short/medium range wireless communication 2
– fading channels– diversity– MIMO wireless
3. Fundamentals of short/medium range wireless communication 3
– Multicarrier modulation and OFDM
Systems I: OFDM based broadband access
4. WLAN 1: IEEE 802.11g, a
5. WLAN 2: IEEE 802.11n
6. WMAN: (mobile) WiMAX
7. Vehicular Networks
Systems II: Wireless short range access technolgies and systems
8. UWB 1: Promises and challenges of Ultra Wideband Systems
9. UWB 2: Physical Layer options
10. Wireless Body Area Network case study: UWB based human motion tracking
11. The IEEE 802.15x family of Wireless Personal Area Networks (WPAN): • Bluetooth, • ZigBee, • UWB
Systems III: RF identification (RFID) and sensor networks
12. RFID 1
13. RFID 2
8Communication Technology LaboratoryWireless Communication Group
Exercises: Motivation
• Simulate, practice, verify, learn and have fun
• We will simulate the theoretical ideas/methods/techniques that we learn throughout the lecture.
• MATLAB (matrix laboratory) will be used for simulations.
• In general we will simulate
– Single carrier transmission– Multi-carrier transmission– Wireless Channel– Channel coding– Simple UWB transceiver
9Communication Technology LaboratoryWireless Communication Group
Exercises: Organization
• Students organize in 2 or 4 groups
• There will be three exercises with two tasks each during the semester.
• Each group will perform one of the two tasks and then present the results.
• The general schedule of tasks:
– Introduction of tasks.
– Working period (2 weeks). Present afterwards.• Each group will work individually.
– Combining period (1 week). Present afterwards.• Two groups will work in collaboration.
• For further details will be presented in the first exercise lecture next week 8:15
10Communication Technology LaboratoryWireless Communication Group
Schedule:
8:15-9:00 9:15-10:00 10:15-11:00 11:15-12:00
Week 1 Fundamentals of wireless
communications. 1 Fundamentals of wireless
communications. 1 Fundamentals of wireless
communications. 1
Week 2Introduction –First Exercise
Fundamentals of wireless communications. 2
Fundamentals of wireless communications. 2
Fundamentals of wireless communications. 2
Week 3 Fundamentals of wireless
communications. 3Fundamentals of wireless
communications. 3 Fundamentals of wireless
communications. 3
Week 4 Presentation of Ex 1/ 1 Presentation of Ex 1/2 WLAN - 1 WLAN - 1
Week 5optional: wrap up of
simulation basicsoptional: revised solutions of Ex
1/1 and EX 1/2 WLAN - 2 WLAN - 2
Week 6Introduction-
Second ExercisePresentation of Ex 1 -
Combination step WiMAX 1 WiMAX 1
Week 7 Vehicular Networks Vehicular Networks
Week 8 Presentation of Ex 2/1 Presentation of Ex 2/2 UWB 1 UWB 1
Week 9Introduction –
Third ExercisePresentation of Ex 2 -
Combination step UWB 2 UWB 2
Week 10 WBAN WBAN
Week 11 Presentation of Ex 3/1 Presentation of Ex 3/2 WPAN WPAN
Week 12 Presentation of Ex 3 -
Combination step RFID 1 RFID 1
Week 13 RFID 2 RFID 2
Wireless Access Systems:Fundamentals of Short Range Wireless Communications
12Communication Technology LaboratoryWireless Communication Group
Fundamentals of Short Range Wireless: Outline
1. Digital transmission and detection on the AWGN channel– digital transmission systems– equivalent baseband model– digital modulation and ML-detection
2. Fading channels– fading channels– diversity– MIMO wireless
3. Modulation schemes for frequency selective channels– multicarrier modulation – Orthogonal Frequency Division Multiplexing (OFDM)
13Communication Technology LaboratoryWireless Communication Group
Equivalent Baseband Representation
5.14Communication Technology LaboratoryWireless Communication Group
Narrowband Case: Equivalent Baseband Model with Bandpass Channel, Different TX and RX Lowpasses and Frequency/Phase Offset
Notes • f0 and are called the reference
frequency and phase of the BB model
• for f0 = f1 the BB model is time-invariant (a filter)
1 12 cos t
1 12 sin t
trI
tsRX
trQ tsTX
tsQ
0 02 cos t
0 02 sin t
+
tsI
( )BP
H f
I Q
s t
s t js t
I Qr t r t jr t
( )TX
H f ( )RX
H f
)( 10 je
( )TX
H f ( )RX
H f
0real AWGN; / 2N
0complex AWGN; N
TXH f 0BPH f f RXH f
Narrowband case:
0 1( )e j t
00
0
TX
RX
H f f f
H f f B
Notation:
for 0
0 elsewhereBP
BP
H f fH f
0
0 0 1with max 0,B f f f
5.15Communication Technology LaboratoryWireless Communication Group
Narrowband Case: Relation of Physical Signals and Their Complex Baseband Representation
• The spectrum of the analytic signal in terms of the physical signal is given by
Re{} Re{}
0( )BPH f f
0 1( )e j t
)( 10 je
0 0( )2 j te
)(ts )(tr
Re{} Im{}
)(tsI )(tsQ ( )TXs t )(tsRX
Re{} Im{}
)(trI )(trQ
( )TX
H f ( )RX
H f
0complex AWGN; N
( ) : complex envelope of ( )
( ): analytic signal (pre-envelope of ( ))
( ): physical passband signal
TX TX
TX TX
TX
s t s t
s t s t
s t
( )TXs t
( )TXs t
Names and Notation:
2 0
0 elsewhereTX
TX
S f fS f
16Communication Technology LaboratoryWireless Communication Group
Transmission of Digital Information I: Generation of Finite Signal Sets (Modulation)
17Communication Technology LaboratoryWireless Communication Group
General Block Diagram of a Digital Modulator
• The information bit vector contains N bit • It is mapped onto a message index (i)• We use a look-up table with 2N transmit waveforms• The transmit signal is selected according to the message index• The process of selecting a transmit signal according to an information bit
vector is called modulation• For finite N this structure models a block transmission
(1)TXs t
Mapper( )i
i
TXs t
(2)TXs t
(2 )N
TXs t
TXs t
18Communication Technology LaboratoryWireless Communication Group
Signal Space Representation of Digital Modulator
• The signal space is defined by a set of orthonormal basepulses
• The basepulses are stacked to form the basepulse vector – orthonormality implies
• The signal space representation of the transmit signals is obtained by the projection
– we refer to as transmit symbol vector
(1)TXs
Mapper( )i
i
TXs
(2)TXs
(2 )N
TXs
H t
2NM
t
( ) ( )i iTX TXs t s t dt
Ht t dt I
TXs t( )i
TXs
TXs
Look-up table
19Communication Technology LaboratoryWireless Communication Group
Linear Modulation
• For linear modulation schemes the transmit symbol vector is obtained by a linear transformation of the input symbol vector– precoding matrix GTX
• Dramatically reduces the size of the look-up table– general modulation: exponential growth with the number N of information
symbols– linear modulation: linear growth
TXG
TXs
H t
TXs t
20Communication Technology LaboratoryWireless Communication Group
Some Popular Linear Modulation Schemes
name symbol alphabet 3TX SG N
2-PAM1 0 0
0 1 0
0 0 1
1 1
4-QAM(QPSK)
1 0 0 0 0
0 0 1 0 0
0 0 0 0 1
j
j
j
2 1 2 0 0 0 0 0 0 0 0
0 0 0 0 2 1 2 0 0 0 0
0 0 0 0 0 0 0 0 2 1 2
j j
j j
j j
16 - QAM
21Communication Technology LaboratoryWireless Communication Group
Filter Implementation of Linear Modulator: Nyquist Basepulses
• Nyquist basepulses (orthonormal)
• Nyquist criterion
TXG
TXs
H t
TXs t
g t
t
H t
g t mT g t nT dt m n
T
2/ 1/
k
G f k T T
t
TXs t
T
22Communication Technology LaboratoryWireless Communication Group
Transmission of Digital Information II: Transmission and Detection
23Communication Technology LaboratoryWireless Communication Group
• Channel is modelled as additive noise source
• In many cases of practical interest the noise can be characterized as zero mean stationary Gaussian random process w(t)
– any set of samples is jointy normally distributed
– autocorrelation function
– power density spectrum
Additive White Gaussian Noise (AWGN) Channel
• For analytical tractability usually a white noise process is assumed
– for physical system models (real-valued signals) we have
– for complex baseband representations as used herein we have
TXs t
w t
r t
*wR E w t w t
wD f R
0 0
2 2w
N ND f R
0 0wD f N R N
24Communication Technology LaboratoryWireless Communication Group
Sufficient Statistic and Symbol Discrete System Model
• Bank of correlators generates the decision vector
• the decision vector is a sufficient statistics (for additive white Gaussian noise; AWGN)
– contains all information for the optimal estimation of the transmit symbol vector
• With the impulse correlation matrix
we obtain the symbol discrete system model
– the elements of the noise vector are statistically independent and identically distributed Gaussian random variables
TXs t
H t
AWGN
w t
r t dTXs
t
Bank of correlators
dTXs
0,w CN I
1/ 2
Ht t dt
d
Symbol discrete system model
Continuous time system model
w
25Communication Technology LaboratoryWireless Communication Group
Frequency Selective Channel
w t
TXG TXs t
H t
h t
channel
TXs t
h t r t
t
d
• The channel is represented by a filter h(t) and AWGN
• A channel matched filter is required prior to the correlator bank in order to obtain a sufficient statistics
• These filters may affect the resulting impulse correlation matrix– intersymbol interference
(ISI)channelmatchedfilter
26Communication Technology LaboratoryWireless Communication Group
P
Form-Invariant Basepulses
TXs t
w t
r t d
TXs
Continuous time system model
impulsemodulator
g(t) h(t) h*(-t) g*(-t)S
kT
d
TXs
0, ppn CN
pp
Symbol discrete system model
0 1 2 3
1 0 1 2
2 1 0 12 2
3 2 1 0
with
and
k
pp
p p p pp p kTp p p p
p p p p
p p p p p t G f H f
27Communication Technology LaboratoryWireless Communication Group
Transmission of Digital Information III: Decoding
28Communication Technology LaboratoryWireless Communication Group
Maximum Likelihood Decoder and Decision Regions
• With orthonormal basepulse vector the impulse correlation matrix becomes the identity matrix
• The decoder observes the decision vector and generates an estimate of the transmit symbol vector
• To minimize the probability of error the decoder selects the hypothesis, which has the minimum Euclidean distance to the decision vector (Maximum Likelihood (ML) decoder)
– decision regions in the signal space
d
TXs
20, ww CN I
I decoder
T̂Xs
2
ˆ
ˆ arg min
ˆ
kTX
k
k
TX TX
k d s
s s
d
TXs T̂Xs
29Communication Technology LaboratoryWireless Communication Group
Example: Error Performance of QPSK
Decision regions
bE
2 22
Bit error probability Symbol error probability
2 1 1 2b
b s b b bw
EP Q P P P P
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Q-Function
Q(x
)x
(1,1)
(1,0)
(0,1)
(0,0)
Gray mapping(bit 1, bit 2)
30Communication Technology LaboratoryWireless Communication Group
Fundamentals of Short Range Wireless: Outline
1. Digital transmission and detection on the AWGN channel– digital transmission systems– equivalent baseband model– digital modulation and ML-detection
2. Fading channels– fading channels– diversity– MIMO wireless
3. Modulation schemes for frequency selective channels– multicarrier modulation – Orthogonal Frequency Division Multiplexing (OFDM)
31Communication Technology LaboratoryWireless Communication Group
Fading I: Time Selective (Narrowband) Fading Channels
Communication Technology LaboratoryWireless Communication Group
Path Loss and Short Term Fading
TX RX
power [dB]
distance(log(x))
free space20 dB/dec
urban40 dB/dec
rural30 dB/dec
distance (log(x))
0( ) expTXs t j t 0( ) ( ) expr t r x j t
210log( ( ) )r x
32
Communication Technology LaboratoryWireless Communication Group
Doppler Shift I: 1800 Angle of Arrival
• Received signal in complex passband notation
• For (small scale effects) we obtain the complex envelope of the receive signal
– depends only on the displacement . In the spectral domain we obtain the (spatial) Doppler shift
e j t0 x0 x
0 0 0
0
( , ) ( ) exp 2 / exp 2 / expcr x t a x x j x j x j t
c
0( ) exp 2 /r x c j x
0( ) ( ) ( 1/ )x xr x R f c f
0( , ) ( ) exp 2 / expcr x t a x j x j t
x
0x x
x1/
33
Communication Technology LaboratoryWireless Communication Group
• For a linear movement of the receiver the spatial variations translate linearly into equivalent temporal variations
– the corresponding frequency shift follows as
Doppler Shift II: Arbitrary Angle of Arrival
• Complex envelope of received signal
– in the spectral domain we obtain the spatial Doppler shift
e j t0
x
xx cos( )
1( ) exp 2 (cos / )r x c j x
cos HzD xD
vf f v
1 1( ) ( ) exp 2 (cos / )r t r x vt c j vt
cosxDf
x v t
cosx
34
Communication Technology LaboratoryWireless Communication Group
Multipath Propagation and Fading
• Complex envelope of the received signal
• Due to the different frequency shifts of the components, the magnitude of the received signal varies with the displacement: fading
• Example:
– note the spaced zero crossingse j t0
xx0 x
,1
( ) exp 2N
n xD nn
r x c j f x
( ) cos 2 /r x x
/x
( )r x
0.5 1
/ 2
,1 ,2 1 21/ ; .5xD xDf f c c
35
Communication Technology LaboratoryWireless Communication Group
Doppler Spectrum: Power Spectral Density of Fading Process
• infinite number of scatterers under average receive power constraint: continuous PSD of fading process
• Scattering coefficients cn modelled as uncorrelated random variables with variance – fading described as random
process• Power spectral density (PSD) of
fading process for
– note the relation between Doppler shift fxD,n and the angle of arrival
,1
( ) exp 2N
n xD nn
r x c j f x
2, ,
1
N
r x c n x xD nn
D f f f
,
cos nxD nf
fxD
PSD
2,c n
n
,1 , xD xD Nf f 0n
E c
36
37Communication Technology LaboratoryWireless Communication Group
Jake's Doppler Spectrum
• Cumulative power distribution versus frequency
• Power spectral density
– "Jake's Spectrum"
cP
arccos xf
-1 -0.5 0 0.5 10
0.2
0.4
0.6
0.8
1
fx
Pc
arccosc x xP f f
2
1
1x c x
xx
dD f P f
df f
uniform continuousscattering around receiver
cumulative power distribution
• Relation of angle of arrival and Dopper shift
38Communication Technology LaboratoryWireless Communication Group
Jake's Channel Model for Linear Movement
• Multiplicative fading• Speed of movement: v
TXs t
z t
AWGN
w t
r t
1/ 421 /D DH f f v
complex whiteGaussian noiseprocess
fD
39Communication Technology LaboratoryWireless Communication Group
Fading II: Frequency Selective Fading
Communication Technology LaboratoryWireless Communication Group
Broadband Channel Measurement
• Channel measurement with a short impulse h(t) (broadband)
• All scatterers, which lead to a given path delay
are located on an ellipse• Typical received signal:( )h t x
x0x
1,
1,,
0
1 1 1 , ,, const
' ''1 1 1
0 1 2 3
40
Communication Technology LaboratoryWireless Communication Group
Scattering Function
• The scattering function describes the average power spectral density of the received signal as a function of Doppler shift fx and delay
x
S2S1
S3
S4
321
2 31
S1
S2
S3
S4
Dopplershift fx
, xS f
41
Communication Technology LaboratoryWireless Communication Group
Doppler Spectrum of Narrowband System
• rms Doppler spread
with the mean Doppler shift
Doppler Spectrum2 31
S1S3
S4Dopplershift
, xS f
,r x xD f S f d
1/ 22
x x r x x
f
r x x
f f D f df
D f df
x r x x
x
r x x
f D f dff
D f df
• Scattering function– 2nd order statistics of the spatio-
temporal fading process • a narrow band system can not
resolve the multiple paths– narrowband fading with Doppler
spectrum
42
Communication Technology LaboratoryWireless Communication Group
Delay Power Spectrum of Broadband System
• Scattering function– 2nd order statistics of the spatio-temporal fading process
• Delay power spectrum
– rms delay spread
with the mean delay
2 31
S1S3
S4Dopplershift
2 31
Delaypowerspectrum
, x xP S f df
, xS f
1/ 22P d
P d
P d
P d
43
44Communication Technology LaboratoryWireless Communication Group
Classification of Multipath Channels
• The signal bandwidth and the duration of the transmit burst determine the fading model
– flat: no significant variation over the interval of interest
– selective: varies significantly over the interval of interest
• Narrowband systems experience frequency-flat fading
• Broadband systems experience frequency-selective fading
• A block fading model is suitable in the time-flat regime
– may be either frequency-flat or frequency selective
• Systems below the red curve are not physically implementable
• Note the role of Doppler spread and delay spread
signal bandwidth B
burst duration TBURST
time-selectivefrequency-selective
time-flatfrequency-selective
time-selectivefrequency-flat
time-flatfrequency-flat
1/
1/ f
TBurst=1/B
Communication Technology LaboratoryWireless Communication Group
Typical Time-Selective/Frequency Selective Channel Model
• A discrete delay power spectrum is specified
– paths (delays) are usually clustered
• For each path (k) (i.e. delay ) a Doppler spectrum is specified
– default: Jake's spectrum– if specified in terms of spatial frequency fx,
substitute f x = f/v for linear movement with velocity v
• The filter coefficients are filtered complex normal random processes
– in line of sight (LoS) situations: nonzero mean
1
( )s t
(1) ( )z t
2
(2) ( )z t
3
(3) ( )z t
+
( )r t
delay power spectrum
delay
k
kD f
white complex normal random process
kD f
( ) ( )kz t( ) ( )kw t
Structure
Generation of fading processes
kP
Specification
45
Communication Technology LaboratoryWireless Communication Group
Special Cases
1
( )s t
(1)z
2
(2)z
3
(3)z
+
( )r t
Block fading channel
• Note that the coefficients are random variables (not processes)
• For each channel realization a new set of random variables is generated
–
– non LoS:
,kk kz CN m P
0km
Frequency-flat fading
( )s t
( )z t ( )r t
white complex normal random process D f
( )z t( )w t
• Generation of fading processes
46
47Communication Technology LaboratoryWireless Communication Group
Fading III: Impact on Error Performance
47
48Communication Technology LaboratoryWireless Communication Group
Frequency-Flat Fading Channel
w t
TXG
H t
fadingchannel
t
d
channelmatched"filter"
z t *z t
1 /d d z
TXs
20, ww CN I
1/ 2
Symbol discrete system model with block fading
z
• block fading: fading variable instead of fading process
• note multiplication with magnitude of fading variable due to
– channel matched "filter"– normalization of decision vector
1 /d d z
49Communication Technology LaboratoryWireless Communication Group
Error Performance of QPSK in Frequency-Flat Block Fading
• In frequency-flat block fading the error performance of QPSK is determined by the instantaneous value of the fading variable
• We can define various figures of merit. Frequently used are– outage probability: probability, that
the instantaneous bit error probability is above a target value
– fading averaged bit error probability
• Clearly these figures of merit depend on the probability density function (pdf) of the fading amplitude
z
2
2 bb
w
EP z Q z
0 0Prout bP P P z P
b bzP E P z
• here is a chi2 random variable with 2 degrees of freedom
2y z
2 20 / dBb wE z E
fadi
ng a
vera
ged
bit e
rror
pro
babi
lity
0P
z
50Communication Technology LaboratoryWireless Communication Group
• Special case L=1– the fading variable z is complex
normally distributed; – is the sum of two
statistically independent squared real-valued normal random variable
– If , is Rayleigh distributed; Rayleigh fading
– if , is Rician distributed. K-factor:
• General case L=N: N-fold diversity– For , is the sum of 2L
squared real-valued Gaussian random variables
– chi2-distribution with 2L degrees of freedom
– e.g. achievable with L receive antennas
• Approximation: BER (c/SNR)L
Diversity
•
2 2 21 2y z x x
2 20 / dBb wE z E
fadi
ng a
vera
ged
bit e
rror
pro
babi
lity
z
22 2
1
L
kk
y z x
2y z
z 0E z
2 2zK E z
0E z
0E z
51Communication Technology LaboratoryWireless Communication Group
Fundamentals of Short Range Wireless: Outline
1. Digital transmission and detection on the AWGN channel– digital transmission systems– equivalent baseband model– digital modulation and ML-detection
2. Fading channels– fading channels– diversity– MIMO wireless
3. Modulation schemes for frequency selective channels– multicarrier modulation – Orthogonal Frequency Division Multiplexing (OFDM)
Vector/Matrix Channels
Single Input/Single Output (SISO)
• channel coefficient
Single Input/Multiple Output (SIMO)
• channel vector
Multiple Input/Multiple Output (MIMO)
• channel matrix
h
h
H H
h
h
52
53
Diversity Techniques
• Wireless channel varies in time, frequency and space Time, frequency and space diversity available
• Examples: – Time diversity: repeat same codeword after channel varied (Repetition Code)
– Frequency diversity: transmit same symbol over two or more OFDM sub-carriers (if fading of the sub-carriers is uncorrelated)
– Space diversity: use more than one antenna at RX or TX or on both sides
– (But usually pure repetition is not an efficient way to code: repetition of the same information in time or frequency sacrifices bandwidth space diversity seems promising)
Diversity, MIMO
54
• Receive diversity: using NRX receive antennas
(spatial dimension)
• High diversity factors available for high carrier frequencies and large bandwidths
• Transmit diversity: in addition a temporal coding needed
Space-Time Codes
Diversity, MIMO
Spatial (or Antenna) Diversity
TX RX
55Communication Technology LaboratoryWireless Communication Group
System Model with RX Diversity and Maximum Ratio Combining
w t
TXG
H t
block fadingvector channel
t
d
channelmatched"filter"
h
Hh
1 /d d h
TXs
20, ww CN I
1/ 2
Scalar symbol discrete system model
h
• note multiplication with magnitude of fading vector due to– channel matched "filter"– normalization of decision vector
1 /d d h
RXN 11TXs
56
• Receive diversity:hi : channel gain between the TX
antenna and the RX antenna i
Diversity, MIMO
Probability of Error
TX RX
1 2, , ,RX
T
Nh h h h
new argument of Q-Function:
2
22 b
Sw
EP Q h
2 2
2 2
1=b b
RXw w RX
E Eh N h
N
Array Gain and Diversity Gain
2
22 b
w
EQ h
Array (Power) gain Diversity gain
• Expression converges to constant for increasing NRX
i.e. fading is eliminated in the limit
• 3 dB gain per doubling of the number of RX antenna
57
Multiple Input/ Multiple Output
Single Input/Single Output (SISO)
• channel coefficient
Single Input/Multiple Output (SIMO)
• channel vector
Multiple Input/Multiple Output (MIMO)
• channel matrix
h
h
H H
h
h
58
Free Space vs. Multipath Propagation
/ 2
scattering
fading
h
h
h
h
59
Multiple Antennas and Spatial Multiplexing
h h
1 1 1
1 1 1
1 1 1
H
0.8 0.4 0.6
0.9 1.3 1.5
0.2 1.0 1.4
H
Channel Matrix
Singular Value Decomposition H H U S V
3 0 0
0 0 0
0 0 0
S
2.9 0 0
0 0.7 0
0 0 0.1
Srank 1• full rank• 3 spatial subchannels• spatial multiplexing
unitary3 3;H H U U I V V I
60
61
MIMO Wireless Capacity (1)
• MIMO channel capacity grows nearly linearly with N = min(NTX, NRX)
[Foschini, Gans, 1998] [Telatar, 1999]
TX RX
• N decoupled spatial sub-channels available (Spatial Multiplexing)
• Higher data rate without need of higher bandwidth spectral efficiency
Diversity, MIMO
K-f
acto
r of
Ric
ian
fadi
ng
62
MIMO Wireless Capacity (2)
TX RX
Diversity, MIMO
20
log detRX
HSN
TX
EC E
N N
I HH
Telatar, Foschini:
NTX: number of TX antennas, NRX: number of RX antennas.
K-f
acto
r of
Ric
ian
fadi
ng
63
MIMO Systems: Spatial Subchannels
Subchannels
0 0
0 0
0 0
S
RXN
TXN
A priori transmit channel state information (CSIT) necessary !
TX Diversity:Take only the “best“subchannel !
Spatial Multiplexing:Take all !
, unitary matricesHH USV U VSVD of MIMO channel matrix:
H H H U H V U U S V V S
Diversity, MIMO
64
MIMO Systems without CSIT: Spatial Subchannels
if no a priori CSIT: TX Combining not possible;Spatial multiplexing leads to ISI
Receiver has to compensate ISI due to V (cf. BLAST);
Diversity, MIMO
65
BLAST Architecture
[Gesbert, et al.: From Theory to Practice: An Overview of MIMO Space–Time Coded Wireless Systems]
Diversity, MIMO
66
BLAST (2)
TX RX
H
•Antenna array at TX and RX
•Spatial Data Pipes in rich scattering (MIMO channel H of high rank) without
increasing the bandwidth
•Spatial Multiplexing achieves ergodic MIMO capacity
•ISI compensation at RX necessary, because no CSIT used in BLAST system
•BLAST: no combination of diversity techniques and spatial multiplexing
Diversity, MIMO
67Communication Technology LaboratoryWireless Communication Group
Fundamentals of Short Range Wireless: Outline
1. Digital transmission and detection on the AWGN channel– digital transmission systems– equivalent baseband model– digital modulation and ML-detection
2. Fading channels– fading channels– diversity– MIMO wireless
3. Modulation schemes for frequency selective channels– multicarrier modulation – Orthogonal Frequency Division Multiplexing (OFDM)
68Communication Technology LaboratoryWireless Communication Group
Multicarrier Modulation I: Continuous Time Implementation
69Communication Technology LaboratoryWireless Communication Group
P
Discrete Channel Impulse Response
2 2* ** * *
k
p t g t g t h t h t G f H f
p p kT
w td
ka t kT g(t) h(t) h*(-t) g*(-t)
S
kT
-T -T T T
p0p-1 p1
+
ka kn
kd
70Communication Technology LaboratoryWireless Communication Group
Low and High Data Rate Systems
* ** **g t g tt h t tp h
gT
2 gT
hT
2 hT
t t
t
2 g hT T
low data rate:
high data rate:
g hT T T
g hT T T
p t
no ISI
severe ISI
transmit basepulse channel impulse response
**g t g t **h t h t
71Communication Technology LaboratoryWireless Communication Group
Multicarrier Modulation
• Transmit in N subbands, for each of which the channel transfer function is approximately constant– minimizes ISI in each subband– subband center frequency fk
– for non-overlapping subbands, there is no inter-subband (inter-carrier) interference (ICI)
• One multicarrier (MC) symbol consists of N transmit symbols:• Subbands implemented by letting
• The symbol rate on each subcarrier is
f
H(f)
TXs
H t
TXp t
exp
sinc( / )
k k
TX MC
t j t
p t t T
1/MC MCf T
1f Nf
TXs
72Communication Technology LaboratoryWireless Communication Group
Transmit and Receive Window
• For sinc-windows there is strictly no interference between adjacent subcarriers (non-overlapping spectra)– the ISI matrix in the discrete system model is diagonal
• Due to their infinite duration sinc-windows are not implementable.• Is it possible to design finite length windows without introducing
interference?
H t
TXp t w t
h(t)
t
RXp t
d
pp
TXs
transmit window
receive window
73Communication Technology LaboratoryWireless Communication Group
Eigenfunction of the Convolution
• We consider the response of the channel h(t) to a step function with center frequency fk
• We observe a transient with duration Th
• After the transient the response is a scaled version of the input signal– scaling factor H(fk)
– complex exponentials are eigenfunctions of convolution
• After an appropriate window, which blanks the transient, we obtain the input-output relation
• This observation is the key to the design of a finite window for MC
hT
t
t
t
exp kt j t
h t
expk kH f j t
transient exp exph tk h k kt j t t T H f j t
t
74Communication Technology LaboratoryWireless Communication Group
Equivalent Diagonal Channel Matrix
expHkt j t
TXp t w t
h(t)
t
RXp t
d
MCT
CT
hT
H t
rect / ct T w t t
RXp t
d
1 0 0
0 0
0 0 N
H f
H f
Equivalent model:
TX and RX window:
equivalent channel matrixTXs
TXs
75Communication Technology LaboratoryWireless Communication Group
Receive Window
• As the equivalent channel matrix is diagonal, it does not affect orthogonality any more
• What is the impact of the receive window?
• Pulse correlation matrix
– the Fourier transform PRX(f) of the receive window pRX(t) determines the pulse correlation matrix
exp
HRX
mn n m RX
RX n m
t t p t dt
j t p t dt
P f f f
• For a uniform subcarrier spacing we have– the Fourier transform of the
receive window needs to have
spaced zeros• In this case the received window
has to fullfil the following condition (temporal dual to the spectral Nyquist condition)
– the most compact window thus is given by
– this implies • A temporal roll off improves the
robustness to frequency offsets
n mf f n m f
/RXk
p t k f const
f
rectRXp t t f 1/MCT f
76Communication Technology LaboratoryWireless Communication Group
Transmit Window
• With we obtain
• Example for N=21; pTX(t)=rect(t/(Tc+Th)
MCT
CT
hT
• The transmit window has to be constant for at least
• This window determines the power spectral density of the transmit signal
h cT T
TXD f
2
1
N
TX TX kk
D f P f f
TX TXP f p t
-50 -40 -30 -20 -10 0 10 20 30 40 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency/f
pow
er s
pect
ral d
ensi
ty
77Communication Technology LaboratoryWireless Communication Group
Multicarrier Modulation II: Discrete Implementation (Orthogonal Frequency Division Multiplexing; OFDM)
78Communication Technology LaboratoryWireless Communication Group
P
Discrete Channel Impulse Response
2 2* ** * *
k
p t g t g t h t h t G f H f
p p kT
w td
ka t kT g(t) h(t) h*(-t) g*(-t)
S
kT
-T -T T T
p0p-1 p1
+
kakn
kdd
a
n
Vector signal model
79Communication Technology LaboratoryWireless Communication Group
Response to Periodic Input Sequence
T T
p0 p1
+
ka kn
kd
d1 ..................................... dNd1 ..................................... dN
1T
Na a
• Discrete channel impulse response with L taps
• for illustration assumed causal
Idea: use periodic input sequence to generate periodic response
1 Na a1 Na a
d
a
n
pp0 1
1 0
1 0
1 0
0 0
0 0
0 0
0 0
pp
p p
p p
p p
p p
Equivalent channel matrix is circulant
1T
Nd d d
80Communication Technology LaboratoryWireless Communication Group
Cyclic Prefix and Circulant Channel Matrix
• Circulant channel matrix due to cyclic prefix of length larger or equal to L-1
T T
p0 p1
+
ka kn
kd
d1 ..................................... dNcyclic prefix
1 Na a
d
a
n
pp0 1
1 0
1 0
1 0
0 0
0 0
0 0
0 0
pp
p p
p p
p p
p p
NCP
• Discrete channel impulse response with L taps
• for illustration assumed causal
1CPN N Na a
81Communication Technology LaboratoryWireless Communication Group
Diagonalization of Circulant Matrix: Orthogonal Frequency Division Multiplexing (OFDM)
• All (NxN) circulant matrices are diagonalized by the Fourier matrix FN
1
1
1 with
DFT C :,1
H H HN N N N N N N N N N
T
N
F C F diag c c F DFT I F F F F IN
c c
w t
d
g(t) h(t) a(t)
kT; k=1.. N+NCP
insertCP
removeCP
HNF NF
a S
P
P
S
d
a
n
diagonal channel matrix CD
diag DFT C :,1CD
circulant channelmatrix C
kT; k=1.. N+NCP IFFTN a
1/ FFTN r
82Communication Technology LaboratoryWireless Communication Group
Comparison of Discrete and Continuous Time Implementation of Multicarrier Modulation
d
LowPass
LowPass
kT; k=1.. N+NCP
insertCP
removeCP
HNF NF
a S
P
P
S
kT; k=1.. N+NCP
expHmt j t
TXp t
t
RXp t
d
a
CPN N T N T
Multicarrier Transmitter Multicarrier Receiver
Note:
[ , ] exp( 2 )N
m
mF m n j n
NT
, 0,..., 1m n N