Resear
h Methods, ELEC6021 (EZ619) S Chen
What's New in Communi
ations
Imagine a few s
enarios:
{ In holiday, use your fan
y mobile phone to take pi
ture and send it to a friend
{ In airport waiting for boarding, swit
h on your laptop and go to your favourite
web side
{ Or play game via Internet with your mobile phone
These are not Resear
h, they are not even Development, they are Developed
Do you know these words:
CDMA, multi
arrier, OFDM, spa
etime pro
essing, MIMO, iterative or turbo
oding, intelligent network, smart antenna
There are plenty of opportunities for R & D
In this introdu
tory
ourse, we only go through some A B C
1
Resear
h Methods, ELEC6021 (EZ619) S Chen
Wireless and Mobile Networks
Current/future: 2G GSM, 3G UMTS (universal mobile tele
ommuni
ation system),
and MBS (mobile broadband system) being developed for 4G mobile system
G
S
M
/
G
P
R
S
G
S
M
G
S
M
/
H
S
C
S
D
G
S
M
/
E
D
G
E
MBS
HIPERLAN
UMTS
B−ISDNISDNFixed
Movable
mobile
Solow
Fast
mobile
mobility
User
data rate
Service
(bps)
9
.
6
k
6
4
k
1
4
4
k
3
8
4
k
2
M
2
0
M
1
5
5
M
Some improved 2G, HSCSD: highspeed
ir
uit swit
hed data, GPRS: general pa
ket radio servi
e, EDGE: enhan
ed
data rates for GSM evolution. Also, HIPERLAN: high performan
e radio lo
al area network
2
Resear
h Methods, ELEC6021 (EZ619) S Chen
For Those Keen to Read
Any good text books on digital
ommuni
ations, e.g.
I.A. Glover and P.M. Grant, Digital Communi
ations. 2nd edition, Pearson, 2004.
J.D. Gibson, Prin
iples of Digital and Analog Communi
ations. 2nd edition,
M
Millan, 1993
More advan
ed level, e.g.
L. Hanzo, W. Webb and T. Keller, Single and MultiCarrier Quadrature
Amplitude Modulation. Wiley, 2000.
L. Hanzo, M. Munster, B.J. Choi and T. Keller, OFDM and MCCDMA. Wiley,
2003
A. Paulraj, R. Nabar and D. Gore, Introdu
tion to Spa
eTime Wireless
Communi
ations. Cambridge University Press, 2003
3
Resear
h Methods, ELEC6021 (EZ619) S Chen
General Comments on Communi
ations
Aim of tele
ommuni
ations: to
ommuni
ate information between geographi
ally
separated lo
ations via a
ommuni
ations
hannel of adequate quality (at
ertain
rate reliably)
channel
input output
The transmission will be based on digital data, whi
h is obtained from (generally)
analogue quantities by
1. sampling (Nyquist: sampling with at least twi
e the maximum frequen
y), and
2. quantisation (introdu
tion of quantisation noise through rounding o)
Transmitting at
ertain rate requires
ertain spe
tral bandwidth
Here
hannel means whole system, whi
h has
ertain
apa
ity, the maximum rate
that
an be used to transmit information through the system reliably
4
Resear
h Methods, ELEC6021 (EZ619) S Chen
General Transmission S
heme
A digital transmission s
heme generally involves:
input source
encoding
channel
encoding lation
modu
output
channel
lation
channel
decodingdecoding
source demodu
Input/output are
onsidered digital (analogue sampled/quantised)
CODEC, MODEM,
hannel (transmission medium)
Your 2G mobile phone, for example,
ontains a pair of transmitter and re
eiver
(trans
eiver),
onsisting of a CODEC and MODEM
5
Resear
h Methods, ELEC6021 (EZ619) S Chen
Sour
e En
oding / De
oding
A digital sour
e is
hara
terised by:
{ sour
e alphabet; symbol rate; symbol probabilities; and
probabilisti
interdependen
e of symbols
Sour
e
oding is about how to
ode symbols (samples) into bits; sour
e de
oding
is about how to
ode bits ba
k into symbols (samples)
Ideally, sour
e en
oding should remove any redundan
y from the signal to be
transmitted, and the sour
e de
oder has to restore the original sour
e signal
distortionless (lossless
oding)
In pra
ti
e, a small (potentially imper
eptible) error may be allowed in the
oding/en
oding (lossy
oding)
e.g. spee
h
oding
an be lossy, but medi
al diagnosis images
annot tolerate lossy
6
Resear
h Methods, ELEC6021 (EZ619) S Chen
Channel En
oding / De
oding
The
hannel exhibits impairments:
{
hannel distortion (e.g. multipath and fading, insuÆ
ient bandwidth), and
{ noise (e.g. thermal noise in re
eiver amplier
ir
uit)
input output
channel
Depending on the severity of impairment, transmission errors may o
ur
Channel
oding adds redundan
y to the transmitted signal to allow error dete
tion
and/or
orre
tion on the re
eiving side
7
Resear
h Methods, ELEC6021 (EZ619) S Chen
Channel Chara
teristi
s
Channel may introdu
e amplitude and phase distortion
{ Bandwidth B, signaltonoise ratio
S
N
, and
{ maximum rate for possible errorfree transmission (
hannel
apa
ity C)
C = B log
2
1 +
S
N
[bits/se
℄
ChannelTx Mod RxDem
analogue channel
digital channel
Channel
hara
teristi
s depend on design of transmission system:
{ transmission power, bandwidth, speed (data rate), reliability (error rate)
8
Resear
h Methods, ELEC6021 (EZ619) S Chen
Modulation / Demodulation
Modulation requires:
{ en
oding of a bit stream into a symbol stream;
{ ltering (pulse shaping) to limit the bandwidth;
{ modulation with a
arrier frequen
y
Demodulation requires:
{
arrier re
overy:
orre
t
arrier phase have to be found;
{ syn
hronisation (timing re
overy):
orre
t sampling instan
es have
to be found;
{ equalisation: to
ope with
hannel distortions
9
Resear
h Methods, ELEC6021 (EZ619) S Chen
Human Spee
h
glottal
sound
vocal tract
transmission
lip
radiation
i
n
t
e
n
s
i
t
y
frequency
vowel
F F F
F
4
321
Spee
h is either voi
ed or unvoi
ed, whi
h results in quasiperiodi
or noiselike
signals, respe
tively; both types have a degree of redundan
y
{ Voi
ed spee
h: vo
al folds vibrate at a fundamental frequen
y (100 . . . 150 Hz
for male, 200 . . . 300 Hz for female)
{ Arti
ulation: spe
tral shaping through the spe
i
resonan
es of the vo
al tra
t
(peaks: formant frequen
ies, whi
h determine the vowel /a/,/i/,et
.)
10
Resear
h Methods, ELEC6021 (EZ619) S Chen
Sour
e Coding for Spee
h
Methods of sour
e
oding for spee
h:
{ Waveform
oding tries to adapt the quantiser
hara
teristi
! good quality, moderate
ompression possible
{ Predi
tive
oding tries to quantise only nonredundant information (i.e. the
predi
tion error and predi
tive model
oeÆ
ients)
! good quality, reasonable
ompression
{ Analysisbysynthesis is based on a model of the vo
al tra
t
! up to a very high
ompression ratio at an arbitrarily poor quality
Spee
h
ode
s:
{ Waveform
ode
s (waveform
oding method)
{ Vo
oders (analysisbysynthesis and predi
tive
oding methods)
{ Hybrid
ode
s (tradeo between waveform
oding and vo
oding)
11
Resear
h Methods, ELEC6021 (EZ619) S Chen
Quality versus Bitrate
Classi
ation of spee
h
ode
s
VOCODERS
CODECS
HYBRID CODECS
WAVEFORM
1 2 4 8 16 32 64
Complexity
Delay
Fair
Poor
Excellent
quality
Speech
Good
Bitrate
(kbps)
12
Resear
h Methods, ELEC6021 (EZ619) S Chen
Waveform Code
s
Time domain waveform
oding:
ITU standard 64 kbps PCM: sampling at 8 kHz with 8 bits quantiser
ITU standard G.721, 32 kbps adaptive dierential PCM (ADPCM)
ITU standards G.726 and G.727
{ G.726
ode
s: variablerate for rates 16 { 40 kbps, allowing the network to
adjust quality/bitrate on instantaneous requirement
{ G.727
ode
s:
orebits and enhan
ement bits, allowing the network to drop
enhan
ement bits under heavy loads and to keep them when in light loads
Frequen
y domain waveform
oding:
Subband
oding and adaptive transform
oding
13
Resear
h Methods, ELEC6021 (EZ619) S Chen
AnalysisbySynthesis Coding
The spee
h is divided into small segments of 20ms duration;
for ea
h segment, a parametri
model (ex
itation and synthesis lter
oe.) is
sought for the spee
h generation:
s[n]
s[n]~
original
speech
synthetic
speech
voiced/
unvoiced
excitation
generator
synthesis
filter
vocal
tract
compare
ex
itation generation: either noise (unvoi
ed) or a pulse train (voi
ed);
the synthesis lter mat
hes the spe
tral shape of the harmoni
s for voi
ed ex
itation,
and the vo
al tra
t
14
Resear
h Methods, ELEC6021 (EZ619) S Chen
Linear Predi
tive Coding
General aim of predi
tive
oding is to make predi
tion error or residual as
unpredi
table as possible
Linear predi
tive
oding (LPC) employs more
omplex ex
itation models than used
in analysisbysynthesis
{ LPC
oeÆ
ients and predi
tion residuals are quantised to give designed bitrate
{ e.g. standard 13 kbps GSM spee
h
ode
: 8 LPC
oeÆ
ients are en
oded with
36 bits/20 ms update interval ! 1.8 kbps
Shortterm predi
tion: spee
h analysis segments 20 ms duration
Longterm predi
tion (LTP): LTP synthesis lter models the ne stru
ture of the
spee
h spe
trum, after shortterm predi
tion
{ When employing a LTP, the residual error be
omes truly unpredi
table !
ode
ex
ited linear predi
tive
oding (CELP)
ode
s
15
Resear
h Methods, ELEC6021 (EZ619) S Chen
HalfRate GSM Spee
h Code
parameter bits/frame
LPC
oeÆ
ients 28
LPC interpolation
ag 1
ex
itation mode 2
mode 0:
odebook 1 index 4 7 = 28
odebook 2 index 4 7 = 28
modes 1, 2, 3:
LTPD (subframe 1) 8
LTPD (subframes 2, 3, 4) 3 4 = 12
odebook 3 index 4 9 = 36
frame energy E
F
5
ex
itation gainrelated
quantity [E
S
1
E
1
℄ 4 5 = 20
total no of bits 112 bits/20 ms
bitrate 5.6 kbps
5.6 kbps ve
tor sum ex
ited linear predi
tive
(VSELP)
ode
, similar to CELP
Four synthesis modes, depending on grade of
voi
ing dete
ted in the spee
h
De
isions on whi
h ex
itation mode to use is
based on LTP gain: high { highly
orrelated
voi
ed; low { noiselike un
orrelated unvoi
ed
5 bits for overall frame energy spans a
dynami
range of 64 dB, when using a
stepsize of 2 dB and 32 steps
Residual error is
oded as a
odeword in a
ode book
16
Resear
h Methods, ELEC6021 (EZ619) S Chen
Video Sour
e Coding
Video signal: luminan
e signal of two spatial and a temporal dimension:
n+1
n+2
+3n
+4n
f
f
f
f
n
ftime
space
f
n
is frame at time n;
there are intra (i.e. spatial) and interframe
orrelations, i.e.
orrelations within f
n
and between f
n
and past frames f
n1
, f
n2
, et
.
17
Resear
h Methods, ELEC6021 (EZ619) S Chen
Video Compression
A pixel in a
olour image
an be presented
{ An independent intensity (luminan
e), and two
olour (
hrominan
e) signals
known as hue and saturation; or
{ Three
olour signals, intensity values of red, green and blue
MPEG standards, basi
blo
ks are
{ Motion
ompensation
{ DCT
{ Variable length
oding
MPEG1: 1.5 Mbps; MPEG2: 2 to 8 Mbps, now upto 30 Mbps for digital TV
MPEG4: initiated in 1993, for intera
tive multimedia appli
ations
MPEG7: started in 1997, for large stored database
18
Resear
h Methods, ELEC6021 (EZ619) S Chen
Channel Chara
teristi
s (I)
Passband
hannel and baseband (remove modulator/demodulator) equivalen
e:
c−f fc
f
B
H (f)
f
H (f)p
2B
carrier modulationb
−B
baseband
hannel bandwidth B $ passband
hannel bandwidth 2B
Channel has nite bandwidth, ideally
phase is linear and amplitude is
at:
Bandwidth is the most pre
ise resour
e
Two killer fa
tors: multipath and fading
f
phase
amplitude
channel bandwidth
19
Resear
h Methods, ELEC6021 (EZ619) S Chen
Channel Chara
teristi
s (II)
Channel noise: AWGN with a
onstant
power spe
trum density (PSD);
N /20
f
0
Power is the area under PSD, so WN has innitely large power;
but
ommuni
ation
hannels are bandlimited, so noise is also bandlimited and has
a nite power:
ΣTx filter Rx filterchannel
n(t)
n (t) B
n(t)
channel
B
y(t) y(k)
y(t) y(k)x(k) x(t)
Σ
Channel has
ertain
apa
ity
20
Resear
h Methods, ELEC6021 (EZ619) S Chen
Digital Modulation
Aim of MODEM: transmit bit stream at
ertain rate reliably
Mod. Demod.Channel
bit stream bit stream
Carrier
ommuni
ations
{ Low frequen
y signals (baseband)
annot travel far
{ Most spe
trum resour
es (
hannels) are in RF bands (high frequen
y passband)
Carrier: A
os(2f
t+ ), three quantities, amplitude, frequen
y and phase
Basi
digital modulation forms: amplitude shift keying (ASK), frequen
y shift
keying (FSK), and phase shift keying (PSK)
We will
onsider quadrature amplitude modulation (QAM), whi
h
an be viewed
as a
ombination of ASK and PSK
21
Resear
h Methods, ELEC6021 (EZ619) S Chen
Quadrature Amplitude Modulation
( )kxq
( )kx i ( )x ti
( )x tq
( )tg
( )tg
(ω t)sin
(ω t)cos
( )ts
Σδ tkT( s )
s/p const.
map
bit
stream
q
QAM symbol D/A conversion QAM modulation
generation
Note: e.g., odd bits go to form x
i
(k) and even bits to form x
q
(k); x
i
(k) and x
q
(k) are inphase and quadrature
omponents of the
x
i
(k) + jx
q
(k) QAM symbol; x
i
(k) and x
q
(k) are M ary symbols.
22
Resear
h Methods, ELEC6021 (EZ619) S Chen
Quadrature Amplitude Demodulation
( )ts
(ω t)sin
(ω t)cos
(g t )
(g t )
( )kx i
( )kxq
( )x ti
( )x tq
const.
map
q
Σδ tkT( )s
LP
LP
p/s bit
stream
QAM demodulation symbol dete
tion bit re
overy
Basi
ir
uits:
arrier re
overy, timingre
overy, dete
tion
23
Resear
h Methods, ELEC6021 (EZ619) S Chen
Pulse Shaping
Channel has nite bandwidth, and transmitted digital signal has to be pulse shaped
To transmit at symbol rate f
s
needs
ertain bandwidth B
T
and B
T
depends on
whi
h pulse shaping used
x(t) = r(t) ?
+1
X
k=1
x[k℄Æ(t kT
s
) =
+1
X
k=1
x[k℄ r(t kT
s
)
Σδ tkT )(
k[ ]x ( )tx( )tr
Pulse shaping lter r(t) would allow to retrieve the original digital data x[k℄ from
x(t): by limiting the bandwidth of x(t) to B
T
hannel bandwidth
24
Resear
h Methods, ELEC6021 (EZ619) S Chen
Pulse Shaping  Time Domain
−10 −8 −6 −4 −2 0 2 4 6 8 10
−0.2
0
0.2
0.4
0.6
0.8
1
time t/T
s
f
i
l
t
e
r
i
m
p
u
l
s
e
r
e
s
p
o
n
s
e
s
sinc
square pulse
raised cosine
Impulse response of all these lters have regular symbolsspa
ed zero
rossing
(Nyquist system), but dierent supports; raised
osine shown is a trun
ated one
25
Resear
h Methods, ELEC6021 (EZ619) S Chen
Pulse Shaping  Frequen
y Domain
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−70
−60
−50
−40
−30
−20
−10
0
frequency 2f/fs
f
i
l
t
e
r
m
a
g
n
i
t
u
d
e
r
e
s
p
o
n
s
e
s
/
[
d
B
]
sinc
square pulse
raised cosine
Spe
trum of the square pulse produ
es
onsiderable ex
ess bandwidth beyond the
symbol rate f
s
; sin
impra
ti
al to realize; trun
ated raised
osine easy to realize
26
Resear
h Methods, ELEC6021 (EZ619) S Chen
Pulse Shaping  Example
Binary (1) x[k℄, ea
h is transmitted as a sin
pulse; the peak of dierent shifted
sin
fun
tions
oin
ide with zero
rossings of all other sin
s:
−5 −4 −3 −2 −1 0 1 2 3 4 5
−1.5
−1
−0.5
0
0.5
1
1.5
time t/T
x
(
t
)
At re
eiver, sampling at
orre
t symbol rate enables re
overy of transmitted x[k℄
27
Resear
h Methods, ELEC6021 (EZ619) S Chen
Transmit and Re
eive Filters
Pulse shaping fullls two purposes: limit the transmitted bandwidth, and enable
to re
over the
orre
t sample values of transmitted symbols; su
h a pulse shaping
r(t) is
alled a Nyquist system
1. sin
has a (passband) bandwidth B
T
= f
s
, (innite) raised
osine has f
s
B
T
2f
s
depending on rollo fa
tor
2. a Nyquist time pulse have regular zero
rossing at symbolrate spa
ings to avoid
interferen
e with neighboring pulses at
orre
t sampling instan
es
The Nyquist system r(t) is separated into transmit lter g(t) and re
eive lter
g(t) (squareroot Nyquist systems)
1. the lter g(t) in the re
eiver is also
alled a mat
hed lter (to g(t)); g(t) and
g(t) are basi
ally identi
al (squareroot of r(t))
2. this division of r(t) enables suppression of outofband noise and results in the
maximum re
eived SNR
28
Resear
h Methods, ELEC6021 (EZ619) S Chen
QAM Modulator / Demodulator
Re
all modulator and demodulator of the QAM s
heme:
(ω t)sin
(ω t)cos(ω t)cos
(ω t)sin
( )ts
( )x tq( )x tq
( )x ti( )x ti LP
LP
i( )x t
q( )x t
( )ts
c
c c
c
Modulation of inphase and quadrature
omponents to
arrier frequen
y !
:
x
i
(t)
os(!
t) and x
q
(t) sin(!
t)
The transmitted signal is: s(t) = x
i
(t)
os(!
t) + x
q
(t) sin(!
t)
29
Resear
h Methods, ELEC6021 (EZ619) S Chen
QAM  Demodulation
To explain the demodulation, assume perfe
t transmission ^s(t) = s(t)
Demodulation for the \inphase"
omponent:
^x
0
i
(t) = s(t)
os(!
t) = (x
i
(t)
os(!
t) + x
q
(t) sin(!
t))
os(!
t)
= x
i
(t)
1
2
1 +
os(2!
t)
+ x
q
(t)
1
2
sin(2!
t)
If the lowpass lter LP is sele
ted appropriately (
uto frequen
y !
), the
omponents modulated at frequen
y 2!
an be ltered out, and hen
e:
^x
i
(t) = LP
^x
0
i
(t)
=
1
2
x
i
(t)
A similar
al
ulation
an be performed for the demodulation of ^x
q
(t):
^x
0
q
(t) = x
i
(t)
1
2
sin(2!
t) + x
q
(t)
1
2
1
os(2!
t)
30
Resear
h Methods, ELEC6021 (EZ619) S Chen
Modulation  Complex Notation
The modulation/demodulation
an be expressed in
omplex notation  inphase
and quadrature
omponents are \real" and \imaginary" part of the signal:
x(t) = x
i
(t) + j x
q
(t)
The transmitted signal is obtained by taking the real part only of a
omplex
arrier
(e
j!
t
) modulated signal:
s(t) = Refv(t)g = Refx(t) e
j!
t
g = x
i
(t)
os(!
t) + x
q
(t) sin(!
t)
Flow graph:


Refg

6
x(t) s(t)
v(t)
e
j!
t
31
Resear
h Methods, ELEC6021 (EZ619) S Chen
Demodulation  Complex Notation
Flow graph for the
omplex demodulation s
heme:


LP

6
^s(t) ^x(t)
^x
0
(t)
e
j!
t
The demodulated signal:
^x
0
(t) = e
j!
t
s(t)
= (
os(!
t) + j sin(!
t)) (x
i
(t)
os(!
t) + x
q
(t) sin(!
t))
= x
i
(t)
1
2
1 +
os(2!
t) + j sin(2!
t)
+
jx
q
(t)
1
2
1
os(2!
t) j sin(2!
t)
The lowpass lter (LP) will again remove
omponents modulated at 2!
32
Resear
h Methods, ELEC6021 (EZ619) S Chen
Bits to Symbols
The bit stream to be transmitted is serial / parallel multiplexed onto a stream z[k℄
of symbols of q bits/symbol (dis
rete 2
q
levels)
Example for q = 2 bits/symbol: 4ary modulation
(0,0)
(0,1)
(1,0)
(1,1)
0
1
1 1 1 1 10 0 0 0 0 time
time
z(k)
bit stream
symbol stream
Symbol rate is half of bit rate, and required bandwidth is half (but transmit power
has to be in
reased); symbol stream is then pulse shaped ...
33
Resear
h Methods, ELEC6021 (EZ619) S Chen
Mapping to Constellation Pattern
The symbols z[k℄ are translated into values for the inphase and quadrature
omponents, x
i
[k℄ and x
q
[k℄, by assigning them to points in a
onstellation pattern
Example for a
ase of q = 2 bits/symbol:
i( )x k
q( )x k
(1,1) (1,0)
(0,1) (0,0)
From the
onstellation pattern, the values x
i
[k℄ and x
q
[k℄ are determined
In the re
eiver, the
onstellation point (and therefore the transmitted symbol) is
determined from ^x
i
[k℄ and ^x
q
[k℄
34
Resear
h Methods, ELEC6021 (EZ619) S Chen
Phase Shift Keying (PSK)
Phase shift keying (PSK):
arrier phase is used to
arry symbol information
Example of QPSK (minimum phase separation
2
)
onstellation pattern and
transmitted signal s(t):
i( )x k
q( )x k
(1,0)
(1,1)
(0,1)
(0,0)
(00) (01) (11) (00) (10)
! time t
There are means to smooth dis
ontinuities in the signal s(t)
35
Resear
h Methods, ELEC6021 (EZ619) S Chen
Amplitude Shift Keying (ASK)
Amplitude shift keying (ASK):
arrier amplitude is used to
arry symbol information
Example of 4ary
onstellation pattern and transmitted signal s(t):
i( )x k
q( )x k
(0,0)(0,1)(1,0)(1,1)
(00) (01) (11) (00) (10)
! time t
Note: (i) the quadrature
omponent is not used; (ii) this is not \purely" ASK, as
a phase shift of is exploited in the modulation s
heme.
36
Resear
h Methods, ELEC6021 (EZ619) S Chen
Combined ASK / PSK
QAM:
ombines features of PSK and
ASK, and is bandwidth very eÆ
ient
Example of 16QAM (4 bits per
symbol):
q( )x k
i( )x k
Depending on the
hannel quality, 64QAM (6 bits/symbol), or 256QAM (8
bits/symbol) are possible
37
Resear
h Methods, ELEC6021 (EZ619) S Chen
Gray Mapping
If noise or distortions are likely
to
ause mis
lassi
ation in the
re
eiver, Gray
ode mapping
an
minimize the bit error rate:
q( )x k
i( )x k
(0000) (0001)
(0101) (0111) (0110)
(0010)(0011)
(1100) (1101)
(1000) (1001)
(1111) (1110)
(1011) (1010)
(0100)
Adja
ent
onstellation points only vary in a single bit (minimum Hamming distan
e)
38
Resear
h Methods, ELEC6021 (EZ619) S Chen
Carrier Re
overy  Phase Oset
Previously, we assume
^s(t) = s(t) = x
i
(t)
os(!
t) + x
q
(t) sin(!
t)
so that we
an use e
j!
t
to remove
arrier in demodulator
Most likely, the transmitted signal having traveled to the re
eiver will a
umulate
a phase oset ':
^s(t) = x
i
(t)
os(!
t+ ') + x
q
(t) sin(!
t+ ')
Thus, the re
eiver has to \re
over" the
arrier e
j(!
t+')
(in fa
t the phase ') in
oder to demodulate the signal
orre
tly
Usually, this is done by means of some phase lo
k loop based
arrier re
overy
39
Resear
h Methods, ELEC6021 (EZ619) S Chen
Carrier Re
overy  Frequen
y Oset
Tx and Rx frequen
y generators are unlikely to mat
h exa
tly. Consider
demodulation with a Rx lo
al \
arrier" having a frequen
y oset !
:


LP

6
^s(t) ^x(t)
^x
0
(t)
e
j(!
+!
)t
Even assuming ^s(t) = s(t), the demodulated signal prior to sampling is ^x(t) =
x(t) e
j!
t
, not ^x(t) = x(t)
The ee
t of
arrier frequen
y mismat
h is !
t and, like the phase dieren
e ',
it has to be
ompensated at the re
eiver
!
t+' is
alled
arrier oset, and has to be \re
overed" in order to demodulate
the signal
orre
tly
40
Resear
h Methods, ELEC6021 (EZ619) S Chen
Syn
hronisation
The pro
ess of sele
ting the
orre
t sampling instan
es is
alled syn
hronisation,
also known as timing or
lo
k re
overy
Tx and Rx
lo
ks are likely to have mismat
h,
lo
k re
overy tries to syn
hronise
the re
eiver
lo
k with the symbolrate transmitter
lo
k to obtain samples at
appropriate instan
es
This is equivalent to repla
ing the impulse train
P
Æ(t kT
s
) by
P
Æ(t kT
s
)
with 0 T
s
:
kTs  τ
k[ ]x( )tx
The demodulated signal
an be oversampled, and from the distribution (histogram)
of the sample sets for dierent , the one with the smallest deviation from dis
rete
levels (depending on the QAM mode, 16QAM, 64QAM, et
.) is
hosen
41
Resear
h Methods, ELEC6021 (EZ619) S Chen
Eye Diagram  Perfe
t Channel
We are looking at sta
ked 2 symbol period intervals of the demodulated signal
^x
i
(t) in a QPSK s
heme (^x
i
(t) is BPSK):
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
time /symbol periods
x
i
(
t
)
This is
alled an eye diagram; ideal sampling of ^x
i
(k) will sample the
rossing
points ^x
i
(t) = 1 !
lo
k/timing re
overy ( 0:85T
s
)
42
Resear
h Methods, ELEC6021 (EZ619) S Chen
Eye Diagram  Noisy Channel
With
hannel noise at 3dB SNR, the eye diagram looks dierent:
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
time /symbol periods
x
i
(
t
)
But as long as the sampling points
an be
learly determined and the eye is \open",
^x
i
[k℄ will
orre
tly resemble x
i
[k℄. At higher noise levels, mis
lassi
ations
an
o
ur if the eye is \
losed"
43
Resear
h Methods, ELEC6021 (EZ619) S Chen
Eye Diagram  Distorting Channel
The
hannel is nonideal with an impulse response
(t) = Æ(t)
1
2
Æ(t T
s
=4),
where T
s
is the symbol period:
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
time /symbol periods
x
i
(
t
)
The eye diagram is distorted; this together with noise ee
t will make the eye
ompletely
losed, leading to mis
lassi
ation due to intersymbol interferen
e
44
Resear
h Methods, ELEC6021 (EZ619) S Chen
Intersymbol Interferen
e (ISI)
The response of an ideal pulse shaping lter with regular symbolspa
ed zero
rossings, and the same system in
ombination with the
hannel impulse response
(t) = Æ(t)
1
2
Æ(t T
s
=4):
0 1 2 3 4 5 6 7 8
−0.2
0
0.2
0.4
0.6
0.8
1
time / symbol periods
t
x
r
x
f
i
l
t
e
r
*
c
h
a
n
n
e
l
The system, Txlter {
hannel { Rx lter, has lost the property of a Nyquist system;
peaks of the fun
tion no longer
oin
ide with zero
rossings of neighbouring pulses
45
Resear
h Methods, ELEC6021 (EZ619) S Chen
Equalisation
For an ideal
hannel without ISI, sampled re
eiver output is
^x[k℄ =
x[k ℄ + n[k℄
If the
hannel has sever amplitude and phase distortion, sampling alone is unable
to re
over the
orre
t symbols; This is be
ause now (note the ISI)
^x[k℄ =
n
X
i=0
i
x[k i℄ + n[k℄
An equaliser is required to
ombat the
hannel distortion, and a typi
al linear
equaliser is dened by:
y[k℄ =
n
w
X
l=0
w
l
^x[k l℄
The equaliser soft output y[k℄ is used to determine the transmitted symbol x[k℄
46
Resear
h Methods, ELEC6021 (EZ619) S Chen
Equalisation Design
Let the ztransforms of the
hannel and equaliser be C(z) and W (z); Similarly
dene X(z),
^
X(z) and Y (z)

X(z)
C(z)

W (z)

^
X(z)
Y (z)
Zerofor
ing: we want to nd an equaliserW (z) su
h that Y (z) is a delayed version
of the transmitted signal, Y (z) = z
X(z)
{ The solution is
W (z) C(z) = z
or W (z) = z
C
1
(z)
{ Completely eliminate ISI, but amplify the noise too mu
h
Minimum mean square error:
hoose the equaliser W (z) to minimise
MSE = E [jx[k ℄ y[k℄j
2
℄
47
Resear
h Methods, ELEC6021 (EZ619) S Chen
Adaptive Equalisation
Training: periodi
ally provide the re
eiver with x[k℄ so that equaliser
an adjust its
weights w
i
using fx[k℄; ^x[k℄g
{ This happens for example in your GSM mobile phone
{ Training requires extra bandwidth and may not always be possible
Blind: equaliser has to adjust its weights having only the re
eived signal f^x[k℄g
{ Constellations of a
blind equaliser's input
^x[k℄ and output y[k℄
20
15
10
5
0
5
10
15
20
20 15 10 5 0 5 10 15 20
I
m
Re
20
15
10
5
0
5
10
15
20
20 15 10 5 0 5 10 15 20
I
m
Re
48
Resear
h Methods, ELEC6021 (EZ619) S Chen
User / Channel Separation
System has large
apa
ity and supports many users; dierent users or \
hannels"
mu
h separate in some way:
{ FDMA: separation is in frequen
y domain, dierent users have dierent
arriers
and
hannels o
upy dierent frequen
y bands
{ TDMA: same
arrier or frequen
y band, but separation is in time domain,
dierent users o
upy dierent time slots
{ CDMA: no physi
al separation, i.e. same
arrier and time slot, but virtual
separation is in \
ode" domain, dierent users have dierent spreading
odes
{ SDMA: if no separation in frequen
y or time or
ode domain, separation
an still
be a
hieved in spatial domain { this further enhan
es spe
trum eÆ
ien
y
CDMA is a key te
hnology in 3G systems, and SDMA has an important role in 4G
systems
49
Resear
h Methods, ELEC6021 (EZ619) S Chen
DSCDMA System
DSCDMA uplink, supporting K users
x (t)1
s (t)1 cos( t)ωc
τ1X X
cos( t)ωc
XX
s (t)
x (t)
2
2
2τ
.
.
.
cos( t)ωc
XX
cos( t)ωc
X
s (t− )1 τ1
x (t)1^
X
x (t)K^x (t)K
s (t)K
τK
n(t)
XΣ
s (t− )2 τ2
X
.
.
.
K τK
x (t)2^
s (t− )
50
Resear
h Methods, ELEC6021 (EZ619) S Chen
OFDM
Channel is divided into many sub
hannels, ea
h supports a sub
arrier; Data stream
is divided into several bit streams, whi
h are used to modulate several
arriers
S ,0 S ,1 ...SN−1 S ,0 1...SN−1
fN−1demodulator
demodulator
demodulatormodulator
modulator fN−1
f 0
f1modulator
.
.
.
.
.
.
S/P P/S
SN−1
S
S0
1
S
S
SN−1
1
0
0f
1f
S ,
OFDM trans
eiver
N−1SS1...S0
S0
S1
SN−1 .
.
.
S
/
P
I
F
F
T
P
/
S
s0
s1
sN−1
.
.
.
add
C.Ext.
cos(2 f t)pi c
picos(2 f t)c
S
/
P
F
F
T
P
/
S
rem.
C.Ext.
r
r
N−1r
1
0
.
.
.
N−1R
R
R
0
1
.
.
.
51
Resear
h Methods, ELEC6021 (EZ619) S Chen
MIMO
SDMA indu
ed MIMO system Spa
etime equalisation
user 1 modulator Σ
modulatoruser 2
.
.
.
modulatoruser K
Σ
Σ
n (t)
n (t)
1
2
L
x (t)1
x (t)L
2x (t)
n (t)
.
.
.
R
e
c
e
i
v
e
r
XXX
...
...
...+
+ +
X
...
+
...
...
+
+
XX
.
.
.
.
.
.
x (k)
x (k)L
x (k)1
∆ ∆ ∆
∆∆∆
∆ ∆ ∆
w
XX
1,0
* w1,1
* w1,D
*
w w w2,0 2,1 2,D
***
w w
w
L,D
L,0 L,1
* *
*
y(k)
+
X
2
52
Resear
h Methods, ELEC6021 (EZ619) S Chen
Channel Capa
ity and Channel Coding
Even in
ase of a noisy
hannel, there is no obstru
tion of reliable transmission,
but only a limitation of the rate at whi
h transmission
an take pla
e
Reliable transmission
an be established by introdu
ing redundan
y into the
transmitted message to a
hieve arbitrarily low bit errors
The
hannel
apa
ity C forms a limit for the
oding rate R:
R =
K
N
C
R = K=N is the ratio between the number of true (information) bits (K) and the
number of bits after redundan
y has been introdu
ed by
hannel
oding (N)
Example: binary symmetri
hannel, P (1) = P (0) with p
e
= 0:1 ! C 0:5
! N 2K, i.e. at least 100% redundan
y needs to be in
orporated into the
transmitted bit stream in order to obtain an errorfree re
eption
53
Resear
h Methods, ELEC6021 (EZ619) S Chen
Convolutional Coding (CC)
A
onvolutional
oder CC(N;K;L) takes a Kbit information symbol, whi
h is
shifted into an Lbit shift register (holding a memory of L+ 1 bits!) and forms by
onvolution over this memory N output bits. Hen
e
oding rate R = K=N
Example: blo
k diagram of a CC(2,1,2) halfrate (R =
1
2
) systemati
oder:
Cn1
C2n
Bn
1Sn Sn
2
Output bits are dened by N generator polynomials; here: g
1
= [1 0 0℄, g
2
= [1 1 1℄
54
Resear
h Methods, ELEC6021 (EZ619) S Chen
CC  State and State Transition Diagrams
With the previous CC(2,1,2) example, a state diagram (left)
an be asso
iated
00
11
01 10
Bn
Bn
=0
=1
Bn
Bn
S2n+1S1n+1S1nS2n Cn1C2n
01 01
00
11
10
00
10
11
=0
=1
11
00
10
01
01
00
10
11
The state transition diagram (right) indi
ates the time dimension, and the
ode
output with ea
h iteration of the CC
55
Resear
h Methods, ELEC6021 (EZ619) S Chen
Trellis Path
Consider the data sequen
e B
n
= [0 0 1 0 1℄
Channel
oding with previous (2,1,2)
oder gives, starting from state S
1
n
S
2
n
= 00:
nS1 nS2
nB
Cn1C2n
01
10
11
00
0 0 1 0 1
00 00 11 01 10
This
an be exploited for the
hannel de
oding
56
Resear
h Methods, ELEC6021 (EZ619) S Chen
Viterbi De
oding (I)
In our example, the transmitted bit sequen
e is C
1
n
C
2
n
= [00 00 11 01 10℄
Assume, the re
eived sequen
e is
~
C
1
n
~
C
2
n
= [00 10 11 11 10℄, i.e. two bit errors have
o
urred
Viterbi de
oding inspe
ts all possible paths in the trellis diagram
A metri
to sele
t the best (or \survivor") path is the minimum Hamming distan
e
(number of dierent bits)
Therefore, starting from state 00, for ea
h possible path the Hamming distan
e is
evaluated and a
umulated
If paths are joined, the ones with the larger Hamming distan
e are dis
arded; for
equal distan
e, a random de
ision is made
57
Resear
h Methods, ELEC6021 (EZ619) S Chen
Viterbi De
oding (II)
Trellis graphs for re
eived sequen
e
~
C
1
n
~
C
2
n
= [00 10 11 11 10℄:
nS1 nS2
Cn1C2n
nB
01
10
11
00 0
00 11 101110
0 1 1
1
0
2
2
2
1
2
4
2 3
0
1
1
2
20
1
1
3
0
1
3
0 2
1
2
0
21
3
0
1 3
2
1 4
~ ~
0 0 1 0 1
path
survivor
58
Resear
h Methods, ELEC6021 (EZ619) S Chen
Viterbi De
oding (III)
The nal survivor path determines the \most likely" transmitted sequen
e; hen
e
the Viterbi de
oder is referred to as a maximum likelihood (ML) dete
tor
If the
orre
t sequen
e is yielded, the
umulative Hamming distan
e of the survivor
path gives the number of o
urred bit errors
If too many bit errors have o
urred or bit errors are awkwardly distributed, Viterbi
de
oding will fail
The above hardde
ision de
oding
an be improved by softde
ision de
oding,
whereby \ner" levels of probability are assigned to the bran
hes in the trellis
diagram
More generally, demodulator
an output softde
ision, thus de
oder has softinput
and
an output softde
ision (SISO)
59
Resear
h Methods, ELEC6021 (EZ619) S Chen
Turbo Coding
Turbo en
oder, assuming
systemati
C(2; 1; 2)
Turbo de
oder
iterative de
oding
output bitspuncturing
and
multiplexing
encoder 1
encoder 2
input bits
interleaver
decoder 1 deinterlv
deinterlvdecoder 2
+
+
−
−
−
−
systematic
parity 1
parity 2
outputs
channel
soft
interleaver
60
Resear
h Methods, ELEC6021 (EZ619) S Chen
Adaptive Equalisation
Re
all the framework of adaptive equalisation with two operation modes, training and de
ision
dire
ted, where the
hannel model is:
r(k) =
n
X
i=0
i
s(k i) + n(k)
symbols are N ary
s(k) 2 fs
i
= 2iN1; 1 i Ng
and AWGN n(k) has varian
e
2
n
^s(k) r(k) r(k) s(kd)
s(kd)

Σ
Σ
n(k)
^
ddelay
y(k)
channel equaliser decisioncircuit
We will rst dis
uss symbolde
ision equalisers and follow it by an introdu
tion to the MLSE
An equaliser de
ision delay d is ne
essary for
oping with nonminimum phase
hannels
The zerofor
ing equaliser H
E
(z) inverses the
hannel H
C
(z): H
C
(z)H
E
(z) z
d
Solving this gives the linear equaliser's weights. Although this zerofor
ing equaliser
ompletely
eliminates ISI, it suers from a serious noise enhan
ement problem
The most popular designs are the linear equaliser and de
ision feedba
k equaliser based on the
mean square error
riterion
61
Resear
h Methods, ELEC6021 (EZ619) S Chen
Linear Transversal Equaliser
The linear equaliser is given by:
y(k) =
M
X
i=0
w
i
r(k i) = w
T
r(k)
where r(k) = [r(k) r(k M)℄
T
and
M is the equaliser order
r(k1) r(kM)
...
s(kd)
z z
^
filtering
r(k)
1 1
y(k)
circuit
decision
Typi
al design is based on mean square error with the MMSE solution:
^
w = R
1
p,
where R = E[r(k)r
T
(k)℄ and p = E[r(k)s(k d)℄
Adaptive implementation typi
ally adopts the LMS:
~
w(k+1) =
~
w(k)+r(k)e(k) with e(k) =
y(k) s(k d); training
y(k) ^s(k d); de
isiondire
ted
62
Resear
h Methods, ELEC6021 (EZ619) S Chen
De
ision Feedba
k Equaliser
The DFE
onsists of a feedforward lter
and a feedba
k lter:
y(k) = w
T
r(k) + b
T
^
s(k d)
=
M
X
i=0
w
i
r(ki)+
n
f
X
i=1
b
i
^s(kdi)
The DFE generally outperforms the LTE
in terms MSE and BER
z z
z z
z
f
. . .
. . .
s(kd)decisionfiltering
r(k) r(k1)
s(kd2) s(kd1)
1 1
1 1 1
^
^^ ^
r(kM)
circuit
s(kdn )
y(k)
Assuming equaliser de
isions
^
s(k d) are
orre
t, the feedba
k lter b
T
^
s(k d) eliminates a
large proportion of ISI without enhan
ing noise and the feedforward lter w
T
r(k) takes
are the
remaining ISI
Error propagation. O
asionally error o
urs in symbol dete
tion, i.e. ^s(k d) 6= s(k d), it
is fed ba
k and will ae
t subsequent symbol dete
tions ! further burst errors
Choi
e of stru
ture parameters. A simple pra
ti
al rule: feedforward lter
overs entire
hannel
dispersion, i.e. M = n
; de
ision delay is set to d = n
; and feedba
k lter order n
f
= n
63
Resear
h Methods, ELEC6021 (EZ619) S Chen
Blind Equalisation
In blind equalisation, there is no training, an equaliser has to estimate the
transmitted symbols and/or
hannel based only on the re
eived samples r(k)
There are three
lasses of blind equalisation algorithms
{ Joint data and
hannel estimation: e.g. using blind or super trellis sear
h
te
hniques. This produ
es the best results but
an be
omputationally prohibitive
{ Higherorder statisti
s based methods: to identify the
hannel using r(k)
only, 2nd order statisti
is insuÆ
ient as it is phase blind. Higherorder statisti
s
based methods
an over
ome this problem. This approa
h produ
es very good
results but
omputational
ost
an be very expensive
{ Bussgangtype adaptive FIR lters: optimize some nonMSE type
ost
fun
tions using sto
hasti
gradient,
omputationally very simple
We will dis
uss the 3rd
lass. Sin
e there is no desired response s(k d) for the
adaptive lter, one has to \invent" some substitute ! the resulting nonMSE
ost
fun
tions generally have lo
al minima, and this often
auses problems
64
Resear
h Methods, ELEC6021 (EZ619) S Chen
Constant Modulus Algorithm
We will
onsider the general QAM
ase and use
omplex notations, e.g. the
hannel
taps
i
=
R;i
+ j
I;i
, the re
eived signals r(k) = r
R
(k) + jr
I
(k), the symbols
s(k) = s
R
(k) + js
I
(k), and the equaliser weights w
i
= w
R;i
+ jw
I;i
Dene the
onstant
2
= E[js(k)j
4
℄=E[js(k)j
2
℄, and
onsider adaptive lter or
blind equaliser:
y(k) = w
T
r(k)
with w = [w
0
w
M
℄
T
and r(k) = [r(k) r(k M)℄
T
Although QAM symbols do not fall on the
onstant modulus
ir
le of radius
p
2
,
by penalizing equaliser output y(k) whi
h deviates from this
ir
le, the
orre
t
symbol
onstellation
an be restored
This leads to the CMA, whi
h is the most popular blind equaliser for highorder
QAM signalling, as it has simple
omputational requirements similar to those of
the LMS
65
Resear
h Methods, ELEC6021 (EZ619) S Chen
CMA (
ontinue)
The CMA
an be viewed to adjust w by minimizing the non
onvex
ost fun
tion
J
CMA
(w) = E[(jy(k)j
2
2
)
2
℄
using a sto
hasti
gradient method, i.e. a
tually through minimizing (jy(k)j
2
2
)
2
At sample k, given y(k) = w
T
(k)r(k), the equaliser weights are updated using:
(k) = y(k)(
2
jy(k)j
2
)
w(k + 1) = w(k) + (k)r
(k)
where is a very small positive adaptive gain and r
(k) is the
onjugate of r(k)
Compare this with the LMS, where (k) = s(k d) y(k)
There are many solutions w
s
that minimize the
ost fun
tion
J
CMA
(w). One of them, w
opt
,
restores the
orre
t signal
onstellation and is
orresponding to the MMSE solution
The weight ve
tors that minimize
J
CMA
(w) are thus
w
s
= exp(j)w
opt
; 0 < 2
This undesired phase shift
annot be resolved by the CMA (all blind equalisers suer more or less a
similar problem), and must be eliminated by other means, e.g. using dierential en
oding
66
Resear
h Methods, ELEC6021 (EZ619) S Chen
Complex Variable Derivative
Complexvalued variable derivative is dened as
J(w)
w
i
=
1
2
J
w
R;i
+ j
J
w
I;i
Note that y(k) = w
0
r(k) + + w
M
r(k M) and
J(w) =
1
2
(jy(k)j
2
2
)
2
=
1
2
(y(k)y
(k)
2
)
2
Hen
e we have
J
w
i
=
1
2
2(y(k)y
(k)
2
)
y(k)y
(k)
w
i
= (jy(k)j
2
2
)
y(k)
w
i
y
(k) + y(k)
y
(k)
w
i
Note
y(k)
w
i
=
1
2
y(k)
w
R;i
+ j
y(k)
w
I;i
y(k)
w
R;i
= r
R
(k i) + jr
I
(k i) and
y(k)
w
I;i
= r
I
(k i) + jr
R
(k i)
This leads to
y(k)
w
i
= 0
67
Resear
h Methods, ELEC6021 (EZ619) S Chen
Complex Variable Derivative (
ontinue)
Note
y
(k)
w
i
=
1
2
y
(k)
w
R;i
+ j
y
(k)
w
I;i
y
(k)
w
R;i
= r
R
(k i) jr
I
(k i) and
y
(k)
w
I;i
= r
I
(k i) jr
R
(k i)
This leads to
y
(k)
w
i
= r
(k i)
Therefore, the gradient
rJ(w) =
J(w)
w
T
= y(k)(jy(k)j
2
2
)r
(k)
Using
w(k + 1) = w(k) + (rJ(w(k)))
leads to
w(k + 1) = w(k) + y(k)(
2
jy(k)j
2
)r
(k)
68