辅导案例-ELEC6021

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
e-time 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: high-speed
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 Multi-Carrier Quadrature Amplitude Modulation. Wiley, 2000. L. Hanzo, M. Munster, B.J. Choi and T. Keller, OFDM and MC-CDMA. Wiley, 2003 A. Paulraj, R. Nabar and D. Gore, Introdu
tion to Spa
e-Time 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, signal-to-noise ratio S N , and { maximum rate for possible error-free 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 quasi-periodi
or noise-like 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 non-redundant information (i.e. the predi
tion error and predi
tive model
oeÆ
ients) ! good quality, reasonable
ompression { Analysis-by-synthesis 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 (analysis-by-synthesis and predi
tive
oding methods) { Hybrid
ode
s (trade-o 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: variable-rate for rates 16 { 40 kbps, allowing the network to adjust quality/bitrate on instantaneous requirement { G.727
ode
s:
ore-bits 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: Sub-band
oding and adaptive transform
oding 13 Resear
h Methods, ELEC6021 (EZ619) S Chen Analysis-by-Synthesis 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 analysis-
by-synthesis { 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 Short-term predi
tion: spee
h analysis segments 20 ms duration Long-term predi
tion (LTP): LTP synthesis lter models the ne stru
ture of the spee
h spe
trum, after short-term 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 Half-Rate 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 gain-related 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 { noise-like 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 inter-frame
orrelations, i.e.
orrelations within f n and between f n and past frames f n 1 , f n 2 , 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 MPEG-1: 1.5 Mbps; MPEG-2: 2 to 8 Mbps, now upto 30 Mbps for digital TV MPEG-4: initiated in 1993, for intera
tive multimedia appli
ations MPEG-7: 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 t-kT( 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 t-kT( )s LP LP p/s bit stream QAM demodulation symbol dete
tion bit re
overy Basi

ir
uits:
arrier re
overy, timing-re
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 t-kT )( 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 symbols-spa
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 roll-o fa
tor 2. a Nyquist time pulse have regular zero-
rossing at symbol-rate 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) (square-root 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 (square-root of r(t)) 2. this division of r(t) enables suppression of out-of-band 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 in-phase 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 \in-phase”
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 (
ut-o 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 perfo
rmed 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 | in-phase 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: 4-ary 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 in-phase 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 4-ary
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 16-QAM (4 bits per symbol): q( )x k i( )x k Depending on the
hannel quality, 64-QAM (6 bits/symbol), or 256-QAM (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 symbol-rate 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, 16-QAM, 64-QAM, 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 non-ideal 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 symbol-spa
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, Tx-lter {
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 z-transforms 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) Zero-for
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 DS-CDMA System DS-CDMA 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
e-time 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 error-free re
eption 53 Resear
h Methods, ELEC6021 (EZ619) S Chen Convolutional Coding (CC) A
onvolutional
oder CC(N;K;L) takes a K-bit information symbol, whi
h is shifted into an L-bit 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) half-rate (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 hard-de
ision de
oding
an be improved by soft-de
ision de
oding, whereby \ner” levels of probability are assigned to the bran
hes in the trellis diagram More generally, demodulator
an output soft-de
ision, thus de
oder has soft-input and
an output soft-de
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 = 2i N 1; 1 i Ng and AWGN n(k) has varian
e 2 n ^s(k) r(k) r(k) s(k-d) s(k-d) – Σ Σ n(k) ^ ddelay y(k) channel equaliser decisioncircuit We will rst dis
uss symbol-de
ision equalisers and follow it by an introdu
tion to the MLSE An equaliser de
ision delay d is ne
essary for
oping with non-minimum phase
hannels The zero-for
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 zero-for
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 T
he 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(k-1) r(k-M) … s(k-d) 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
ision-dire
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(k i)+ n f X i=1 b i ^s(k d i) The DFE generally outperforms the LTE in terms MSE and BER z z z z z f . . . . . . s(k-d)decisionfiltering r(k) r(k-1) s(k-d-2) s(k-d-1) -1 -1 -1 -1 -1 ^ ^^ ^ r(k-M) circuit s(k-d-n ) 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 { Higher-order statisti
s based methods: to identify the
hannel using r(k) only, 2nd order statisti
is insuÆ
ient as it is phase blind. Higher-order statisti
s based methods
an over
ome this problem. This approa
h produ
es very good results but
omputational
ost
an be very expensive { Bussgang-type adaptive FIR lters: optimize some non-MSE 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 non-MSE
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 high-order 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 Complex-valued 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