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Manh Le Tran

This document summarizes a lecture on transmitter design for digital communication systems. It discusses: 1) The basic components of a transmitter including constellations for linear modulation such as PAM, PSK, and QAM, and transmit filters. 2) Preliminaries on passband versus baseband transmission and how a baseband equivalent model can be obtained using complex envelope signals. 3) Details on common constellation designs including distance metrics for PAM, PSK, and QAM in an AWGN channel. 4) Analysis of bit error rate performance for the transmission of a single symbol over an AWGN channel for different constellations. The document also discusses designing transmit pulses to eliminate

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27/4/00 p. 1 Postacademic Course on Telecommunications Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven/ESAT-SISTA Module-3 : Transmission Lecture-3 (27/4/00) Marc Moonen Dept. E.E./ESAT, K.U.Leuven marc.moonen@esat.kuleuven.ac.be www.esat.kuleuven.ac.be/sista/~moonen/
Postacademic Course on Telecommunications 27/4/00 p. 2 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Lecture-3: Transmitter Design Overview • Transmitter : Constellation + Transmit filter • Preliminaries : Passband vs. baseband transmission • Constellations for linear modulation ->M-PAM / M-PSK / M-QAM ->BER performance in AWGN channel for transmission of 1 symbol (Gray coding, Matched filter reception) • Transmission pulses : ->Zero-ISI-forcing design procedure for transmit pulse (and receiver front-end filter), Nyquist pulses, RRC pulses
Postacademic Course on Telecommunications 27/4/00 p. 3 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Lecture-3: Transmitter Design Lecture partly adopted from Module T2 `Digital Communication Principles’ M.Engels, M. Moeneclaey, G. Van Der Plas 1998 Postgraduate Course on Telecommunications Special thanks to Prof. Marc Moeneclaey
Postacademic Course on Telecommunications 27/4/00 p. 4 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmitter: Constellation + Transmit Filter PS: channel coding (!) not considered here s k E a . r(t) k â transmit pulse s(t) n(t) p(t) + AWGN transmitter receiver (to be defined) h(t) channel ... constellation transmit filter (linear modulation)    k s k s kT t p a E t s ) ( . . ) (
Postacademic Course on Telecommunications 27/4/00 p. 5 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmitter: Constellation + Transmit Filter -> s(t) with infinite bandwidth, not the greatest choice for p(t).. -> implementation: upsampling/digital filtering/D-to-A/S&H/... s k E a . transmit pulse s(t) p(t) transmitter discrete-time symbol sequence continuous-time transmit signal t p(t) Example: t
Postacademic Course on Telecommunications 27/4/00 p. 6 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries: Passband vs. baseband transmission (I) Baseband transmission • transmitted signal is (linear modulation) • transmitted signals have to be real, hence = real, p(t)=real • baseband means for f B -B 0 ) (  f SLP B f  | | ) ( f SLP    k s k s LP kT t p a E t s ) ( . . ) ( k a
Postacademic Course on Telecommunications 27/4/00 p. 7 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (II) Baseband transmission model/definitions g(t)=p(t)*h(t)*f(t) (convolution) everything is real here! s k E a . r(t) k â transmit pulse s(t) n(t) p(t) + f(t) front-end filter AWGN 1/Ts transmitter receiver (first version, see also Lecture4) h(t) channel
Postacademic Course on Telecommunications 27/4/00 p. 8 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (III) Bandpass transmission transmitted signal is modulated baseband signal ) (t sLP ) . 2 cos( 0t f  f B -B ) ( f SLP ) (t sBP -fo f ) ( f SBP fo fo+B
Postacademic Course on Telecommunications 27/4/00 p. 9 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (IV) Bandpass transmission: • note that modulated signal has 2x larger bandwidth, hence inefficient scheme ! • solution = accommodate 2 baseband signals in 1 bandpass signal : I =`in-phase signal’ Q=`quadrature signal’ such that energy in BP is energy in LP 2
Postacademic Course on Telecommunications 27/4/00 p. 10 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (V) • Convenient notation for `two-signals-in-one’ is complex notation : • re-construct `complex envelope’ from BP-signal (mathematics omitted) ) ( . ) ( ) ( t s j t s t s Q I LP   low-pass filter
Postacademic Course on Telecommunications 27/4/00 p. 11 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Assignment 2.1 • Prove for yourself that this is indeed a correct complex-envelope reconstruction procedure! low-pass filter
Postacademic Course on Telecommunications 27/4/00 p. 12 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (VI) Passband transmission model/definitions (mathematics omitted): a convenient and consistent (baseband) model can be obtained, based on complex envelope signals, that does not have the modulation/demodulation steps: k â f(t) front-end filter 1/Ts receiver (first version) r(t) n’(t) + AWGN s k E a . transmit pulse s(t) p(t) transmitter h’(t) channel
Postacademic Course on Telecommunications 27/4/00 p. 13 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (V) k â f(t) front-end filter 1/Ts receiver (first version) r(t) n’(t) + AWGN s k E a . transmit pulse s(t) p(t) transmitter h’(t) channel =complex symbols =usually a complex filter ) ( ) ( ' 0 2 t h e t h t f j    =complex AWGN =complex =real-valued transmit pulse Q k I k k a j a a , , .  
Postacademic Course on Telecommunications 27/4/00 p. 14 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (VI) • In the sequel, we will always use this baseband- equivalent model, with minor notational changes (h(t) and n(t), i.o. h’(t) and n’(t)). Hence no major difference between baseband and passband transmission/models (except that many things (e.g. symbols) can become complex-valued). • PS: modulation/demodulation steps are transparent (hence may be omitted in baseband model) only if receiver achieves perfect carrier synchronization (frequency fo & phase). Synchronization not addressed here (see e.g. Lee & Messerschmitt, Chapter 16).
Postacademic Course on Telecommunications 27/4/00 p. 15 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (I) Transmitted signal (envelope) is: Constellations: PAM PSK QAM pulse amplitude modulation phase-shift keying quadrature amplitude modulation 4-PAM (2bits) 8-PSK (3bits) 16-QAM (4bits) ps: complex constellations for passband transmission I R I R I R    k s k s kT t p a E t s ) ( . . ) (
Postacademic Course on Telecommunications 27/4/00 p. 16 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (II) M-PAM pulse amplitude modulation • energy-normalized iff • then distance between nearest neighbors is larger d -> noise immunity (see below) I R   PAM PAM PAM k A M A A a ) 1 ( ,....., 3 ,      k a 1 3 ) ( 2   M M APAM 1 12 ) ( 2   M M dPAM d
Postacademic Course on Telecommunications 27/4/00 p. 17 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (III) M-PSK phase-shift keying • energy-normalized iff …. • Then distance between nearest neighbors is          1 ,..., 1 , 0 | ) 2 . exp( M m M m j ak  k a ) sin( . 2 ) ( M M dPSK   d I R
Postacademic Course on Telecommunications 27/4/00 p. 18 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (IV) M-QAM quadrature amplitude modulation • distance between nearest neighbors is 1 6 ) (   M M dQAM d I R   QAM QAM QAM k Q k I A M A A a a ) 1 ( ,....., 3 , , , ,      k Q k I k a j a a , , .   ) ( ) ( ) ( M d M d M d QAM PSK PAM  
Postacademic Course on Telecommunications 27/4/00 p. 19 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel BER=(# bit errors)/(# transmitted bits) g(t)=p(t)*f(t) (convolution) n’(t)=n(t)*f(t) BER for different constellations? r(t) k â transmit pulse s(t) n(t) p(t) + s k E a . f(t) front-end filter AWGN channel 1/Ts transmitter receiver r’(t)
Postacademic Course on Telecommunications 27/4/00 p. 20 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel definitions: - transmitted signal - received signal (at front-end filter) - received signal (at sampler) g(t) =p(t)*f(t) = transmitted pulse p(t) filtered by front-end filter n’(t) =n(t)*f(t) = AWGN filtered by front-end filter ) ( ' ) ( . . ) ( ' t n kT t g a E t r k s k s        k s k s kT t p a E t s ) ( . . ) ( ) ( ) ( . . ) ( t n kT t p a E t r k s k s    
Postacademic Course on Telecommunications 27/4/00 p. 21 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel Received signal sampled @ time t=k.Ts is... 1 = useful term 2= `ISI’, intersymbol interference (from symbols other than ) 3= noise term Strategy : a) analyze BER in absence of ISI (=`transmission of 1 symbol’) b) analyze pulses for which ISI-term = 0 (such that analysis under a. applies) c) for non-zero ISI, see Lecture 4-5                3 2 0 1 ) . ( ' ) . ( . ) 0 ( . . ) . ( ' s m s m k k s s T k n T m g a g a E T k r       k a
Postacademic Course on Telecommunications 27/4/00 p. 22 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (I) BER for different constellations? k â transmit pulse n(t) p(t) + s E a . 0 f(t) front-end filter AWGN channel 1/Ts ...take 1 sample at time 0.Ts transmit 1 symbol at time 0.Ts ...
Postacademic Course on Telecommunications 27/4/00 p. 23 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (II) Received signal sampled @ time t=0.Ts is.. • `Minimum distance’ decision rule/device :          3 2 1 0 ) . 0 ( ' 0 ) 0 ( . . ) . 0 ( ' s s s T n g a E T r    n s s M n i s s i g E T r g E T r a            ) 0 ( . ) . 0 ( ' min ) 0 ( . ) . 0 ( ' ˆ 1 0 0
Postacademic Course on Telecommunications 27/4/00 p. 24 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (III) `Minimum distance’ decision rule : Example : decision regions for 16-QAM I R
Postacademic Course on Telecommunications 27/4/00 p. 25 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (IV) Preliminaries :BER versus SER (symbol-error-rate) • aim: each symbol error (1 symbol = n bits) introduces only 1 bit error • how? : GRAY CODING make nearest neighbor symbols correspond to groups of n bits that differ only in 1 bit position… • …hence `nearest neighbor symbol errors’ (=most symbol errors) correspond to 1 bit error
Postacademic Course on Telecommunications 27/4/00 p. 26 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (V) Gray Coding for 8-PSK
Postacademic Course on Telecommunications 27/4/00 p. 27 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VI) Gray Coding for 16-QAM
Postacademic Course on Telecommunications 27/4/00 p. 28 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VII) • Computations : skipped (compute probability that additive noise pushes received sample in wrong decision region) • Results: neighbors of number average ) ( ) 2 exp( . 2 1 ) ( ) ( ) 0 ( ) ( log ). ( . 2 . ( . log ) ( 2 2 2 2 2 0 2              M N du u x Q df f F g M M d N E Q M M N BER x b   
Postacademic Course on Telecommunications 27/4/00 p. 29 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VIII) Interpretation (I) : Eb/No • Eb= energy-per-bit=Es/n=(signal power)/(bitrate) • No=noise power per Hz bandwidth lower BER for higher Eb/No
Postacademic Course on Telecommunications 27/4/00 p. 30 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (IX) Interpretation (II) : Constellation for given Eb/No, it is found that… BER(M-QAM) =< BER(M-PSK) =< BER(M-PAM) BER(2-PAM) = BER(2-PSK) = BER(4-PSK) = BER(4-QAM) higher BER for larger M (in each constellation family)
Postacademic Course on Telecommunications 27/4/00 p. 31 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (X) Interpretation (III): front-end filter f(t) It is proven that and that is obtained only when this is known as the `matched filter receiver’ (see also Lecture-4)       df f F g 2 2 ) ( ) 0 (  1 0   1   ) ( ) ( and ) ( ) ( i.e. , ) ( ) ( 2 * * f P f G t p t f f P f F    
Postacademic Course on Telecommunications 27/4/00 p. 32 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XI) Interpretation (IV) with a matched filter receiver, obtained BER is independent of pulse p(t)
Postacademic Course on Telecommunications 27/4/00 p. 33 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XII) BER for M-PAM (matched filter reception)
Postacademic Course on Telecommunications 27/4/00 p. 34 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XIII) BER for M-PSK (matched filter reception)
Postacademic Course on Telecommunications 27/4/00 p. 35 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XIV) BER for M-QAM (matched filter reception)
Postacademic Course on Telecommunications 27/4/00 p. 36 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Symbol sequence over AWGN channel (I) • ISI (intersymbol interference) results if • ISI results in increased BER 0 ) . ( such that 0    s T m g m g(t)=p(t)*f(t)
Postacademic Course on Telecommunications 27/4/00 p. 37 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Symbol sequence over AWGN channel (II) • No ISI (intersymbol interference) if • zero ISI -> 1-symbol BER analysis still valid • design zero-ISI pulses ? 0 ) . ( : 0    s T m g m
Postacademic Course on Telecommunications 27/4/00 p. 38 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (I) • No ISI (intersymbol interference) if • Equivalent frequency-domain criterion: This is called the `Nyquist criterion for zero-ISI’ Pulses that satisfy this criterion are called `Nyquist pulses’ 0 ) . ( : 0    s T m g m ) 0 ( constant ) ( 1 g T k f G T k s s       
Postacademic Course on Telecommunications 27/4/00 p. 39 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (II) • Nyquist Criterion for Bandwidth = 1/2Ts Nyquist criterion can be fulfilled only when G(f) is constant for |f|<B, hence ideal lowpass filter.
Postacademic Course on Telecommunications 27/4/00 p. 40 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (III) • Nyquist Criterion for Bandwidth < 1/2Ts Nyquist criterion can never be fulfilled
Postacademic Course on Telecommunications 27/4/00 p. 41 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (IV) • Nyquist Criterion for Bandwidth > 1/2Ts Infinitely many pulses satisfy Nyquist criterion
Postacademic Course on Telecommunications 27/4/00 p. 42 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (V) • Nyquist Criterion for Bandwidth > 1/2Ts practical choices have 1/T>Bandwidth>1/2Ts Example: Raised Cosine (RC) Pulses 1 0 factor' off - `roll :    (%) 100 . Bandwidth Excess 2T 1 Bandwidth      s
Postacademic Course on Telecommunications 27/4/00 p. 43 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VI) Example: Raised Cosine Pulses (time-domain)
Postacademic Course on Telecommunications 27/4/00 p. 44 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VII) Procedure: 1. Construct Nyquist pulse G(f) (*) e.g. G(f) = raised cosine pulse (formulas, see Lee & Messerschmitt p.190) 2. Construct F(f) and P(f), such that (**) F(f)=P*(f) and P(f).F(f)=G(f) -> P(f).P*(f)=G(f) e.g. square-root raised cosine (RRC) pulse (formulas, see Lee & Messerschmitt p.228) (*) zero-ISI, hence 1-symbol BER performance (**) matched filter reception = optimal performance
Postacademic Course on Telecommunications 27/4/00 p. 45 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VIII) • PS: Excess BW simplifies implementation -`shorter’ pulses (see time-domain plot) - sampling instant less critical (see eye diagrams) `eye diagram’ is `oscilloscope view’ of signal before sampler, when symbol timing serves as a trigger 20% excess-BW 100% excess-BW
Postacademic Course on Telecommunications 27/4/00 p. 46 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (IX) • PPS: From the eye diagrams, it is seen that selecting a proper sampling instant is crucial (for having zero-ISI) ->requires accurate clock synchronization, a.k.a. `timing recovery’, at the receiver (clock rate & phase) ->`timing recovery’ not addressed here see e.g. Lee & Messerschmitt, Chapter 17
Postacademic Course on Telecommunications 27/4/00 p. 47 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Questions…. 1. What if channel is frequency-selective, cfr. h(t) ? - Matched filter reception requires that F(f)=P*(f).H*(f) - Zero-ISI requires that P(f).H(f).F(f)=Nyquist pulse Is this an optimal design procedure ? k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
Postacademic Course on Telecommunications 27/4/00 p. 48 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Assignment 2.2 Analyze this design procedure for the case where the channel is given as H(f) = Ho for |f|<B/2 H(f) = 0.1 Ho for B/2<|f|<B discover a phenomenon known as `noise enhancement’ (=zero-ISI-forcing approach ignores the additive noise, hence may lead to an excessively noise-amplifying receiver) k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
Postacademic Course on Telecommunications 27/4/00 p. 49 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Questions…. 2. Is the receiver structure (matched filter front-end + symbol-rate sampler + slicer) optimal at all ? Sampler works at symbol rate. With non-zero excess bandwidth this is below the Nyquist rate. Didn’t your signal processing teacher tell you never to do sample below the Nyquist rate? Could this be o.k. ???? k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
Postacademic Course on Telecommunications 27/4/00 p. 50 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Conclusion • Transmitter structure: symbol constellation + transmit pulse p(t) • Symbol constellation: PAM/PSK/QAM BER-analysis for transmission of 1 symbol over AWGN-channel -> Performance of matched filter receiver is independent of transmit pulse • Transmit pulse p(t): -> Zero-ISI-forcing design procedure for transmit pulse p(t) and front-end filter f(t), for AWGN channels (-> RRC pulses) -> Even though for more general channels this is not an optimal procedure (see Lecture 4), transmit pulses are usually designed as RRC’s.

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lecture3.ppt

  • 1. 27/4/00 p. 1 Postacademic Course on Telecommunications Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven/ESAT-SISTA Module-3 : Transmission Lecture-3 (27/4/00) Marc Moonen Dept. E.E./ESAT, K.U.Leuven marc.moonen@esat.kuleuven.ac.be www.esat.kuleuven.ac.be/sista/~moonen/
  • 2. Postacademic Course on Telecommunications 27/4/00 p. 2 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Lecture-3: Transmitter Design Overview • Transmitter : Constellation + Transmit filter • Preliminaries : Passband vs. baseband transmission • Constellations for linear modulation ->M-PAM / M-PSK / M-QAM ->BER performance in AWGN channel for transmission of 1 symbol (Gray coding, Matched filter reception) • Transmission pulses : ->Zero-ISI-forcing design procedure for transmit pulse (and receiver front-end filter), Nyquist pulses, RRC pulses
  • 3. Postacademic Course on Telecommunications 27/4/00 p. 3 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Lecture-3: Transmitter Design Lecture partly adopted from Module T2 `Digital Communication Principles’ M.Engels, M. Moeneclaey, G. Van Der Plas 1998 Postgraduate Course on Telecommunications Special thanks to Prof. Marc Moeneclaey
  • 4. Postacademic Course on Telecommunications 27/4/00 p. 4 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmitter: Constellation + Transmit Filter PS: channel coding (!) not considered here s k E a . r(t) k â transmit pulse s(t) n(t) p(t) + AWGN transmitter receiver (to be defined) h(t) channel ... constellation transmit filter (linear modulation)    k s k s kT t p a E t s ) ( . . ) (
  • 5. Postacademic Course on Telecommunications 27/4/00 p. 5 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmitter: Constellation + Transmit Filter -> s(t) with infinite bandwidth, not the greatest choice for p(t).. -> implementation: upsampling/digital filtering/D-to-A/S&H/... s k E a . transmit pulse s(t) p(t) transmitter discrete-time symbol sequence continuous-time transmit signal t p(t) Example: t
  • 6. Postacademic Course on Telecommunications 27/4/00 p. 6 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries: Passband vs. baseband transmission (I) Baseband transmission • transmitted signal is (linear modulation) • transmitted signals have to be real, hence = real, p(t)=real • baseband means for f B -B 0 ) (  f SLP B f  | | ) ( f SLP    k s k s LP kT t p a E t s ) ( . . ) ( k a
  • 7. Postacademic Course on Telecommunications 27/4/00 p. 7 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (II) Baseband transmission model/definitions g(t)=p(t)*h(t)*f(t) (convolution) everything is real here! s k E a . r(t) k â transmit pulse s(t) n(t) p(t) + f(t) front-end filter AWGN 1/Ts transmitter receiver (first version, see also Lecture4) h(t) channel
  • 8. Postacademic Course on Telecommunications 27/4/00 p. 8 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (III) Bandpass transmission transmitted signal is modulated baseband signal ) (t sLP ) . 2 cos( 0t f  f B -B ) ( f SLP ) (t sBP -fo f ) ( f SBP fo fo+B
  • 9. Postacademic Course on Telecommunications 27/4/00 p. 9 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (IV) Bandpass transmission: • note that modulated signal has 2x larger bandwidth, hence inefficient scheme ! • solution = accommodate 2 baseband signals in 1 bandpass signal : I =`in-phase signal’ Q=`quadrature signal’ such that energy in BP is energy in LP 2
  • 10. Postacademic Course on Telecommunications 27/4/00 p. 10 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (V) • Convenient notation for `two-signals-in-one’ is complex notation : • re-construct `complex envelope’ from BP-signal (mathematics omitted) ) ( . ) ( ) ( t s j t s t s Q I LP   low-pass filter
  • 11. Postacademic Course on Telecommunications 27/4/00 p. 11 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Assignment 2.1 • Prove for yourself that this is indeed a correct complex-envelope reconstruction procedure! low-pass filter
  • 12. Postacademic Course on Telecommunications 27/4/00 p. 12 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (VI) Passband transmission model/definitions (mathematics omitted): a convenient and consistent (baseband) model can be obtained, based on complex envelope signals, that does not have the modulation/demodulation steps: k â f(t) front-end filter 1/Ts receiver (first version) r(t) n’(t) + AWGN s k E a . transmit pulse s(t) p(t) transmitter h’(t) channel
  • 13. Postacademic Course on Telecommunications 27/4/00 p. 13 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (V) k â f(t) front-end filter 1/Ts receiver (first version) r(t) n’(t) + AWGN s k E a . transmit pulse s(t) p(t) transmitter h’(t) channel =complex symbols =usually a complex filter ) ( ) ( ' 0 2 t h e t h t f j    =complex AWGN =complex =real-valued transmit pulse Q k I k k a j a a , , .  
  • 14. Postacademic Course on Telecommunications 27/4/00 p. 14 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Preliminaries : Passband vs. baseband transmission (VI) • In the sequel, we will always use this baseband- equivalent model, with minor notational changes (h(t) and n(t), i.o. h’(t) and n’(t)). Hence no major difference between baseband and passband transmission/models (except that many things (e.g. symbols) can become complex-valued). • PS: modulation/demodulation steps are transparent (hence may be omitted in baseband model) only if receiver achieves perfect carrier synchronization (frequency fo & phase). Synchronization not addressed here (see e.g. Lee & Messerschmitt, Chapter 16).
  • 15. Postacademic Course on Telecommunications 27/4/00 p. 15 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (I) Transmitted signal (envelope) is: Constellations: PAM PSK QAM pulse amplitude modulation phase-shift keying quadrature amplitude modulation 4-PAM (2bits) 8-PSK (3bits) 16-QAM (4bits) ps: complex constellations for passband transmission I R I R I R    k s k s kT t p a E t s ) ( . . ) (
  • 16. Postacademic Course on Telecommunications 27/4/00 p. 16 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (II) M-PAM pulse amplitude modulation • energy-normalized iff • then distance between nearest neighbors is larger d -> noise immunity (see below) I R   PAM PAM PAM k A M A A a ) 1 ( ,....., 3 ,      k a 1 3 ) ( 2   M M APAM 1 12 ) ( 2   M M dPAM d
  • 17. Postacademic Course on Telecommunications 27/4/00 p. 17 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (III) M-PSK phase-shift keying • energy-normalized iff …. • Then distance between nearest neighbors is          1 ,..., 1 , 0 | ) 2 . exp( M m M m j ak  k a ) sin( . 2 ) ( M M dPSK   d I R
  • 18. Postacademic Course on Telecommunications 27/4/00 p. 18 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Constellations for linear modulation (IV) M-QAM quadrature amplitude modulation • distance between nearest neighbors is 1 6 ) (   M M dQAM d I R   QAM QAM QAM k Q k I A M A A a a ) 1 ( ,....., 3 , , , ,      k Q k I k a j a a , , .   ) ( ) ( ) ( M d M d M d QAM PSK PAM  
  • 19. Postacademic Course on Telecommunications 27/4/00 p. 19 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel BER=(# bit errors)/(# transmitted bits) g(t)=p(t)*f(t) (convolution) n’(t)=n(t)*f(t) BER for different constellations? r(t) k â transmit pulse s(t) n(t) p(t) + s k E a . f(t) front-end filter AWGN channel 1/Ts transmitter receiver r’(t)
  • 20. Postacademic Course on Telecommunications 27/4/00 p. 20 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel definitions: - transmitted signal - received signal (at front-end filter) - received signal (at sampler) g(t) =p(t)*f(t) = transmitted pulse p(t) filtered by front-end filter n’(t) =n(t)*f(t) = AWGN filtered by front-end filter ) ( ' ) ( . . ) ( ' t n kT t g a E t r k s k s        k s k s kT t p a E t s ) ( . . ) ( ) ( ) ( . . ) ( t n kT t p a E t r k s k s    
  • 21. Postacademic Course on Telecommunications 27/4/00 p. 21 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA BER Performance for AWGN Channel Received signal sampled @ time t=k.Ts is... 1 = useful term 2= `ISI’, intersymbol interference (from symbols other than ) 3= noise term Strategy : a) analyze BER in absence of ISI (=`transmission of 1 symbol’) b) analyze pulses for which ISI-term = 0 (such that analysis under a. applies) c) for non-zero ISI, see Lecture 4-5                3 2 0 1 ) . ( ' ) . ( . ) 0 ( . . ) . ( ' s m s m k k s s T k n T m g a g a E T k r       k a
  • 22. Postacademic Course on Telecommunications 27/4/00 p. 22 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (I) BER for different constellations? k â transmit pulse n(t) p(t) + s E a . 0 f(t) front-end filter AWGN channel 1/Ts ...take 1 sample at time 0.Ts transmit 1 symbol at time 0.Ts ...
  • 23. Postacademic Course on Telecommunications 27/4/00 p. 23 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (II) Received signal sampled @ time t=0.Ts is.. • `Minimum distance’ decision rule/device :          3 2 1 0 ) . 0 ( ' 0 ) 0 ( . . ) . 0 ( ' s s s T n g a E T r    n s s M n i s s i g E T r g E T r a            ) 0 ( . ) . 0 ( ' min ) 0 ( . ) . 0 ( ' ˆ 1 0 0
  • 24. Postacademic Course on Telecommunications 27/4/00 p. 24 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (III) `Minimum distance’ decision rule : Example : decision regions for 16-QAM I R
  • 25. Postacademic Course on Telecommunications 27/4/00 p. 25 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (IV) Preliminaries :BER versus SER (symbol-error-rate) • aim: each symbol error (1 symbol = n bits) introduces only 1 bit error • how? : GRAY CODING make nearest neighbor symbols correspond to groups of n bits that differ only in 1 bit position… • …hence `nearest neighbor symbol errors’ (=most symbol errors) correspond to 1 bit error
  • 26. Postacademic Course on Telecommunications 27/4/00 p. 26 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (V) Gray Coding for 8-PSK
  • 27. Postacademic Course on Telecommunications 27/4/00 p. 27 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VI) Gray Coding for 16-QAM
  • 28. Postacademic Course on Telecommunications 27/4/00 p. 28 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VII) • Computations : skipped (compute probability that additive noise pushes received sample in wrong decision region) • Results: neighbors of number average ) ( ) 2 exp( . 2 1 ) ( ) ( ) 0 ( ) ( log ). ( . 2 . ( . log ) ( 2 2 2 2 2 0 2              M N du u x Q df f F g M M d N E Q M M N BER x b   
  • 29. Postacademic Course on Telecommunications 27/4/00 p. 29 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (VIII) Interpretation (I) : Eb/No • Eb= energy-per-bit=Es/n=(signal power)/(bitrate) • No=noise power per Hz bandwidth lower BER for higher Eb/No
  • 30. Postacademic Course on Telecommunications 27/4/00 p. 30 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (IX) Interpretation (II) : Constellation for given Eb/No, it is found that… BER(M-QAM) =< BER(M-PSK) =< BER(M-PAM) BER(2-PAM) = BER(2-PSK) = BER(4-PSK) = BER(4-QAM) higher BER for larger M (in each constellation family)
  • 31. Postacademic Course on Telecommunications 27/4/00 p. 31 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (X) Interpretation (III): front-end filter f(t) It is proven that and that is obtained only when this is known as the `matched filter receiver’ (see also Lecture-4)       df f F g 2 2 ) ( ) 0 (  1 0   1   ) ( ) ( and ) ( ) ( i.e. , ) ( ) ( 2 * * f P f G t p t f f P f F    
  • 32. Postacademic Course on Telecommunications 27/4/00 p. 32 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XI) Interpretation (IV) with a matched filter receiver, obtained BER is independent of pulse p(t)
  • 33. Postacademic Course on Telecommunications 27/4/00 p. 33 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XII) BER for M-PAM (matched filter reception)
  • 34. Postacademic Course on Telecommunications 27/4/00 p. 34 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XIII) BER for M-PSK (matched filter reception)
  • 35. Postacademic Course on Telecommunications 27/4/00 p. 35 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Transmission of 1 symbol over AWGN channel (XIV) BER for M-QAM (matched filter reception)
  • 36. Postacademic Course on Telecommunications 27/4/00 p. 36 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Symbol sequence over AWGN channel (I) • ISI (intersymbol interference) results if • ISI results in increased BER 0 ) . ( such that 0    s T m g m g(t)=p(t)*f(t)
  • 37. Postacademic Course on Telecommunications 27/4/00 p. 37 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Symbol sequence over AWGN channel (II) • No ISI (intersymbol interference) if • zero ISI -> 1-symbol BER analysis still valid • design zero-ISI pulses ? 0 ) . ( : 0    s T m g m
  • 38. Postacademic Course on Telecommunications 27/4/00 p. 38 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (I) • No ISI (intersymbol interference) if • Equivalent frequency-domain criterion: This is called the `Nyquist criterion for zero-ISI’ Pulses that satisfy this criterion are called `Nyquist pulses’ 0 ) . ( : 0    s T m g m ) 0 ( constant ) ( 1 g T k f G T k s s       
  • 39. Postacademic Course on Telecommunications 27/4/00 p. 39 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (II) • Nyquist Criterion for Bandwidth = 1/2Ts Nyquist criterion can be fulfilled only when G(f) is constant for |f|<B, hence ideal lowpass filter.
  • 40. Postacademic Course on Telecommunications 27/4/00 p. 40 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (III) • Nyquist Criterion for Bandwidth < 1/2Ts Nyquist criterion can never be fulfilled
  • 41. Postacademic Course on Telecommunications 27/4/00 p. 41 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (IV) • Nyquist Criterion for Bandwidth > 1/2Ts Infinitely many pulses satisfy Nyquist criterion
  • 42. Postacademic Course on Telecommunications 27/4/00 p. 42 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (V) • Nyquist Criterion for Bandwidth > 1/2Ts practical choices have 1/T>Bandwidth>1/2Ts Example: Raised Cosine (RC) Pulses 1 0 factor' off - `roll :    (%) 100 . Bandwidth Excess 2T 1 Bandwidth      s
  • 43. Postacademic Course on Telecommunications 27/4/00 p. 43 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VI) Example: Raised Cosine Pulses (time-domain)
  • 44. Postacademic Course on Telecommunications 27/4/00 p. 44 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VII) Procedure: 1. Construct Nyquist pulse G(f) (*) e.g. G(f) = raised cosine pulse (formulas, see Lee & Messerschmitt p.190) 2. Construct F(f) and P(f), such that (**) F(f)=P*(f) and P(f).F(f)=G(f) -> P(f).P*(f)=G(f) e.g. square-root raised cosine (RRC) pulse (formulas, see Lee & Messerschmitt p.228) (*) zero-ISI, hence 1-symbol BER performance (**) matched filter reception = optimal performance
  • 45. Postacademic Course on Telecommunications 27/4/00 p. 45 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (VIII) • PS: Excess BW simplifies implementation -`shorter’ pulses (see time-domain plot) - sampling instant less critical (see eye diagrams) `eye diagram’ is `oscilloscope view’ of signal before sampler, when symbol timing serves as a trigger 20% excess-BW 100% excess-BW
  • 46. Postacademic Course on Telecommunications 27/4/00 p. 46 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Zero-ISI-forcing pulse design (IX) • PPS: From the eye diagrams, it is seen that selecting a proper sampling instant is crucial (for having zero-ISI) ->requires accurate clock synchronization, a.k.a. `timing recovery’, at the receiver (clock rate & phase) ->`timing recovery’ not addressed here see e.g. Lee & Messerschmitt, Chapter 17
  • 47. Postacademic Course on Telecommunications 27/4/00 p. 47 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Questions…. 1. What if channel is frequency-selective, cfr. h(t) ? - Matched filter reception requires that F(f)=P*(f).H*(f) - Zero-ISI requires that P(f).H(f).F(f)=Nyquist pulse Is this an optimal design procedure ? k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
  • 48. Postacademic Course on Telecommunications 27/4/00 p. 48 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Assignment 2.2 Analyze this design procedure for the case where the channel is given as H(f) = Ho for |f|<B/2 H(f) = 0.1 Ho for B/2<|f|<B discover a phenomenon known as `noise enhancement’ (=zero-ISI-forcing approach ignores the additive noise, hence may lead to an excessively noise-amplifying receiver) k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
  • 49. Postacademic Course on Telecommunications 27/4/00 p. 49 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Questions…. 2. Is the receiver structure (matched filter front-end + symbol-rate sampler + slicer) optimal at all ? Sampler works at symbol rate. With non-zero excess bandwidth this is below the Nyquist rate. Didn’t your signal processing teacher tell you never to do sample below the Nyquist rate? Could this be o.k. ???? k â f(t) front-end filter 1/Ts receiver (see lecture-4) n(t) + AWGN s k E a . transmit pulse p(t) transmitter h(t) channel
  • 50. Postacademic Course on Telecommunications 27/4/00 p. 50 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA Conclusion • Transmitter structure: symbol constellation + transmit pulse p(t) • Symbol constellation: PAM/PSK/QAM BER-analysis for transmission of 1 symbol over AWGN-channel -> Performance of matched filter receiver is independent of transmit pulse • Transmit pulse p(t): -> Zero-ISI-forcing design procedure for transmit pulse p(t) and front-end filter f(t), for AWGN channels (-> RRC pulses) -> Even though for more general channels this is not an optimal procedure (see Lecture 4), transmit pulses are usually designed as RRC’s.