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Module-3 : Transmission Lecture-3 (27/4/00)

This lecture provides an overview of transmitter design, including constellations for linear modulation and the design procedure for transmit pulses. It also covers the difference between passband and baseband transmission.

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Module-3 : Transmission Lecture-3 (27/4/00)

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  1. Module-3 : TransmissionLecture-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/ Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven/ESAT-SISTA

  2. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  3. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  4. Transmitter: Constellation + Transmit Filter constellation PS: channel coding (!) not considered here transmit filter (linear modulation) s(t) r(t) ... p(t) h(t) + transmit pulse n(t) AWGN channel receiver (to be defined) transmitter Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  5. s(t) p(t) transmit pulse transmitter Transmitter: Constellation + Transmit Filter p(t) -> s(t) with infinite bandwidth, not the greatest choice for p(t).. -> implementation: upsampling/digital filtering/D-to-A/S&H/... Example: t t discrete-time symbol sequence continuous-time transmit signal Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  6. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  7. 1/Ts Preliminaries : Passband vs. baseband transmission (II) Baseband transmission model/definitions g(t)=p(t)*h(t)*f(t) (convolution) everything is real here! s(t) r(t) p(t) f(t) h(t) + front-end filter transmit pulse n(t) AWGN receiver (first version, see also Lecture4) channel transmitter Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  8. Preliminaries : Passband vs. baseband transmission (III) Bandpass transmission transmitted signal is modulated baseband signal `envelope’ f f -B B -fo fo fo+B Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  9. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  10. 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) `complex envelope’ low-pass filter Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  11. Assignment 2.1 • Prove for yourself that this is indeed a correct complex-envelope reconstruction procedure! low-pass filter Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  12. s(t) r(t) p(t) f(t) + h’(t) front-end filter transmit pulse n’(t) AWGN 1/Ts channel receiver (first version) transmitter 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: Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  13. s(t) r(t) p(t) f(t) h’(t) + front-end filter transmit pulse n’(t) AWGN 1/Ts channel receiver (first version) transmitter Preliminaries : Passband vs. baseband transmission (V) =complex symbols =real-valued transmit pulse =complex =complex AWGN =usually a complex filter Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  14. 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). Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  15. I I I R R R 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  16. I R 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) d Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  17. Constellations for linear modulation (III) M-PSK phase-shift keying • energy-normalized iff …. • Then distance between nearest neighbors is I R d Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  18. I R Constellations for linear modulation (IV) M-QAM quadrature amplitude modulation • distance between nearest neighbors is d Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  19. 1/Ts 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? s(t) r(t) r’(t) f(t) p(t) + front-end filter transmit pulse n(t) AWGN channel transmitter receiver Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  20. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  21. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  22. 1/Ts Transmission of 1 symbol over AWGN channel (I) BER for different constellations? transmit 1 symbol at time 0.Ts ... ...take 1 sample at time 0.Ts f(t) p(t) + front-end filter transmit pulse n(t) AWGN channel Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  23. Transmission of 1 symbol over AWGN channel (II) Received signal sampled @ time t=0.Ts is.. • `Minimum distance’ decision rule/device : Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  24. Transmission of 1 symbol over AWGN channel (III) `Minimum distance’ decision rule : Example : decision regions for 16-QAM I R Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  25. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  26. Transmission of 1 symbol over AWGN channel (V) Gray Coding for 8-PSK Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  27. Transmission of 1 symbol over AWGN channel (VI) Gray Coding for 16-QAM Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  28. Transmission of 1 symbol over AWGN channel (VII) • Computations : skipped (compute probability that additive noise pushes received sample in wrong decision region) • Results: Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  29. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  30. 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) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  31. 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) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  32. Transmission of 1 symbol over AWGN channel (XI) Interpretation (IV) with a matched filter receiver, obtained BER is independent of pulse p(t) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  33. Transmission of 1 symbol over AWGN channel (XII) BER for M-PAM (matched filter reception) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  34. Transmission of 1 symbol over AWGN channel (XIII) BER for M-PSK (matched filter reception) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  35. Transmission of 1 symbol over AWGN channel (XIV) BER for M-QAM (matched filter reception) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  36. Symbol sequence over AWGN channel (I) • ISI (intersymbol interference) results if • ISI results in increased BER g(t)=p(t)*f(t) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  37. Symbol sequence over AWGN channel (II) • No ISI (intersymbol interference) if • zero ISI -> 1-symbol BER analysis still valid • design zero-ISI pulses ? Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  38. 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’ Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  39. 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. Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  40. Zero-ISI-forcing pulse design (III) • Nyquist Criterion for Bandwidth < 1/2Ts Nyquist criterion can never be fulfilled Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  41. Zero-ISI-forcing pulse design (IV) • Nyquist Criterion for Bandwidth > 1/2Ts Infinitely many pulses satisfy Nyquist criterion Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  42. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  43. Zero-ISI-forcing pulse design (VI) Example: Raised Cosine Pulses (time-domain) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  44. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  45. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  46. 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 Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  47. p(t) f(t) h(t) + front-end filter transmit pulse n(t) AWGN 1/Ts channel receiver (see lecture-4) transmitter 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 ? Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  48. p(t) f(t) h(t) + front-end filter transmit pulse n(t) AWGN 1/Ts channel receiver (see lecture-4) transmitter 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) Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  49. p(t) f(t) h(t) + front-end filter transmit pulse n(t) AWGN 1/Ts channel receiver (see lecture-4) transmitter 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. ???? Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

  50. 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. Module-3 Transmission Marc Moonen Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

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