Chapter 6 Passband Data Transmission

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Chapter 6 Passband Data Transmission

Passband Data Transmission concerns the Transmission of the Digital Data over the real Passband channel.

© Po-Ning [email protected] Chapter 6-2

6.1 Introduction – Categories of digital communications (ASK/PSK/FSK)

o Three basic signaling schemes in digital communications

Amplitude-shift keying (ASK)

Phase-shift keying (PSK)

Frequency-shift keying (FSK)

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Tb

0 0 1 1 0 0 0 1 1 0

4-ary Amplitude-shift keying (ASK)

4-ary Phase-shift keying (PSK)

4-ary Frequency-shift keying (FSK)

o Three basic signaling schemes in M-ary digital communications

6.1 Introduction – Categories of M-ary digital communications (ASK/PSK/FSK)

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6.1 Introduction – Categories of M-ary digital communications (Constant Envelope versus Non-Constant Envelope)

o Constant envelope: A necessity for non-linear channels

Non-constant envelope (ASK)

Constant envelope (PSK)

Constant evnelope (FSK)

0 0 1 1 0 0 0 1 1 0

Tb

T

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6.1 Introduction – Categories of digital communications (Coherent versus Non-Coherent)

o Coherent techniquen The transmitter and receiver are required to be

synchronized in both carrier phase and bit timing.o Non-Coherent technique

n The transmitter and receiver are not required to be synchronized in both carrier phase and bit timing.


6.1 Introduction – Roadmap

o In this chapter, we will focus onn Power : A resource in communication

o Power Spectran The relation between passband signal and

baseband signal is easier to identify in spectra view

n Bandwidth: Another resource in communicationo Bandwidth efficiency : The ratio of data rate in bits

per second to the effectively utilized bandwidth. (Bits/Second/Hz)

n Probability of M-ary symbol error (Union bound)

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6.1 Introduction – Relation between passband and baseband signals

o Math relation between passband and baseband signals (spectrum view)



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Signal Spectrum



o Math relation between passband and baseband signals (power spectrum view subject to wise-sense stationarity)

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o Let

o



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6.1 Introduction – Relation between passband signal and baseband signal



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Power Spectral Density



o Integration of the Power Spectral Density gives the Power.n Integration of the Prabability Density gives the

Prabability.

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6.2 Passband transmission model – Message source


6.2 Passband transmission model – Signal space analysis

2-dimensional vector codeword (N=2) N-dimensional vector codeword

Recall Chapter 5: Signal Space Analysis

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Recall Chapter 5: Signal Space Analysis



o

n What is an energy signal?

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o

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o


6.2 Passband transmission model –Communication channel

o Communication channeln Linear: Principle of superposition

n Sufficient bandwidth

n AWGN

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o Detector


6.2 Passband transmission model – Decoder

o Signal transmission decoder

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6.3 Coherent phase-shift keying

o Binary PSK


6.3 Coherent phase-shift keying – Antipodal signal

o Vector space analysis of binary PSKn Antipodal signal

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6.3 Coherent phase-shift keying – Signal space analysis

Signal-space diagram


6.3 Coherent phase-shift keying – Optimal decision region

o Error probability of binary PSK

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Recall:


6.3 Coherent phase-shift keying – Error probability

o Error probability of binary PSKn Based on the decision rule

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6.3 Coherent phase-shift keying – Block diagram

o Block diagram for PSK transmitter and (coherent) receiver

(coherent)


6.3 Coherent phase-shift keying – Baseband signal

o (Complex) Baseband signal of binary PSK passband signal

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6.3 Coherent phase-shift keying – Sequential baseband signal

o Sequence of complex baseband signalsn No autocorrelation function for one-shot single random

variablen Calculation of autocorrelation function requires a

random process.


6.3 Coherent phase-shift keying – Autocorrelation function

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o Power spectrum of binary PSK

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o Power spectrum of binary PSK

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2


6.3 Coherent phase-shift keying – Quadriphase-shift keying

E is the transmitted energy per QPSK symbol, andT is the symbol duration.

o Vector space analysis of QPSK

o QPSK

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o Two-dimensional signal space diagram of QPSK



o Example 6.1

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o Error probability of QPSK



6.3 Coherent phase-shift keying – Error probability of QPSK

o Following the same derivation as that in Slide 6-32

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o Symbol error rate of QPSK



o Alternative approach to derive the symbol error rate of QPSK

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6.3 Coherent phase-shift keying – Summary

o Partial summaryn QPSK (with Gray code mapping) and BPSK have the

same BER under the same Eb/N0.n QPSK however doubles the transmission bit rate per

second (or uses half the bandwidth under the same bit rate) by introducing another quadrature.

n In its implementation, QPSK is more complex since it involves two quadratures.


6.3 Coherent phase-shift keying – QPSK diagram

o Block diagram of QPSK transmitter and receiver

coherent

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o Sequence of complex baseband signalsn No autocorrelation function of one-shot (namely, single)

random variable.n Calculation of autocorrelation function requires a

random process.



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o Power spectrum of BPSK and QPSK under the same Eb and Tb

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2

QPSK

BPSK


6.3 Coherent phase-shift keying – Offset QPSK

90+90=180 degreephase shift

90+0=90 degreephase shift

90 degree

90 degree

90 degree

0 degree

o Example 6.1: n QPSK

Single sign change = 90 degree shiftDouble sign change = 180 degree shift

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90 degreephase shift



o Example 6.1: n Offset QPSK

© Po-Ning [email protected] 6-53



o Offset QPSKn By “offseting” the quadrature component by half a symbol interval

with respect to the in-phase component, Offset QPSK limits the amplitude fluctuation to 90 degree.

n The 90 degree phase transition in OQPSK occurs twice as frequently encountered in QPSK.o Personal comment: One 180 degree phase transition in QPSK

becomes two 90 degree phase transitions in OQPSK. Hence, “twice” is an over-estimate.

n Under AWGN and coherent receiver, the error rate of OQPSK is exactly the same as that of QPSK.

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o p/4-shifted DQPSK (D=Differential)n The input dibit does not determine the absolute phase,

but the phase change.

6.3 Coherent phase-shift keying – p/4-shifted DQPSK


6.3 Coherent phase-shift keying – p/4-shifted DQPSK

o p/4-shifted DQPSKn The phase transition is restricted to either 45 or 135

degree. o No 0 degree phase transition occurs now!

n Noncoherent receiver is feasible.

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6.3 Coherent phase-shift keying – Detection of p/4-shifted DQPSK

o Noncoherent receivern Differential detector


6.3 Coherent phase-shift keying – M-ary PSK

E is the transmitted energy per M-ary PSK symbol, andT is the symbol duration.

o Vector space analysis of M-ary PSK

o M-ary PSK

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6.3 Coherent phase-shift keying – M-ary PSK

o Example – 8PSK (Octaphase-shift keying)


6.3 Coherent phase-shift keying – Union bound of M-ary PSK error

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o If the signal constellation is symmetric in the sense that

then



o Example – 8PSK

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This is the lower bound of the upper bound.So it is not really an upper bound!


6.3 Coherent phase-shift keying – Power spectra of M-ary PSK signals

o Same as Slide 6-50

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6.3 Coherent phase-shift keying – Power spectra of M-ary PSK signals


6.3 Coherent phase-shift keying – Bandwidth efficiency

o Bandwidth efficiency of M-ary PSK signalsn Null-to-null bandwidth

n Bandwidth efficiency

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Chapter 6-67

6.3 Coherent phase-shift keying – Bandwidth efficiency

o Final noten There is a trade-off

between symbol error rate and bandwidth efficiency for M-aryPSK signals.

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6.4 Hybrid amplitude/phase modulation schemes

o For M-ary PSK signals, the in-phase and quadrature components are “dependent”.n How about making them “independent” (to increase the

data rate)?n Answer: M-ary quadrature amplitude modulation (QAM)

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o Square constellation

n Gray-encoded quadbitso Gray-encode the first two

bits by quadrants (PSK)o Gray-encode the

remaining two bits within quadrants (ASK)

PSK



o Symbol error rate of square QAM

o Symbol error rate of equal-prior L-ary ASK

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o Symbol error rate of equal-prior L-ary ASK




o Average transmitted energy of M-ary QAM

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o Square constellation QAMn M is usually even power of

two. n For example, M = 22, 24, 26,

28, … (in such case L = 2, 22, 23, 24, …)

o Question: How about M = 23, 25, 27, …n Answer: Cross

constellation QAM



o Symbol error rate of cross-constellation QAM

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6.4 Hybrid amplitude/phase modulation schemes –Carrierless amplitude/phase modulation (CAP)

o QAM can be viewed as one of the family members in carrierless amplitude/phase modulation (CAP)

o Re-express QAM into CAP form


Carrierless since no carrier fc appears in this formula.

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o Properties of the passband in-phase and quadrature pulses in CAP

n Property 1:



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A2.3 Hilbert transform

o Let P(f) be the spectrum of a real function p(t).n By convention, denote by u(f) the unit step function,

i.e.,

o Put g+(t) to be the function corresponding to 2u(f)P(f).

Multiply by 2 to unchange the area.

Chapter 6-79



o How to obtain g+(t)?o Answer: Hilbert Transformer.

Proof: Observe that

Then by the next slide, we learn that

Chapter 6-80

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By extended Fourier transform,

Chapter 6-81



Chapter 6-82

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ptt 1) =(h

Chapter 6-83



Chapter 6-84

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A2.3 Hilbert transformn Hence, Hilbert

transform is basically a 90 degree phase shifter.

Chapter 6-85



ptt 1) =(h

ptt 1) =(h Ä

1-Chapter 6-86

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A2.3 Hilbert Transform

o An important property of Hilbert transform is that:

(Examples of Hilbert transform pairs can be found in Table A6.4.)

Chapter 6-87

© Po-Ning [email protected] Chapter 1-88Chapter 6-88

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o Properties of the passband in-phase and quadrature pulses in CAPn Property 2:

n Property 3:

o This is similar to use another pulse shaping function as g(t)*l(t).

o One is thus free to choose the pulse shaping function (to, e.g., improve the bandwidth efficiency) without affecting the orthogonality of two quadratures.

o Example 6.4: Bandwidth-efficient spectral shapingn a = 0.2

© Po-Ning [email protected] 6-90

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o Block diagram of CAP transmitter (See Slide 6-76)



o Block diagram of CAP receiver

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o How about channels with intersymbol interferences, in addition to AWGN?

Lineartime-variant

filter h(t)

Channel w(t)

s(t) x(t)+

o Recall in Section 4.9: Optimum linear receiver.

n Design of receiver c(t) as an MMSE equalizer


Recall the below terms:1. Zero-forcing equalizer2. Nyquist criterion/ISI3. Noise enhancement4. MMSE equalizer

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o This leads to Fig. 6.23 in text.

o Can we implement the above structure in “digital” form?



Combine into one FIR filter

May be adaptive when required

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o Applications of CAPn Passband transmission of digital data over twisted-pair

wiring of lengths less than 100m.n Data rates may range from 51 upto 155 Mbps with

bandwidth being strictly limited to 30 MHz.


6.5 Coherent frequency-shift keying

o (M-ary) ASK, (M-ary) PSK and (M-ary) FSK are three major categories of digital modulations, in which QAM can be viewed/analyzed similarly to (M-ary) PSK.

o In this section, the last one, i.e., (M-ary) FSK, will be introduced and discussed.

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6.5 Coherent frequency-shift keying

Eb is the transmitted energy per bit, andTb is the bit duration.

o Vector space analysis of binary FSK

o Binary FSK


With this multiple-(1/Tb) restriction, it becomes “continuous-phase” in every inter-bit transition. Such kind of forced “continuous-phase” signals, known as Sunde’s FSK, surely belongs to the general continuous-phase FSK (CPFSK) family.

E. D. Sunde, "Ideal binary pulse transmission by AM and FM," Bell Labs Technical Journal, 38, pp. 1357-1426, November 1959.

Chapter 6 Passband Data Transmission

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