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S-72.1140 Transmission Methods in Telecommunication Systems (5 cr). Digital Transmission. I Baseband Digital Transmission. Why to Apply Digital Transmission? Digital Transmission Symbols and Bits M-level Pulse Amplitude Modulation (PAM) Line codes (Binary PAM Formats)

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S 72 1140 transmission methods in telecommunication systems 5 cr l.jpg

S-72.1140 Transmission Methods in Telecommunication Systems (5 cr)

Digital Transmission

I baseband digital transmission l.jpg
I Baseband Digital Transmission

  • Why to Apply Digital Transmission?

  • Digital Transmission

  • Symbols and Bits

    • M-level Pulse Amplitude Modulation (PAM)

    • Line codes (Binary PAM Formats)

  • Baseband Digital Transmission Link

    • Baseband Unipolar Binary Error Probability

    • Determining Decision Threshold

    • Error rate and Q-function

    • Baseband Binary Error Rate in Terms of Pulse Shape and g

  • Pulse Shaping and Band-limited Transmission

    • Signaling With Cosine Roll-off Signals

    • Matched Filtering

    • Root-raised cos-filtering

  • Eye diagram

Ii carrier wave digital transmission l.jpg
II Carrier Wave Digital Transmission

  • Waveforms of Digital Carrier Wave Communications

  • Detection of Digital CW

    • Coherent Detection

      • Error rate; General treatment

    • Non-coherent Detection

      • Example of error rate determination (OOK)

  • Timing and Synchronization

  • Error rate for M-PSK

  • Error rate for M-QAM

  • Comparison of digital CW methods

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Why to Apply Digital Transmission?

  • Digital communication withstands channel noise, interference and distortion better than analog system. For instance in PSTN inter-exchange STP*-links NEXT (Near-End Cross-Talk) produces several interference. For analog systems interference must be below 50 dB whereas in digital system 20 dB is enough. With this respect digital systems can utilize lower quality cabling than analog systems

  • Regenerative repeaters are efficient. Note that cleaning of analog-signals by repeaters does not work as well

  • Digital HW/SW implementation is straightforward

  • Circuits can be easily configured and programmed by DSP techniques

  • Digital signals can be coded to yield very low error rates

  • Digital communication enables efficient exchange of SNR to BW-> easy adaptation into different channels

  • The cost of digital HW continues to halve every two or three years

STP: Shielded twisted pair

Digital transmission l.jpg

Transmitted power;

bandpass/baseband signal BW



- analog:BW & dynamic range

- digital:bit rate



  • ‘Baseband’ means that no carrier wave modulation is used for transmission








Maximization of information transferred



In baseband systems

these blocks are missing





Message protection & channel adaptation;

convolution, block coding





Fights against burst errors

Received signal(may contain errors)




M-PSK/FSK/ASK..., depends on channel BW & characteristics






Symbols and bits m ary pam l.jpg
Symbols and Bits – M-ary PAM













Generally: (a PAM* signal)

For M=2 (binary signalling):

For non-Inter-Symbolic Interference (ISI), p(t) must


This means that at the instant of decision, received signal component is

*Pulse Amplitude Modulation

Binary pam formats 1 l.jpg
Binary PAM Formats (1)

Bit stream

Unipolar RZ and NRZ

Polar RZ and NRZ

Bipolar NRZ or

alternate mark inversion


Split-phase Manchester

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Binary PAM Formats (2)

  • Unipolar RZ, NRZ:

    • DC component has no information, wastes power

    • Transformers and capacitors in route block DC

    • NRZ, more energy per bit, synchronization more difficult

  • Polar RZ, NRZ:

    • No DC term if ´0´and ´1´ are equally likely

  • Bipolar NRZ

    • No DC term

  • Split-phase Manchester

    • Zero DC term regardless of message sequence

    • Synchronization simpler

    • Requires larger bandwidth

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Baseband Digital Transmission Link

original message bits

received wave y(t)

Unipolar PAM

decision instances

message reconstruction at yields

Gaussian bandpass noise



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Baseband Unipolar Binary Error Probability

Assume binary & unipolar x(t)

The sample-and-hold circuit yields:

Establish H0and H1 hypothesis:


pN(y): Noise probability density

function (PDF) at the time instance of sampling

Determining decision threshold l.jpg
Determining Decision Threshold

The comparator implements decision rule:

Choose Ho (ak=0) if Y<V

Choose H1 (ak=1) if Y>V

Average error error probability:

Transmitted ‘0’

but detected as ‘1’

Channel noise is Gaussian with the pfd:

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Error rate and Q-function

This can be expressed by using the Q-function


and also

m: mean

s2: variance

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Baseband Binary Error Rate in Terms of Pulse Shape

setting V=A/2 yields then

for unipolar, rectangular NRZ [0,A] bits

probability of occurrence for bits ’0’ and ’1’

for polar, rectangular NRZ [-A/2,A/2] bits

and hence

Assignment l.jpg

  • Determine average power for the following signals









Solution17 l.jpg









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Pulse Shaping and Band-limited Transmission

  • In digital transmission signaling pulse shape is chosen to satisfy the following requirements:

    • yields maximum SNR at the time instance of decision (matched filtering)

    • accommodates signalto channel bandwidth:

      • rapid decrease of pulse energy outside the main lobe in frequency domain alleviates filter design

      • lowers cross-talk in multiplexed systems

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Signaling With Cosine Roll-off Signals

  • Maximum transmission rate can be obtained with sinc-pulses

  • However, they are not time-limited. A more practical choice is the cosine roll-off signaling:

for raised cos-pulsesb=r/2

Unipolar and polar error rates in terms of eb no l.jpg
Unipolar and Polar Error Rates in Terms of Eb/No

  • Eb/No is often indicated by

  • For sinc- pulse signalling the transmission BW is limited toand therefore noise before decision is limited toand therefore

Matched filtering l.jpg



Matched Filtering

Peak amplitude to be maximized

Post filter noise

Should be maximized

Using Schwartz’s inequality

Assignment22 l.jpg

  • What is the impulse response of the matched filter for the following signaling waveform?

  • How would you determine the respective output signal (after the matched filter)?



Monitoring transmission quality by eye diagram l.jpg
Monitoring Transmission Quality by Eye Diagram

Required minimum bandwidth isNyqvist’s sampling theorem:

Given an ideal LPF with the

bandwidth B it is possible to

transmit independent symbols at the rate:

Assignment25 l.jpg

  • How many eye/openings you have in an M-level signaling?

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Carrier Wave Communications (5 cr)

  • Carrier wave modulation is used to transmit messages over a distance by radio waves (air, copper or coaxial cable), by optical signals (fiber), or by sound waves (air, water, ground)

  • CW transmission allocates bandwidtharound the applied carrier that depends on

    • message bandwidth and bit rate

    • number of encoded levels(word length)

    • source and channel encoding methods

  • Examples of transmission bandwidths for certain CW techniques:


  • Binary FSK (fd=rb/2)

  • MSK (CPFSK fd=rb/4), QAM:

FSK: Frequency shift keying

CPFSK: Continuous phase FSK

Digital cw detection l.jpg
Digital CW Detection (5 cr)

  • At the receiver, detection can be

    • coherent (carrier phase information used for detection)

    • non- coherent(no carrier phase used for detection)

    • differentially coherent(‘local oscillator’ synthesized from received bits)

  • CW systems characterized by bit or symbol error rate(number of decoded errors(symbols)/total number of bits(symbols))

  • Number of allocated signaling levels determines constellation diagram (=lowpass equivalent of the applied digital modulation format)

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Coherent Detection by Integrate and Dump / Matched Filter Receiver

  • Coherent detection utilizes carrier phase information and requires in-phase replica of the carrier at the receiver (explicitly or implicitly)

  • It is easy to show that these two techniques have the same performance:

Non coherent detection l.jpg

2-ASK Receiver


Non-coherent Detection

  • Base on filtering signal energy on allocated spectra and using envelope detectors

  • Has performance degradation of about 1-3 dB when compared to coherent detection (depending on Eb/N0)

  • Examples:

Coherent optimum binary detection l.jpg
Coherent (Optimum) Binary Detection Receiver

  • Received signal consists of bandpass filtered signal and noise that is sampled at the decision time instants tk yielding decision variable:

  • Quadrature presentation of the signaling waveform is

  • Assuming that the BPF has the impulse response h(t),signal component at the sampling instants is then expressed by

Optimum binary detection error rate l.jpg
Optimum Binary Detection - Error Rate Receiver

  • Assuming ‘0’ and ‘1’ reception is equally likely, error happens when H0 (‘0’ transmitted) signal hits the dashed region or for H1 error hits the left-hand side of the decision threshold that is at

For optimum performancewe have the maximized

SNR that is obtained

by matched filtering/

integrate and dump receiver

Errors for ‘0’ or/and ‘1’ are equal alike, for instance for ‘0’:

Optimum binary detection cont l.jpg
Optimum Binary Detection (cont.) Receiver

  • Express energy / bit embedded in signaling waveforms by

  • Therefore, for coherent CW we have the SNR and error rate

Note that the signaling waveform

correlation greatly influences the SNR!

Example coherent binary on off keying ook l.jpg
Example: Coherent Binary On-off Keying (OOK) Receiver

  • For on-off keying (OOK) the signaling waveforms areand the optimum coherent receiver can be sketched by

Timing and synchronization l.jpg
Timing and Synchronization Receiver

  • Performance of coherent detection is greatly dependent on how successful local carrier recovery is

  • Consider the bandpass signal s(t) with width Tbrectangular pulsespTb(t), that is applied to the matched filter h(t):

yelding after filtering:

nominal point

of inspection at Tb

Analyzing phase error by mathcad l.jpg

Analyzing phase error by Mathcad

Example l.jpg
Example Receiver

  • Assume data rate is 2 kbaud/s and carrier is 100 kHz for an BPSK system. Hence the symbol duration and carrier period aretherefore the symbol duration is in radians

  • Assume carrier phase error is 0.3 % of the symbol duration. Then the resulting carrier phase error isand the error rate for instance for isthat should be compared to the error rate without any phase errors or

  • Hence, phase synchronization is a very important point to remember in coherent detection

(or carrier cycles)

Error rate for m psk l.jpg

decision region Receiver

Error rate for M-PSK

  • In general,PSK error rate can be expressed bywhere d is the distance between constellation points (or a=d/2 is the distance from constellation point to the decision region border) and is theaverage number of constellation points in the immediate neighborhood. ThereforeNote that for matched filter reception

Error rate for m qam example 16 qam l.jpg
Error rate for M-QAM, example 16-QAM Receiver

symbol error rate

Constellation follows from 4-bit words and therefore

Example non coherent on off keying ook l.jpg
Example: Non-coherent On-off Keying (OOK) Receiver

  • Bandpass filter is matched to the signaling waveform (not to carrier phase), in addition fc>>fm, and therefore the energy for ‘1’ is simply

  • Envelopes follow Rice and Rayleigh distributions for ‘1’ and ‘0’ respectively:

distribution for ”0”"

distribution for "1"

Noncoherent ook error rate l.jpg
Noncoherent OOK Error Rate Receiver

  • The optimum decision threshold is at the intersection of Rice and Rayleigh distributions (areas of error probability are the same on both sides of decision threshold)

  • Usually high SNR is assumed and hence the threshold is approximately at the half way and the error rate is the average of '0' and '1' reception probabilities

  • Therefore, error rate for noncoherent OOK equals

probability to detect "0" in error

probability to detect "1" in error

Comparison l.jpg
Comparison Receiver

Error rate comparison l.jpg
Error Rate Comparison Receiver

a: Coherent BPSK


c:Coherent OOK

d: Noncoherent FSK

e: noncoherent OOK

Comparison of quadrature modulation methods l.jpg
Comparison of Quadrature Modulation ReceiverMethods

Note that still the performance is good, envelope is not

constant. APK (or M-QASK) is used for instance in modems




M-APK: Amplitude Phase Shift Keying