Modulation, Demodulation and Coding Course

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Modulation, Demodulation and Coding Course

• Period 3 - 2005
• Sorour Falahati
• Lecture 6

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Last time we talked about

• Another source of error due to filtering effect
  of the system
• Inter-symbol interference (ISI)
• The techniques to reduce ISI
• Pulse shaping to have zero ISI at the sampling
  time
• Equalization to combat the filtering effect of
  the channel

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Today, we are going to talk about

• A bit more about pulse shaping and equalization
• Some examples about pulse shaping
• Eye pattern
• Structure of transversal filters for equalization
• Some bandpass modulation schemes used in DCS for
  transmitting information over channel
• M-PAM, M-PSK, M-FSK, M-QAM
• How to detect the transmitted information at the
  receiver
• Coherent detection
• Non-coherent detection

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Pulse shaping and equalization to remove ISI
No ISI at the sampling time

• Square-Root Raised Cosine (SRRC) filter and
  Equalizer

Taking care of ISI caused by channel
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Example of pulse shaping

• Square-root Raised-Cosine (SRRC) pulse shaping

Amp. V
Baseband tr. Waveform
Third pulse
t/T
First pulse
Second pulse
Data symbol
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Example of pulse shaping

• Raised Cosine pulse at the output of matched
  filter

Amp. V
Baseband received waveform at the matched filter
output (zero ISI)
t/T
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Eye pattern

• Eye patternDisplay on an oscilloscope which
  sweeps the system response to a baseband signal
  at the rate 1/T (T symbol duration)

Distortion due to ISI
Noise margin
amplitude scale
Sensitivity to timing error
Timing jitter
time scale
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Example of eye patternBinary-PAM, SRRQ pulse

• Perfect channel (no noise and no ISI)

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Example of eye patternBinary-PAM, SRRQ pulse

• AWGN (Eb/N020 dB) and no ISI

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Example of eye patternBinary-PAM, SRRQ pulse

• AWGN (Eb/N010 dB) and no ISI

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More about Equalization

• ISI due to filtering effect of the communications
  channel (e.g. wireless channels)
• Channels behave like band-limited filters

Non-constant amplitude Amplitude distortion
Non-linear phase Phase distortion
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Equalization Channel examples

• Example of a frequency selective, slowly changing
  (slow fading) channel for a user at 35 km/h

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Equalization Channel examples

• Example of a frequency selective, fast changing
  (fast fading) channel for a user at 35 km/h

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Example of eye pattern with ISIBinary-PAM, SRRQ
pulse

• Non-ideal channel and no noise

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Example of eye pattern with ISIBinary-PAM, SRRQ
pulse

• AWGN (Eb/N020 dB) and ISI

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Example of eye pattern with ISIBinary-PAM, SRRQ
pulse

• AWGN (Eb/N010 dB) and ISI

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Equalizing filters

• Baseband system model
• Equivalent model

Tx filter
Channel
Rx. filter
Detector
Equalizer
Equivalent system
Detector
Equalizer
filtered noise
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Equalization by transversal filtering

• Transversal filter
• A weighted tap delayed line that reduces the
  effect of ISI by proper adjustment of the filter
  taps.

Coeff. adjustment
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Trasnversal equalizing filter

• Zero-forcing equalizer
• The filter taps are adjusted such that the
  equalizer output is forced to be zero at N sample
  points on each side
• Mean Square Error (MSE) equalizer
• The filter taps are adjusted such that the MSE of
  ISI and noise power at the equalizer output is
  minimized.

Adjust
Adjust
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Example of equalizer
Matched filter outputs at the sampling time

• 2-PAM with SRRQ
• Non-ideal channel
• One-tap DFE

ISI-no noise, No equalizer
ISI-no noise, DFE equalizer
ISI- noise No equalizer
ISI- noise DFE equalizer
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Bandpass modulation

• Bandpass modulation The process of converting
  data signal to a sinusoidal waveform where its
  amplitude, phase or frequency, or a combination
  of them, is varied in accordance with the
  transmitting data.
• Bandpass signal
• where is the baseband pulse shape with
  energy .
• We assume here (otherwise will be stated)
• is a rectangular pulse shape with unit
  energy.
• Gray coding is used for mapping bits to symbols.
• denotes average symbol energy given by

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Bandpass modulation contd

• One dimensional waveforms
• Amplitude Shift Keying (ASK)
• M-ary Pulse Amplitude Modulation (M-PAM)
• Two dimensional waveforms
• M-ary Phase Shift Keying (M-PSK)
• M-ary Quadrature Amplitude Modulation (M-QAM)
• Multidimensional waveforms
• M-ary Frequency Shift Keying (M-FSK)

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Demodulation and detection

• Demodulation The receiver signal is converted to
  baseband, filtered and sampled.
• Detection Sampled values are used for detection
  using a decision rule such as ML detection rule.

Decision circuits (ML detector)
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Coherent and non-coherent detections

• Coherent detection
• requires carrier phase recovery at the receiver
  and hence, circuits to perform phase estimation.
• Source of carrier-phase mismatch at the receiver
• Propagation delay causes carrier-phase offset in
  the received signal.
• The oscillators at the receiver which generate
  the carrier signal, are not usually phased locked
  to the transmitted carrier.

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Coherent and non-coherent detection contd

• Circuits such as Phase-Locked-Loop (PLL) are
  implemented at the receiver for carrier phase
  estimation ( ).
• Non-coherent detection
• does not require carrier phase recovery (uses
  differentially encoded mod. or energy detectors)
  and hence, has less complexity at the price of
  higher error rate.

I branch
Q branch
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One dimensional modulation, demodulation and
detection

• Amplitude Shift Keying (ASK) modulation

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One dimensional mod., contd

• M-ary Pulse Amplitude modulation (M-PAM)

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Example of bandpass modulationBinary PAM
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One dimensional mod.,...contd

• Coherent detection of M-PAM

ML detector (Compare with M-1 thresholds)
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Two dimensional modulation, demodulation and
detection (M-PSK)

• M-ary Phase Shift Keying (M-PSK)

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Two dimensional mod., (MPSK)
BPSK (M2)
8PSK (M8)
QPSK (M4)
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Two dimensional mod.,(MPSK)

• Coherent detection of MPSK

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Two dimensional mod., (M-QAM)

• M-ary Quadrature Amplitude Mod. (M-QAM)

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Two dimensional mod., (M-QAM)
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Two dimensional mod., (M-QAM)

• Coherent detection of M-QAM

ML detector
Parallel-to-serial converter
ML detector
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Multi-dimensional modulation, demodulation and
detection

• M-ary Frequency Shift keying (M-FSK)

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Multi-dimensional mod.,(M-FSK)
ML detector Choose the largest element in the
observed vector
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Non-coherent detection

• No need in a reference in phase with the received
  carrier
• Differentially coherent detection
• Differential PSK (DPSK)
• The information bits and previous symbol,
  determine the phase of the current symbol.
• Energy detection
• Non-coherent detection for orthogonal signals
  (e.g. M-FSK)
• Carrier-phase offset causes partial correlation
  between I and Q braches for each candidate
  signal.
• The received energy corresponding to each
  candidate signal is used for detection.

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Non-coherent detection-contd

• Differentially encoding binary PSK (DPSK)
• The symbol phase changes if the current bit is
  different from the previous bit.
• Non-coherent detection
• assumes slow variation in carrier-phase mismatch
  during two symbol intervals.
• uses the phase difference between two successive
  symbols for detection.

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Non-coherent detection-contd

• Non-coherent detection of BFSK

Decision stage

-