Chapter Four

1
Chapter Four

• Bandpass Modulation and Demodulation

2
Bandpass Signaling
3
Why Modulate?

• The transmission of EM fields through space is
  accomplished with the antenna
• The size of the antenna depends on the wavelength
  l
• Telephone industry benchmark of l/4 as the
  antenna dimension
• Example 3kHz baseband signal needs about 15
  miles for the antenna diameter
• Example 900MHz signal needs about 8cm for the
  antenna diameter
• Bandpass modulation is an essential step for all
  systems involving radio transmission
• Modulation can separate the different signals
  (Ex. FDMA)
• Modulation can also be used to place a signal in
  a frequency band where design requirement can be
  easily met

4
Digital Bandpass Modulation Techniques

• Bandpass modulation is the process by which an
  information signal is converted to a sinusoidal
  waveform (carrier waveform)
• Three features can be used to distinguish the
  sinusoidal waveform
• Amplitude, frequency, phase
• Coherent detection
• The receiver exploits knowledge of the carriers
  phase to detect the signa
• PSK, FSK, ASK, CPM, and Hybrid forms
• Non-coherent detection
• The receiver does not utilize the carriers
  phase reference information
• DPSK, FSK, ASK, CPM, and Hybrid forms

5
Digital Modulations
6
Detection of Signals in Gaussian Noise

• Bandpass model of the detection process is
  virtually identical to the baseband model
• Decision regions
• Minimum error decision rule is to choose the
  signal class that the distance d(r,si) is
  minimized, where r is the received signal
• Correlation receiver
• Transform the received waveform into a point in
  the decision space
• Determine in which decision region the point is
  located
• Choose the si(t) whose index corresponds to
  max zi(T)

7
Decision Regions
8
Correlator Receiver with Reference Signals
9
Binary Correlator Receiver
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Coherent Detection of PSK

• BPSK signal
• Decision stage chooses the signal with largest
  output value of matched filter

11
Sampled Matched Filter
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Coherent Detection of MPSK

• MPSK signal
• Signal space and decision regions for a QPSK
  (M4) system
• As shown in Fig.4.11
• Make a decision by the phase information

13
Demodulator for MPSK Signals
14
Coherent Detection of FSK

• FSK signal
• The distance between any two signal vectors is
• Choose the largest output of matched filter

15
Signal Space for a 3-ary FSK Signal
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Signal Space for DPSK
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Detection of Differential PSK

• Differential encoding for the PSK signal
• Signaling characteristics
• Non-coherent detection
• Compare with PSK and DPSK
• PSK detection is with only one noise signal
• DPSK detection is with two noise signal
  (differentially decoding)

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Binary Differential PSK Example
Suboptimum detection
Optimum detection
19
Non-coherent Detection of FSK
Quadrature Receiver
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Non-coherent Detection of FSK
Non-coherent detection of FSK with envelop
detector
21
Tone Spacing for Non-coherent Orthogonal FSK
Signaling

• Two tones f1 and f2 are orthogonal
• For a transmitted tone f1, the sampled envelop of
  the receiver output filter tuned to f2 is zero
• Minimum tone spacing for orthogonal FSK signaling
• Non-coherently detected FSK
• Coherent FSK signaling is 2/T

22
Minimum Tone Spacing for Non-coherent Orthogonal
FSK

• For binary FSK, bandwidth is two times the tone
  spacing
• For M-ary FSK, bandwidth is M/T

23
D8PSK Modulator
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D8PSK Demodulator
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Error Performance for Binary Systems

• Bit error probability for BPSK signaling
• Probability of bit error for coherent detected,
  differential encoded binary PSK
• Probability of bit error for coherently detected
  binary orthogonal FSK
• Probability of bit error for non-coherently
  detected binary orthogonal FSK

26
Binary DPSK

• DPSK signaling
• Pairs of DPSK signals, S1(t) and S2(t) are
  orthogonal
• DPSK detection can be implemented by matching
  signal envelopes
• Bit error probability is similar to the one for
  non-coherently detected binary FSK

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DPSK Detection
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Bit Error Probability of Binary Systems
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M-ary Signals and Performance
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Ideal Probability of Bit Error Performance
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Bit Error Performance for M-ary Orthogonal
Signaling
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Bit Error Performance for Multiple Phase
Signaling
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M-ary Signaling

• M-ary signaling instructs the modulator to
  produce one of M2k waveforms
• M-ary multiple phase signaling
• The BER curve moves in the direction of degraded
  error performance as k increases
• A larger bit rate can be transmitted within the
  same bandwidth as k increases
• M-ary orthogonal signaling
• The BER curve moves in the direction of improved
  error performance as k increases
• The required system bandwidth increases as k
  increases

34
Vectorial View of MPSK Signaling
35
Relation Between Eb/N0 and S/N

• General relationship between Eb/N0 and S/N
• For the QPSK signaling
• QPSK bit stream is usually partitioned into an
  even and odd stream each new stream is at half
  the bit rate of the original stream
• Each of the quadrature BPSK signals has half of
  the average power of the original QPSK signal (as
  shown in Fig. 4.31)

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Vectorial View of MFSK Signaling
37
Symbol Error Performance for Coherent FSK
Signaling
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Eb/N0 and SNR in the MFSK
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Symbol Error Versus Bit Error for FSK Signaling
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Symbol Error Performance for M-ary Systems

• Symbol error performance for coherently detected
  M-ary PSK
• Symbol error performance for differentially
  coherent detection of MPSK signal
• Probability of symbol error for coherently
  detected MFSK signal
• Probability of symbol error for non-coherently
  detected MFSK signal

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Symbol Error Performance for Coherently Detected
MPSK
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Symbol Error Performance for Coherently Detected
MFSK
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Symbol Error Performance for Non-coherently
Detected MFSK
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Bit Error Versus Symbol Error Probability

• Orthogonal signal

45
Bit Error Versus Symbol Error Probability

• Multiple Phase signals with Gray coded
• For BPSK and QPSK signaling