dept. of ee, ndhu 1 chapter four bandpass modulation and demodulation
TRANSCRIPT
1Dept. of EE, NDHU
Chapter Four
Bandpass Modulation and Demodulation
2Dept. of EE, NDHU
Bandpass Signaling
3Dept. of EE, NDHU
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 transmis
sion
• Modulation can separate the different signals (Ex. FDMA)
• Modulation can also be used to place a signal in a frequency band where design r
equirement can be easily met
4Dept. of EE, NDHU
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 carrier’s phase to detect the signa
– PSK, FSK, ASK, CPM, and Hybrid forms
• Non-coherent detection
– The receiver does not utilize the carrier’s phase reference information
– DPSK, FSK, ASK, CPM, and Hybrid forms
5Dept. of EE, NDHU
Digital Modulations
6Dept. of EE, NDHU
Detection of Signals in Gaussian Noise
• Bandpass model of the detection process is virtually identical to the baseband mo
del
• Decision regions
– Minimum error decision rule is to choose the signal class that the distance d(r,si) is mi
nimized, 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)
MidttstrTzT
ii ,,1 , )()()(
0
7Dept. of EE, NDHU
Decision Regions
8Dept. of EE, NDHU
Correlator Receiver with Reference Signals
9Dept. of EE, NDHU
Binary Correlator Receiver
10Dept. of EE, NDHU
Coherent Detection of PSK
• BPSK signal
• Decision stage chooses the signal with largest output value of matched
filter
)()( and )()(
0for cos2
)(function basis a and
0 )cos(2
)(
0 )cos(2
)(
1211
01
02
01
tEtstEts
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t
TttT
Ets
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11Dept. of EE, NDHU
Sampled Matched Filter
12Dept. of EE, NDHU
Coherent Detection of MPSK
• MPSK signal
• Signal space and decision regions for a QPSK (M=4) system
– As shown in Fig.4.11
– Make a decision by the phase information
)()2
sin( )()2
cos()(
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iEts
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it
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i
i
13Dept. of EE, NDHU
Demodulator for MPSK Signals
14Dept. of EE, NDHU
Coherent Detection of FSK
• FSK signal
• The distance between any two signal vectors is
• Choose the largest output of matched filter
otherwise 0
for Therefore
cos2
cos2
,,1 cos2
)( functions basis and
,,1 , 0 )cos(2
)(
0
jiEa
tdtT
tT
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t
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ij
j
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iij
jj
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E2
15Dept. of EE, NDHU
Signal Space for a 3-ary FSK Signal
16Dept. of EE, NDHU
Signal Space for DPSK
17Dept. of EE, NDHU
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)
MiTttnttT
Etr
MiTtttT
Ets
i
ii
,,1 , 0 , )(])(cos[2
)( : signal received
,,1 , 0 , )](cos[2
)( : waveformdtransmitte
0
0
)()()(])([])([ 21212 TTTTT ijkjk
18Dept. of EE, NDHU
Binary Differential PSK Example
Suboptimum detection
Optimum detection
)()1()( kmkckc
19Dept. of EE, NDHU
Non-coherent Detection of FSK
Quadrature Receiver
20Dept. of EE, NDHU
Non-coherent Detection of FSK
Non-coherent detection of FSK with envelop detector
21Dept. of EE, NDHU
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
Tff
dttftfT
1 is spacing toneminimum
0 2cos)2cos(
21
021
Tff
dttftfT
2
1 is spacing toneminimum
0 2cos 2cos
21
021
22Dept. of EE, NDHU
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
23Dept. of EE, NDHU
D8PSK Modulator
24Dept. of EE, NDHU
D8PSK Demodulator
25Dept. of EE, NDHU
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
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26Dept. of EE, NDHU
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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27Dept. of EE, NDHU
DPSK Detection
28Dept. of EE, NDHU
Bit Error Probability of Binary Systems
29Dept. of EE, NDHU
M-ary Signals and Performance
30Dept. of EE, NDHU
Ideal Probability of Bit Error Performance
31Dept. of EE, NDHU
Bit Error Performance for M-ary Orthogonal Signaling
32Dept. of EE, NDHU
Bit Error Performance for Multiple Phase Signaling
33Dept. of EE, NDHU
M-ary Signaling
• M-ary signaling instructs the modulator to produce one of M=2k waveforms
• M-ary multiple phase signaling
– The BER curve moves in the direction of degraded error performance as k increa
ses
– 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 i
ncreases
– The required system bandwidth increases as k increases
34Dept. of EE, NDHU
Vectorial View of MPSK Signaling
35Dept. of EE, NDHU
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 ne
w 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 ori
ginal QPSK signal (as shown in Fig. 4.31)
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RSR
W
N
S
N
Eb
)()2/
(2/
0 R
W
N
S
R
W
N
S
N
Eb
36Dept. of EE, NDHU
Vectorial View of MFSK Signaling
37Dept. of EE, NDHU
Symbol Error Performance for Coherent FSK Signaling
38Dept. of EE, NDHU
Eb/N0 and SNR in the MFSK
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39Dept. of EE, NDHU
Symbol Error Versus Bit Error for FSK Signaling
40Dept. of EE, NDHU
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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41Dept. of EE, NDHU
Symbol Error Performance for Coherently Detected MPSK
42Dept. of EE, NDHU
Symbol Error Performance for Coherently Detected MFSK
43Dept. of EE, NDHU
Symbol Error Performance for Non-coherently Detected MFSK
44Dept. of EE, NDHU
Bit Error Versus Symbol Error Probability
• Orthogonal signal
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1
2/
12
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45Dept. of EE, NDHU
Bit Error Versus Symbol Error Probability
• Multiple Phase signals with Gray coded
• For BPSK and QPSK signaling
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BBBE
BE
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:BPSK