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BER of BPSK
Figure 6.3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s1(t) and s2(t), displayed in the inserts, assume nc = 2.
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Figure 6.3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s1(t) and s2(t), displayed in the inserts, assume nc = 2.
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Generation and Detection of Coherent BPSK
Figure 6.4 Block diagrams for (a) binary PSK transmitter and (b) coherent binary PSK receiver.
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Figure 6.5 Power spectra of binary PSK and FSK signals.
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Figure 6.6 Signal-space diagram of coherent QPSK system.
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Generation and Detection of Coherent BPSK si1
odd
See Table 6.1
even si2
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Figure 6.8 Block diagrams of (a) QPSK transmitter and (b) coherent QPSK receiver.
, g(t) denotes the symbol shaping function.
The baseband QPSK PSD equals the sum of the inphase and quadrature PSD
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Figure 6.9 Power spectra of QPSK and MSK signals. 20
Figure 6.7 (a) Input binary sequence. (b) Odd-numbered bits of input sequence and associated binary PSK wave. (c) Even-numbered bits of input sequence and associated binary PSK wave. (d) QPSK waveform defined as s(t) = si1f1(t) + si2f2(t).
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Offset QPSK ( Reducing Carrier Amplitude Change)
Figure 6.10 Possible paths for switching between the message points in (a) QPSK and (b) offset QPSK. 22
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π /4 –shifted QPSK Two ordinary QPSK constellations
Figure 6.11 Two commonly used signal constellations of QPSK; the arrows indicate the paths along which the QPSK modulator can change its state. 24
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Figure 6.14 Illustrating the possibility of phase angles wrapping around the positive real axis.
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Figure 6.13 Block diagram of the π/4-shifted DQPSK detector.
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Figure 6.15 (a) Signal-space diagram for octaphase-shift keying (i.e., M = 8). The decision boundaries are shown as dashed lines. (b) Signal-space diagram illustrating the application of the union bound for octaphase-shift keying.
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Figure 6.16 Power spectra of M-ary PSK signals for M = 2, 4, 8.35
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QAM Cross Constellation M=2n where n is odd (e.g., 5,7,…)
Figure 6.18 Illustrating how a square QAM constellation can be expanded to form a QAM cross-constellation.
1 Eb pe ≈ 21 − ) erfc( N0 2M
(6.65) 40
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BFSK has a two-dimensional signal space Eb 0 s1 = and s 2 = E 0 b
(6.90), (6.91)
Figure 6.25 Signal-space diagram for binary FSK system. The diagram also includes two 42 inserts showing example waveforms of the two modulated signals s1(t) and s2(t).
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Generation and Detection of Coherent BPSK
Figure 6.26 Block diagrams for (a) binary FSK transmitter and (b) coherent
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Figure 6.5 Power spectra of binary PSK and FSK signals.
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Figure 6.27 Phase tree. 57
Figure 6.28 Phase trellis; boldfaced path represents the sequence 1101000. 58
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Fig. 6.28
Figure 6.30 (a) Input binary sequence. (b) Waveform of scaled time function s1f1(t). (c) Waveform of scaled time function s2f2(t). (d) Waveform of the MSK signal s(t) obtained 61 by adding s1f1(t) and s2f2(t) on a bit-by-bit basis.
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Figure 6.29 Signal-space diagram for MSK system.
The constellation of MSK is similar to that of QPSK
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Generation and Detection of MSK Signals
Figure 6.31 Block diagrams for (a) MSK transmitter and (b) coherent MSK receiver.
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Let W denote the 3dB baseband bandwidth of te pulse-shaping filter.
log 2 f 2 ⇒ H ( f ) = exp(− ( ) ) 2 W
(6.132)
Figure 6.33 Power spectra of MSK and GMSK signals for varying timebandwidth product. (Reproduced with permission from Dr. Gordon Stüber, Georgia Tech.)
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PSD of MFSK
f c − f c −1 =
1 (Hz) 2T
Figure 6.36 Power spectra of M-ary PSK signals for M = 2, 4, 8. 71
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Figure 6.38 Output of matched filter for a rectangular RF wave: (a) θ = 0, and (b) θ = 180 degrees.
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Figure 6.41 Calculation of the conditional probability that l2 > l1, given l1.
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Figure 6.42 Noncoherent receiver for the detection of binary FSK signals.
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0 ≤ t ≤ Tb
Tb ≤ t ≤ 2Tb , sent s2 (t ) Figure 6.44 Signal-space diagram of received DPSK signal.
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Figure 6.45 Comparison of the noise performance of different PSK and FSK schemes.
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Figure 6.46 Signal constellation for (a) M-ary PSK and (b) corresponding M-ary QAM, for M = 16.
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BER of BPSK
Figure 6.3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s1(t) and s2(t), displayed in the inserts, assume nc = 2.
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Figure 6.3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s1(t) and s2(t), displayed in the inserts, assume nc = 2.
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Generation and Detection of Coherent BPSK
Figure 6.4 Block diagrams for (a) binary PSK transmitter and (b) coherent binary PSK receiver.
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Figure 6.5 Power spectra of binary PSK and FSK signals.
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Figure 6.6 Signal-space diagram of coherent QPSK system.
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Generation and Detection of Coherent BPSK si1
odd
See Table 6.1
even si2
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Figure 6.8 Block diagrams of (a) QPSK transmitter and (b) coherent QPSK receiver.
, g(t) denotes the symbol shaping function.
The baseband QPSK PSD equals the sum of the inphase and quadrature PSD
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Figure 6.9 Power spectra of QPSK and MSK signals. 20
Figure 6.7 (a) Input binary sequence. (b) Odd-numbered bits of input sequence and associated binary PSK wave. (c) Even-numbered bits of input sequence and associated binary PSK wave. (d) QPSK waveform defined as s(t) = si1f1(t) + si2f2(t).
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Offset QPSK ( Reducing Carrier Amplitude Change)
Figure 6.10 Possible paths for switching between the message points in (a) QPSK and (b) offset QPSK. 22
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π /4 –shifted QPSK Two ordinary QPSK constellations
Figure 6.11 Two commonly used signal constellations of QPSK; the arrows indicate the paths along which the QPSK modulator can change its state. 24
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Figure 6.14 Illustrating the possibility of phase angles wrapping around the positive real axis.
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Figure 6.13 Block diagram of the π/4-shifted DQPSK detector.
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Figure 6.15 (a) Signal-space diagram for octaphase-shift keying (i.e., M = 8). The decision boundaries are shown as dashed lines. (b) Signal-space diagram illustrating the application of the union bound for octaphase-shift keying.
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Figure 6.16 Power spectra of M-ary PSK signals for M = 2, 4, 8.35
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QAM Cross Constellation M=2n where n is odd (e.g., 5,7,…)
Figure 6.18 Illustrating how a square QAM constellation can be expanded to form a QAM cross-constellation.
1 Eb pe ≈ 21 − ) erfc( N0 2M
(6.65) 40
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BFSK has a two-dimensional signal space Eb 0 s1 = and s 2 = E 0 b
(6.90), (6.91)
Figure 6.25 Signal-space diagram for binary FSK system. The diagram also includes two 42 inserts showing example waveforms of the two modulated signals s1(t) and s2(t).
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Generation and Detection of Coherent BPSK
Figure 6.26 Block diagrams for (a) binary FSK transmitter and (b) coherent
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Figure 6.5 Power spectra of binary PSK and FSK signals.
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Figure 6.27 Phase tree. 57
Figure 6.28 Phase trellis; boldfaced path represents the sequence 1101000. 58
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Fig. 6.28
Figure 6.30 (a) Input binary sequence. (b) Waveform of scaled time function s1f1(t). (c) Waveform of scaled time function s2f2(t). (d) Waveform of the MSK signal s(t) obtained 61 by adding s1f1(t) and s2f2(t) on a bit-by-bit basis.
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Figure 6.29 Signal-space diagram for MSK system.
The constellation of MSK is similar to that of QPSK
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Generation and Detection of MSK Signals
Figure 6.31 Block diagrams for (a) MSK transmitter and (b) coherent MSK receiver.
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Let W denote the 3dB baseband bandwidth of te pulse-shaping filter.
log 2 f 2 ⇒ H ( f ) = exp(− ( ) ) 2 W
(6.132)
Figure 6.33 Power spectra of MSK and GMSK signals for varying timebandwidth product. (Reproduced with permission from Dr. Gordon Stüber, Georgia Tech.)
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PSD of MFSK
f c − f c −1 =
1 (Hz) 2T
Figure 6.36 Power spectra of M-ary PSK signals for M = 2, 4, 8. 71
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Figure 6.38 Output of matched filter for a rectangular RF wave: (a) θ = 0, and (b) θ = 180 degrees.
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Figure 6.41 Calculation of the conditional probability that l2 > l1, given l1.
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Figure 6.42 Noncoherent receiver for the detection of binary FSK signals.
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0 ≤ t ≤ Tb
Tb ≤ t ≤ 2Tb , sent s2 (t ) Figure 6.44 Signal-space diagram of received DPSK signal.
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Figure 6.45 Comparison of the noise performance of different PSK and FSK schemes.
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Figure 6.46 Signal constellation for (a) M-ary PSK and (b) corresponding M-ary QAM, for M = 16.
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