1 2 3 4 5 BER of BPSK

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BER of BPSK Figure 6. 3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s 1(t) and s 2(t), displayed in the inserts, assume nc 2. 6

Figure 6. 3 Signal-space diagram for coherent binary PSK system. The waveforms depicting the transmitted signals s 1(t) and s 2(t), displayed in the inserts, assume nc 2. 7

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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. 10

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Figure 6. 5 Power spectra of binary PSK and FSK signals. 12

Figure 6. 6 Signal-space diagram of coherent QPSK system. 13

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Generation and Detection of Coherent BPSK si 1 odd See Table 6. 1 even si 2 18 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 19

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) si 1 f 1(t) si 2 f 2(t). 21

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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p/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. 31

Figure 6. 13 Block diagram of the p/4 -shifted DQPSK detector. 32

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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. 34

Figure 6. 16 Power spectra of M-ary PSK signals for M 2, 4, 8. 35

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QAM Cross Constellation M=2 n 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. 40

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BFSK has a two-dimensional signal space 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 s 1(t) and s 2(t).

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Generation and Detection of Coherent BPSK Figure 6. 26 Block diagrams for (a) binary FSK transmitter and (b) coherent binary FSK receiver. 45

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Figure 6. 5 Power spectra of binary PSK and FSK signals. 47

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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 s 1 f 1(t). (c) Waveform of scaled time function s 2 f 2(t). (d) Waveform of the MSK signal s(t) obtained 61 by adding s 1 f 1(t) and s 2 f 2(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 63

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Generation and Detection of MSK Signals Figure 6. 31 Block diagrams for (a) MSK transmitter and (b) coherent MSK receiver. 66

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Let W denote the 3 d. B basebandwidth of te pulse-shaping filter. Figure 6. 33 Power spectra of MSK and GMSK signals for varying timebandwidth product. (Reproduced with permission from Dr. Gordon Stüber, Georgia Tech. ) 69