24. Frequency-Shift Keying (FSK) Modulation and Quadrature Amplitude Modulation (QAM)

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1 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac 4. Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) Frequency-Shif Keying (BFSK) [-3] binary frequency-shif keying (BFSK) signal can be defined by s() = cos π f, cos π f, (4.) where is a consan, f and f are he ransmied frequencies, and is he bi duraion. he signal has a power P = /, so ha = P. hus equaion (4.) can be wrien as s() = = = Pcos π f, P cos π f, P cos π f, P cos π f, cos π f, cos π f, (4.) where = P is he energy conained in a bi duraion. For orhogonaliy, f = m/ and f = n/ for ineger n > ineger m and f - f mus be an ineger muliple of /. We can ake φ () = cos πf and φ () = sin πf as he orhonormal basis funcions [3]. he applicable signal consellaion diagram of he orhogonal BFSK signal is shown in Figure 4.. Figure 4. Orhogonal BFSK signal consellaion diagram. Figure 4. shows he BFSK signal generaed by he binary. Figure 4., BFSK signal, and (c) binary modulaing and BSK signals. 4.

2 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac I can be seen ha phase coninuiy is mainained a ransiions. Furher, he BFSK signal is he sum of wo BSK signals generaed by wo modulaing signals m () and m (). herefore, he Fourier ransform of he BFSK signal s() is S(f) = [m () e j πf ] e -jπf d+ [m () e - j πf ] e -jπf d+ [m () e j πf ] e -jπf d+ [m () e - j πf ] e -jπf d = M (f - f ) + M (f + f ) + M (f - f ) + M (f + f ) (4.3) Figure 4.3 shows he ampliude specrum of he BFSK signal when m () and m () are periodic pulse rains. Figure 4.3 Modulaing signals, Specrum of, and (c) specrum of BFSK signal (posiive frequencies only). n alernaive represenaion of he BFSK signal consiss of leing f = f c - f and f = f c + f. hen f - f = f (4.4) and s() = cosπ( f c + f) (4.5) where f c is he carrier frequency, f = β B is he frequency deviaion, β is he modulaion index, and B = / is he bandwidh of he modulaing signal. When f >> /, we have a wideband BFSK signal. he bandwidh is approximaely equal o f. When f << /, we have a narrowband BFSK signal. he bandwidh is approximaely equal o B. Figure 4.4 shows he modulaor and coheren demodulaor for BFSK signals []. Figure 4.4 BFSK modulaor and coheren demodulaor. 4.

3 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac M-ary Frequency-Shif Keying (M-FSK) [-4] n M-ary frequency-shif keying (M-FSK) signal can be defined by s() = cos( πf i + θ' ),, (4.6) for i =,,..., M -. Here, is a consan, f i is he ransmied frequency, θ' is he iniial phase angle, and is he symbol duraion. I has a power P = /, so ha = P. hus equaion (4.6) can be wrien as s() = P cos(πf i + θ'), < < = P cos(πfi + θ'), < < = cos(πfi + θ'), < < (4.7) where = P is he energy of s() conained in a symbol duraion for i =,,..., M -. For convenience, he arbirary phase angle θ' is aken o be zero. If we choose f = k /, f = (k + )/, f 3 = (k + 4)/,..., k >, we can ake φ () = cos π f, φ () = sin πf,... as he orhonormal basis funcions [3]. Figure 4.5 shows he signal consellaion diagram of an orhogonal 3-FSK signal. Figure 4.5 Orhogonal 3-FSK signal consellaion diagram. Figure 4.6 shows he 4-FSK signal generaed by he binary. Figure FSK modulaion: binary signal and 4-FSK signal. Figure 4.7 shows he modulaor and coheren demodulaor for M-FSK signals [4]. he mapping able simply maps he deeced index i ono a binary vecor. Figure 4.7 M-FSK modulaor and coheren demodulaor. 4.3

4 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac M-ary Quadraure mpliude Modulaion (M-QM) n M-ary quadraure ampliude modulaion (M-QM) signal can be defined by s() = = i cos( πf c + θi),, i cosθ i cosπf c i sinθ i sin πf c,, (4.8) (4.9) for i =,,..., M -. Here, i is he ampliude, f c is he carrier frequency, θ i is he phase angle, and is he symbol duraion. I has a power P i = i /, so ha i = P i. hus equaion (4.9) can be wrien as s() = P i cosθ i cosπf c - = i cosθ i cosπf c - P i sinθ i i sinθ i sinπf c sinπf c (4.) where i = P i is he energy of s() conained in a symbol duraion for i =,,..., M -. If we ake φ () = cos πf c and φ () = - sin πf c as he orhonormal basis funcions, he applicable signal consellaion diagrams of he 6-QM and 4-QM signals are shown in Figure 4.8. Figure QM and 4-QM signal consellaion diagrams. Figure 4.9 shows he modulaor and a possible implemenaion of he coheren demodulaor for M-QM signals. References Figure 4.9 M-QM modulaor and coheren demodulaor. [] M. Schwarz, Informaion ransmission, Modulaion, and Noise, 4/e, McGraw Hill, 99. [] P. Z. Peebles, Jr., Digial Communicaion Sysems, Prenice Hall, 987. [3] H. aub and D. L. Schilling, Principles of Communicaion Sysems, /e, McGraw Hill,

5 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac [4] F. Xiong, Digial Modulaion echniques, rech House,. 4.5

6 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac φ ( ) = cos π f s s φ ( = cos π ) f Figure 4. Orhogonal BFSK signal consellaion diagram. s ( ) ime BFSK signal - ime m ( ) ime BSK signal BSK signal - m ( ) - (c) ime ime ime Figure 4., BFSK signal, and (c) binary modulaing and BSK signals. 4.6

7 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac S ( f ) m ( ) m ( ) 3 B... f f f f + 3 f + f f c (c) -3 f 3 - M ( f) or nvelope - nvelope - B = f f - M ( f) B 3 β = B f f + f 3 + f f Figure 4.3 Modulaing signals, Specrum of, and (c) specrum of BFSK signal (posiive frequencies only). m ( ) s ( ) cos π f Σ m ( ) cos π f s ( ).5m ( ) cos 4π f +.5 m ( ) cos π f cos π f ~.5m ( ) cos 4π f +.5m ( ) ~.5m ( ) + Σ -.5 m ( ) m ( ) or m ( ) Figure 4.4 BFSK modulaor and coheren demodulaor. 4.7

8 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac φ ( ) = cos π f s s s φ = ( ) cos π f φ 3 ( ) = cos π f Figure 4.5 Orhogonal 3-FSK signal consellaion diagram. s ( ) ime 4-FSK signal - ime Figure FSK modulaion: binary signal and 4-FSK signal. 4.8

9 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac log M bis Serial o parallel converer : D/ converer Frequency modulaor s ( ) (.) d l s ( ) cos π f (.) d l Choose max l i Mapping able : cos π f cos π f M - : (.) d l M - Figure 4.7 M-FSK modulaor and coheren demodulaor. 4.9

10 Frequency-Shif Keying (FSK) Modulaion and Quadraure mpliude Modulaion (QM) on Mac φ ( ) = - sin π f c s s s s 3 φ ( ) s s 7 s 6 s 5 s s 4 4 θ 4 φ = θ ( ) cos π f c s 8 s 9 s s s s 3 φ ( ) s s 5 4 s 3 s Figure QM and 4-QM signal consellaion diagrams. Serial o parallel converer log M bis : ssign ampliude i and phase θ i i cos θ i cos π f c i sinθ i + Σ - s ( ) sin π f c s ( ).5i cos θ i cos 4π f c -.5 i sin θ i sin 4 π f c +.5 i cos θ i ~.5i cos θ i cos π f c ^.5 cos θ i sin 4 π f c + θ i = an - (.) i.5i sin θ i cos 4π f c -.5i sin θ i ~ -.5i sin θ i Mapping able sin π f c Figure 4.9 M-QM modulaor and coheren demodulaor. 4.