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1 . mplitude-shift Keying (SK) Modulation Introduction he transmission of digital signals is increasing at a rapid rate. Low-frequency analogue signals are often converted to digital format (PM) before transmission. he source signals are generally referred to as baseband signals. Of course, we can send analogue and digital signals directly over a medium. From electro-magnetic theory, for efficient radiation of electrical energy from an antenna it must be at least in the order of magnitude of a wavelength in size; c = fλ, where c is the velocity of light, f is the signal frequency and λ is the wavelength. For a khz audio signal, the wavelength is 3 km. n antenna of this size is not practical for efficient transmission. he low-frequency signal is often frequency-translated to a higher frequency range for efficient transmission. he process is called modulation. he use of a higher frequency range reduces antenna size. In the modulation process, the baseband signals constitute the modulating signal and the high-frequency carrier signal is a sinusiodal waveform. here are three basic ways of modulating a sine wave carrier. For binary digital modulation, they are called binary amplitude-shift keying (BSK), binary frequency-shift keying (BFSK) and binary phaseshift keying (BPSK). Modulation also leads to the possibility of frequency multiplexing. In a frequency-multiplexed system, individual signals are transmitted over adjacent, nonoverlapping frequency bands. hey are therefore transmitted in parallel and simultaneously in time. If we operate at higher carrier frequencies, more bandwidth is available for frequency-multiplexing more signals. Binary mplitude-shift Keying (BSK) binary amplitude-shift keying (BSK) signal can be defined by s(t) = m(t) cos πf c t, < t < (.) where is a constant, m(t) = or, f c is the carrier frequency, and is the bit duration. It has a power P = /, so that = P. hus equation (.) can be written as s(t) = P cos πf c t, < t < = P cos πfc t, < t < = E cos πfc t, < t < (.).

2 where E = P is the energy contained in a bit duration. If we take φ (t) = cos πf ct as the orthonormal basis function, the applicable signal space or constellation diagram of the BSK signals is shown in Figure.. Figure. BSK signal constellation diagram. Figure. shows the BSK signal generated by the binary. he amplitude of a carrier is switched or keyed by the binary signal m(t). his is sometimes called on-off keying (OOK). Figure. Binary modulating signal and BSK signal. he Fourier transform of the BSK signal s(t) is S(f) = [m(t) e j πf c t ] e -jπft dt + [m(t) e - j πf c t ] e -jπft dt S(f) = M(f - f c ) + M(f + f c ) (.3) he effect of multiplication by the carrier signal cos πf c t is simply to shift the spectrum of the modulating signal m(t) to f c. Figure.3 shows the amplitude spectrum of the BSK signals when m(t) is a periodic pulse train. Figure.3 Modulating signal, spectrum of, and (c) spectrum of BSK signals. Since we define the bandwidth as the range occupied by the baseband signal m(t) from Hz to the first zero-crossing point, we have B Hz of bandwidth for the baseband signal and B Hz for the BSK signal. Figure.4 shows the modulator and a possible implementation of the coherent demodulator for BSK signals. Figure.4 BSK modulator and coherent demodulator. M-ary mplitude-shift Keying (M-SK) n M-ary amplitude-shift keying (M-SK) signal can be defined by s(t) = i cos πf c t, t, elsewhere (.4).

3 where i = [i - (M - )] (.5) for i =,,..., M - and M > 4. Here, is a constant, f c is the carrier frequency, and is the symbol duration. he signal has a power P i = i /, so that i = P i. hus equation (.4) can be written as s(t) = P i cos πf c t, < t < = P i cos πfc t, < t < = E i cos πfc t, < t < (.6) where E i = P i is the energy of s(t) contained in a symbol duration for i =,,..., M -. Figure.5 shows the signal constellation diagrams of M-SK and 4-SK signals. Figure.5 M-SK and 4-SK signal constellation diagrams. Figure.6 shows the 4-SK signal generated by the binary. Figure.6 4-SK modulation: binary, 4-ary signal, and 4-SK signal. Figure.7 shows the modulator and a possible implementation of the coherent demodulator for M-SK signals. References Figure.7 M-SK modulator and coherent demodulator. [] M. Schwartz, Information ransmission, Modulation, and Noise, 4/e, McGraw Hill, 99. [] P. Z. Peebles, Jr., Digital Communication Systems, Prentice Hall,

4 s s φ = ( t ) E cos π f c t Figure. BSK signal constellation diagram. Binary m(t ) ime BSK signal - ime Figure. Binary modulating signal and BSK signal..4

5 M( f ) m ( t ) 3 t -3 Envelope - - B = 3 f 3 B -f c -f c - -f c + -f 3 c + S ( f ) Envelope B f fc f 3 f f c + f 3 c - c - c + (c) Figure.3 Modulating signal, spectrum of, and (c) spectrum of BSK signals. m (t ) x s ( t ).5 m (t ) cos 4 π f c t +.5 m (t ) x ~.5 m (t ) cos π f c t cos π f c t Figure.4 BSK modulator and coherent demodulator..5

6 s... i... E i φ ( t ) = cos π f c t s s s s 3 φ ( t ) Figure.5 M-SK and 4-SK signal constellation diagrams. Binary m (t ) ime 4-ary signal ime 3 4-SK signal - -3 (c) ime Figure.6 4-SK modulation: binary, 4-ary signal, and 4-SK signal..6

7 log M bits Binary Serial to parallel converter : D/ converter m (t ) x cos π f c t.5 m ( t ) cos 4π f c t +.5 m( t ) x ~ cos π f c t :.5 m ( t ) Comparator m (t ) Binary /D converter Figure.7 M-SK modulator and coherent demodulator..7

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