# Basic digital passband_modulat

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- 1. Basic DigitalPassband ModulationReference : HA H. NGUYEN and ED SHWEDYK A First Course in Digital Communications , 2009

2. Binary amplitude-shift keying (BASK) 3. s(t) = m(t)c(t)where m(t) is the modulating signal (the baseband signal, an NRZsignal) and c(t) = V cos(2fct) is the sinusoidal carrier.Optimum Receiver Threshold 4. BASK signaling scheme: (a) signal space plot; (b) optimum receiverimplementation; (c) decision regions 5. Error probabilityPower Spectral Density (PSD) 6. PSD of BASKApproximately 95% of the total transmittedpower lies in a band of 3/Tb (hertz),centered at fc. 7. Binary phase-shift keying (BPSK)A BPSK signal is generated by amplitude modulatingthe sinusoidal carrier with a NRZ-L signal of amplitude1. The transmitted signal is s(t) = m(t)c(t) (where m(t) isa NRZ-L signal) with a resultant phase that is either 0 or radians.Signal space plot of BPSK. 8. PSD for the BPSKThe PSD of BPSK is similar to that of BASK except thatthere are no impulse functions at fc, reflecting the factthat there is no power at the carrier. This is reasonablesince BPSK is really a double sideband suppressedcarrier modulation. 9. Binary frequency-shift keying (BFSK)Simple BFSKmodulators: (a) by gatingtwo oscillators;(b) using avoltagecontrolledoscillator(VCO).Two oscillators 10. s1(t) and s2(t) are orthogonalover the interval [0, Tb]If the two phases are the same 11. If the two phases are different 12. VCOwhere n and m are positive integers, and n m. 13. Signal space plot and decision regions of BFSK. 14. Performance comparison of BASK, BPSK, andBFSK 15. BPSK is 3 dB more efficient than BFSK, which has thesame performance as BASK. BFSK occupies a larger bandwidth than BPSK and BASK (recall that BPSK and BASK occupy the same bandwidth).Each of the three modulation techniques has a spectrumthat decays as 1/f ^2 for frequencies away from thecarrier, reflecting the fact that for each modulation thetransmitted signal has discontinuities. 16. Digital modulation techniques for spectral efficiencyQuadrature phase-shift keying (QPSK)QPSK signals and a mapping to the messages 17. An example of a QPSK signalThe basic idea behind QPSK exploits the fact thatcos(2fct) and sin(2fct) are orthogonalover theinterval [0, Tb] when fc = k/Tb, k integer. 18. Therefore only two orthonormal functions are needed torepresent the four signals 19. Signal space plot of QPSK modulation. 20. Optimum Receiver for QPSKThe optimum receiver is derived by expanding the receivedsignal r(t) = si(t) + w(t) over the interval of Ts secondsinto a series as follows:The criterion will be to find a receiver that minimizes thesymbol (message) error probability.Rather than minimizing the error, consider instead theequivalent criterion, that of maximizing the probability ofa correct decision. 21. Assign the observation vector r = (r1, r2, . . . , rm)in the m-dimensional signal space to the regionfor which the integrand Pi f(r|si(t)) is the largest. 22. P1 = P2 = P3 = P4 Minimum-distance receiverP[error] = P[error|si(t)] = 1 P[correct|si(t)]. 23. Decision regions of the minimum-distance receiver ofQPSK 24. Signal space diagram of QPSK: to compute P[correct|s1(t)] one finds the volume of f(r1, r2|s1(t)) over theshaded quadrant 25. same as that of BPSK 26. An alternative representation of QPSKInphase carrier V cos(2fct)Quadrature carrier V sin(2fct),A different blockdiagram of a QPSKmodulator 27. Signal space plots for inphase and quadrature bit streams 28. Receiver implementation for QPSK 29. Offset quadrature phase-shift keying (OQPSK)To prevent the phase change of in QPSK, offset (orstaggered) quadrature phase-shift keying (OQPSK) isused so that signal amplification can be done moreefficiently. OQPSK differs from QPSK only in that in OQPSKthe aI(t) and aQ(t) bit streams are offset by onebit interval Tb. 30. Minimum shift keying (MSK)The transmitted signals s(t) have sudden jumps atmultiples of symbol duration for QPSK), or multiples of bitduration (for OQPSK).The two carriers V cos(2fct) and Vsin(2fct) areweighted by sinusoids of frequency 1/(4Tb). 31. The signals are orthogonal over the interval of Tbseconds, or any integer multiple of TbThe bit error probability of MSK is the same as that ofBPSK, QPSK, and OQPSK 32. The expression in (7.64) shows that s(t) not only has aconstant envelope, but also a continuousphase. Furthermore, the transmitted signal is of eitherfrequency f2 = fc + 1/4Tb or frequency f1 = fc 1/4Tb depending on the ratio aQ(t)/aI (t). 33. Thus the transmitted signal may beconsidered to be a frequency shift keyingsignal with continuous phase (CPFSK).Note also that the frequency separation isf2 f1 = 1/2Tb, which is the minimumseparation possible for the two sinusoidalcarriers to be coherently orthogonal.This explains the name minimum shiftkeying of the modulation scheme.