Introduction to Digital Data Transmission

1 Chapter5 Introduction to Digital .. Classes .. Modulation .. Phase-Shift Keying (BPSK) .. Keying (QPSK) and Vari-ations .. Shaping .. Cosine Pulse .. Raised Cosine .. Baseband Representation .. Baseband Representation .. Space Representation .. Two-Dimensional Schemes .. Modulation Techniques .. Frequency-Shift Keying .. Shift Keying .. Channel Interference .. Amplifier Nonlinearity .. Comparison .. Channel .. Channel .. Estimation and Tracking .. Detection .. Transmission .. Receiver Bit Error Probability Performance .. AWGN Channel .. Frequency Flat, Slow fading Channel .. Theme Example: OFDM .. Cyclic Prefix .. Theme Example: Cordless Telephone .. 5-645-2 ECE 5625 Communication Systems ICONTENTSThis chapter introduces a variety Digital modulation schemes foundin modern wireless systems.

2 The block diagram of a generic band-pass wireless link is shown (t) d(t)s(t) s(t) st(t)st(t)fSt(f)fc fcfS(f)0ffc fcN0/2 St(f)f0 S(f)ChannelGeneric bandpass wireless systemBy its very nature, sending Digital information involves a mes-sage signal that takes on only a finite number of values. At thewaveform level the encoded Digital message signal can be a con-tinuous function time,t. The data likely speech thathas been digitally encoded using a compression 5625 Communication Systems ModulationThe process of modulation varies some aspect of the carrier wavewith respect to the modulating signal, , Demodulation per-forms the opposite operation, so as to gain recover an estimate of theinformation bearing practical benefits of modulation include:1. Shift the spectral content to an operating frequency band thatis easily transmitted and received2. The modulation operation may make the signal less vulnerableto noise and interference, , frequency modulation3.

3 The scheme easily supports the use of a multiple-access tech-niqueGeneric Carrier fctC Modulation ClassesModulation schemes can be compared via a number of classifica-tions. Three such classifications are briefly explored before detailedinvestigations of selected schemes vs NonlinearTwo basic classes of modulation arelinearandnonlinear. If theprinciple of superposition holds the modulation is 5625 Communication Systems MODULATIONThe attributes of both linear and nonlinear modulation are ex-plored in the remainder of this vs DigitalModulation can also be classified along the lines of analog and dig-ital. Here analog means the message signal, a continuousfunction of time, so the modulated carrier, , has attributes varycontinuously over some parameter Digital modulation the message signal, , takes on dis-crete values, , 1with the switching instants occurring at timeintervalTs. The modulated still be a function ofcontinuous varibalet, but the values the signal takes on will have adiscrete nature, , amplitude, frequency, or focus in this chapter will be on Digital modulation vs AngleThe particular attribute of the carrier is varied formsanother basis for modulation classification.

4 Two broad classes areamplitude and angle modulation. Angle modulation further breaksdown into phase and frequency modulation. Amplitude modulation simply requires the carrier amplitudeActo vary linearly with respect With angle modulation we consider the entire argument of the angle .t/D2 fctC .t/ECE 5625 Communication Systems I5-5 CONTENTSof the carrier, and design a modulator so that it varies Specifically with frequency modulation, the derivatived .t/=dtis made to vary linearly with the message signal Specifically with phase modulation the carrier phase .t/is made to vary linearly with the Linear Binary Phase-Shift Keying (BPSK)To create BPSK we first construct a baseband data signal of the kT/wherebkis a bipolar bit sequence of the formbkD(C1;binary symbol 1 1;binary symbol 0 A fundamental pulse the rectangle (1; 0 t T0;otherwisep(t) 5625 Communication Systems LINEAR MODULATION BPSK constitutes a form a Digital phase modulation in the car-rier phase is switched between.))

5 T/D0and radians depend-ing upon the sign ofbk Since a phase of radians simply changes the sign of the car-rier signal, we observe that for the case of is of the same form as double sideband suppressed car-rier (DSB-SC) modulationd(t)st(t)tt123456!1! !1! using a rectangle pulse The power spectral density of BPSK can be shown to be of /DA2c4T fc/j2 /DF ECE 5625 Communication Systems I5-7 CONTENTS For the rectangular pulse f T/2 f T/where sin. x/=. x/ fcfcfSt(f)2/T2/TTA2c4 BPSK spectrum For a rectangular pulse shape the main lobe bandwidth, alsoknown as the RF bandwidth isBRFD2=TD2Rb, whereRbD1=Tis the bit rate Another useful bandwidth measure is the fractional contain-ment bandwidth,Bf, defined asPfDRfcCBf=2fc Bf= /dfwherePfis a fraction of the total power 5625 Communication Systems LINEAR MODULATIONE xample :BPSK with Rectangle Pulse ShapeBf The fractional containment bandwidth of rectangle pulse shapedBPSK can be found fromPfDRBf= T/df We first work with the denominator using Parseval s T/dfD12Z1 T/dfD12TZ1 Inserting in the numerator, and changing variables, we havePfD2 ZBfT= AtBfTD2the contained power is only , while atBfTD5the contained power has only increased to The 99% containment bandwidth occurs whenBfTD20.

6 57 Clearly pulse shaping beyond the rectangular pulse shape isneededECE 5625 Communication Systems PfNormalizedRFContainmentBandwidthBfT90% 95%Rect pulse BPSK fractional out-of-band Quadriphase-Shift Keying (QPSK) and Vari-ationsTo make more effective use of the available spectrum we may chooseto modulate both the sin and cos carriers (quadrature multiplexing). Consider a binary data into twoequal bit rate streams, kTs/5-10 ECE 5625 Communication Systems LINEAR MODULATION whereTsD2 Tbis the symbol duration, which is twice the bitduration Note that the symbol rate isRsD1=TsDRb=2 With QPSK we transmit two bits per symbol The data streams are applied to orthogonal, but at the samefrequency, fct/ 1:2 Demux d(t)d1(t)d2(t)s1t(t)s2t(t)st(t)Accos(2 fct)Acsin(2 fct)QPSKQPSK modulator block diagramStandard QPSKWith this form of QPSK it looks like we have two equal bit rateBPSK modulators operating in parallel.

7 The two carrier signals are aid to be inphase quadraturesincethe sine lags the cosine by90 ECE 5625 Communication Systems I5-11 CONTENTS The , modulating the cosine carrier, is known asthein-phase signalorIcomponent, while the ,modulating the sine carrier, is known as thequadrature signal Assuming equal bit rates and pulse shaping on theIandQcomponents, the spectrum of QPSK is identical to that of BPSK,that /DA2c2Ts fc/j2 Note the scale factor difference from BPSK because we havetwo equal power carriers forming the QPSK signal. Rectangular pulse shaping the main lobe RF bandwidth is nowBRFD2 RsDRb, and bandwidth reduction of 2 comparedwith BPSK Since each carrier phase is modulated between0 and180 ,and are in phase quadrature, composite carrier phase takes onthe four values off45 ;135 ;225 ;315 g A specific property of standard QPSK is that the compositecarrier phase may undergo phase jumps of0 , 90 , or 180 every2 TbDTsseconds5-12 ECE 5625 Communication Systems LINEAR MODULATION246810!

8 1! !1! !1! (t)d2(t)t(symbols)ttst(t) 2Ts=1 QPSK using a rectangle pulseOffset QPSK (OQPSK)The 180 phase jumps in QPSK can be a problem when the signalis filtered and then amplified by a nonlinear power amplifier. OQPSK, also known asstaggered QPSK, is formed by delay-ing the quadrature signal bit stream byTs=2 DTb, thus limit-ing phase jumps to just0 and 90 The transmitted signal now takes the Ts=2 fct/ ECE 5625 Communication Systems I5-13 CONTENTS The waveforms change accordingly246810!1! (t)t(symbols)ttst(t) 2246810!1! !1! (t Ts/2)Ts=1 OQPSK using a rectangle Pulse ShapingFor both BPSK and QPSK we have seen how the rectangular pulseshape, while easy to implement, creates a wide spectral footprint inthe neighborhood of the carrier frequency,fc. We now consider theuse of pulse shaping or apremodulation filterto better match thetransmitted signal spectrum to the available channel bandwidth. Wespecifically desire:5-14 ECE 5625 Communication Systems PULSE SHAPING1.

9 A more compact spectrum to allow more digitally modulatedcarriers to occupy a frequency band allocation2. A means to manage channel induced bandlimiting, , dueto multipath, which introducesintersymbol interference(ISI),which occurs when the energy of previous symbols interferes/overlapswith the energy of the present symbol (pulse) Raised Cosine Pulse A premodulation filter and/or pulse shaping satisfies, in part,both of the above requirements A popular class of pulse shaping that achieves both band lim-iting and ISI control is theraised cosine(RC) pulse The RC pulse has a spectrum with adjustable bandwidth in theRF (two-sided) sense running fromWDRbto2WD2Rb The pulse spectrum (Fourier transform) is defined /D8 < :12W;0 jfj< f114Wh1 Ccos 2W jfj / i; f1 jfj< 2W f10;otherwisewheref1sets the edge of the flat portion of the spectrum andis related to the roll-off factor andWvia0 D1 f1W 1 ECE 5625 Communication Systems I5-15 CONTENTS The parameter (elsewhere denoted ) controls the excessbandwidth relative to the minimum value ofWDRb(one-sided W/2) when D0!

10 1! (f) =0,1/2,1RC spectrum, /, for various values The RC pulse gets its name from in thespectrum definition The corresponding RC pulse, , can be obtained by inverseFourier /gD Wt/1 16 2W2t2 The zero ISI property of the RC pulse is that , :::; 2; 1;1;2;:::5-16 ECE 5625 Communication Systems PULSE SHAPING!3!2!1123! (t)NormalizedTimet/T =0,1/2,1RC pulse, , for various valuesExample :RC Waveform for a Bit PatternConsider the waveform produced by the bit sequencef0;0;1;1;0;1gor in bipolar formf 1; 1;1;1; 1; pulsesforming seq..,-1,-1,1,1,-1,1,..Note zero ISI!4!224!1! created with bit pattern -1,-1,1,1,-1,1 ECE 5625 Communication Systems I5-17 CONTENTStComposite ofpulsesforming seq..,-1,-1,1,1,-1,1,..!4!224!1! waveform created with bit pattern -1,-1,1,1,-1, Square-Root Raised CosineThe zero ISI response holds for the RC pulse, but optimal filtering inan additive noise environment, requires that filtering/pulse shapingbe distributed between the transmitter and receiver.