Quadrature Amplitude Modulation (QAM) Transmitter - PowerPoint Presentation

1. Quadrature Amplitude Modulation (QAM) TransmitterProf. Brian L. EvansDept. of Electrical and Computer EngineeringThe University of Texas at Austin

2. 15 - 2IntroductionDigital Pulse Amplitude Modulation (PAM)Modulates digital information (symbols) onto amplitude of pulseMay be later upconverted (e.g. to radio frequency)Digital Quadrature Amplitude Modulation (QAM)Two-dimensional extension of digital PAMBaseband signal requires sinusoidal amplitude modulationMay be later upconverted (e.g. to radio frequencies)Digital QAM modulates digital information onto pulses that are modulated ontoAmplitudes of a sine and a cosine, or equivalentlyAmplitude and phase of single sinusoid

3. Baseband PAM TransmitterBit stream to continuous-time pulse streamGroup stream of bits into symbols of J bitsMap symbol of J bits to unique symbol amplitudeInterpolate from discrete-time to continuous-timeSerial/Parallel1Jbit streamJ bits per symbolMap to PAMconstellationansymbol amplitudes*(t)baseband waveformDiscrete-to-Continuous TimeConversion (Interpolation)PulseshapergTsym[m] LSerial/Parallel1JMap to PAMconstellationans*(t)D/Afs@fs@fs@fsym@fsymfs = L fsym4-PAM Mapdd3d3d00011011symbol of bitssymbol ampl.ReviewL samples/symbol (upsampling factor)15 - 3

4. Amplitude Modulation by Cosiney1(t) = x1(t) cos(wc t)Review15 - 4Demodulation: modulation then lowpass filteringAssume x1(t) is an ideal lowpass signal with bandwidth w1Assume w1 < wcY1(w) is real-valued if X1(w) is real-valuedw01w1-w1X1(w)Baseband signal½Upconverted signalw0Y1(w)½-wc - w1-wc + w1-wcwc - w1wc + w1wc½X1(w - wc)½X1(w + wc)1See Slides 1-6 and 1-7

5. Amplitude Modulation by Siney2(t) = x2(t) sin(wc t)Revieww01w2-w2X2(w)Baseband signalDemodulation: modulation then lowpass filteringAssume x2(t) is an ideal lowpass signal with bandwidth w2Assume w2 < wcY1(w) is imaginary-valued if X1(w) is real-valuedwY2(w)j ½-wc – w2-wc + w2-wcwc – w2wc + w2wc-j ½X2(w - wc)j ½X2(w + wc)-j ½Upconverted signalSee Slides 1-8 and 1-915 - 5

6. How to Use Bandwidth Efficiently?+cos(c t)sin(c t)x1(t)x2(t)s(t)Cosine modulated signal is in theory orthogonal to sine modulated signal at transmitterReceiver separates x1(t) and x2(t) through demodulationSend two baseband signals in same transmission bandwidthCalled Quadrature Amplitude Modulation (QAM)Used in DSL, cable, Wi-Fi, LTESinusoidal mod doubles transmission bandwidth

7. QAM Transmitter Architecture #1Use D/A converter for each baseband PAM channeli[n]q[n]Map to 2-D constellationSerial/parallelconverter1BitsJIndexD/A power consumption  4-level QAM ConstellationIQdd-d-d+s(t)  4-QAM is 2-PAM in the in-phase dimension and 2-PAM in the quadrature dimension00011011PulseshapergTsym[m] LD/AfsPulseshapergTsym[m] LD/AB1B1 

8. QAM Transmitter Architecture #2Use only one D/A converterPulseshapergTsym[m]PulseshapergTsym[m]Serial/parallelconverter1BitsJIndexMap to 2-D constellationi[n]q[n] L L4-level QAM ConstellationIQdd-d-d00011011D/A power consumption  4-QAM is 2-PAM in the in-phase dimension and 2-PAM in the quadrature dimension+cos(0 m)sin(0 m)s[m]D/As(t)fsB2 B1B1

9. Comparison for 64-QAM (J=6 bits)Serial/parallelconverter1Bits6Index+s(t)  D/AfsD/Ai[n] and q[n] are 8-PAMsymbol amplitudes, e.g.{ -7, -5, -3, -1, 1, 3, 5, 7 } for d = 1 which needs 4 bitsMap to 2-D constellationi[n]q[n]44PulseshapergTsym[m]PulseshapergTsym[m]4+Bp4+BpUpsampling copies input sample to output and then L-1 zeros, and repeats L44 L+cos(0 m)sin(0 m)s[m]D/As(t)fsB24+ Bp +Bf4+ Bp+BfBf fractional bits for each sinusoidal value#1#2FIR filtering using Ng L coefficients has Ng non-zero multiplications due to upsampling. With C-bit FIR coefficients, FIR output will haveBp  additional bits in worst case (see next slide)

10. Wordlength Needed for Pulse Shaping

11. 15 - 11Performance Analysis of PAMIf we sample matched filter output at correct time instances, nTsym, without any ISI, received signalfor i = -M/2+1, …, M/2v(nT) ~ N(0; 2/Tsym)4-level PAM Constellationdd3 d 3 dMatched filter has impulse response gr(t)where transmitted signal isv(t) output of matched filter Gr() for input ofchannel additive white Gaussian noise N(0; 2)Gr() passes frequencies from -sym/2 to sym/2 ,where sym = 2  fsym = 2 / Tsym

12. 15 - 12Performance Analysis of PAMDecision errorfor inner points-7d-5d-3d-dd3d5d7dO-IIIIIIO+8-level PAM ConstellationDecision errorfor outer points Symbol error probability

13. 15 - 13Performance Analysis of QAMIf we sample matched filter outputs at correct time instances, nTsym, without any ISI, received signal4-level QAM ConstellationIQdd-d-dTransmitted signalwhere i,k  { -1, 0, 1, 2 } for 16-QAMNoiseFor error probability analysis, assume noise terms independent and each term is Gaussian random variable ~ N(0; 2/Tsym) In reality, noise terms have common source of additive noise in channel

14. 15 - 14Performance Analysis of 16-QAMType 1 correct detection3333222222221111IQ16-QAM1 - interior decision region2 - edge region but not corner3 - corner region

15. 15 - 15Performance Analysis of 16-QAMType 2 correct detection3333222222221111IQ16-QAM1 - interior decision region2 - edge region but not corner3 - corner regionType 3 correct detection

16. Performance Analysis of 16-QAMProbability of correct detectionSymbol error probability (lower bound)What about other rectangular QAM constellations?

17. ExamplesDetermine decision regions for the receiverDraw boundaries at midpoint of every pair of constellation pointsRectangular constellationsPAM in I and Q dimensionsI and Q axes become boundariesGray coding always possible    15 - 17  

18. 15 - 18Average Power AnalysisAssume each symbol is equally likelyAssume energy in pulse shape is 14-PAM constellationAmplitudes are in set { -3d, -d, d, 3d }Total power 9 d2 + d2 + d2 + 9 d2 = 20 d2Average power per symbol 5 d24-QAM constellation pointsPoints are in set { -d – jd, -d + jd, d + jd, d – jd }Total power 2d2 + 2d2 + 2d2 + 2d2 = 8d2Average power per symbol 2d24-level PAM Constellationd-d-3 d 3 d4-level QAM ConstellationIQdd-d-d