1. Lab 6: Week 1 Quadrature Amplitude Modulation (QAM) Transmitter
Yeong Choo and Sam Kanawati
Dept. of Electrical and Computer Engineering
The University of Texas at Austin

2. Introduction Digital Pulse Amplitude Modulation (PAM)
Modulates digital information onto amplitude of pulse
May be later upconverted (e.g. to radio frequency)
Digital Quadrature Amplitude Modulation (QAM)
Two-dimensional extension of digital PAM
Baseband signal requires sinusoidal amplitude modulation
Digital QAM modulates digital information onto pulses that are modulated onto
Amplitudes of a sine and a cosine, or equivalently
Amplitude and phase of single sinusoid

3. Amplitude Modulation by Cosine
Review
Amplitude Modulation by Cosine
y1(t) = x1(t) cos(wc t)
Assume x1(t) is an ideal lowpass signal with bandwidth w1
Assume w1 << wc
Y1(w) is real-valued if X1(w) is real-valued
Demodulation: modulation then lowpass filtering w 1 w1
-w1
X1(w) w
Y1(w)
-wc - w1
-wc + w1
-wc
wc - w1
wc + w1 wc
½X1(w - wc)
½X1(w + wc)
Baseband signal
Upconverted signal

4. Amplitude Modulation by Sine
Review
Amplitude Modulation by Sine
y2(t) = x2(t) sin(wc t)
Assume x2(t) is an ideal lowpass signal with bandwidth w2
Assume w2 << wc
Y2(w) is imaginary-valued if X2(w) is real-valued
Demodulation: modulation then lowpass filtering w 1 w2
-w2
X2(w) w
Y2(w)
j ½
-wc – w2
-wc + w2
-wc
wc – w2
wc + w2 wc
-j ½X2(w - wc)
j ½X2(w + wc)
-j ½
Baseband signal
Upconverted signal

5. Baseband Digital QAM Transmitter
Continuous-time filtering and upconversion
Impulse modulator
gT(t)
i[n]
Index
Pulse shapers (FIR filters)
s(t)
Bits
Delay
Serial/ parallel converter
Map to 2-D
constellation
Local
Oscillator + 1 J
90o
4-level QAM Constellation I Q d -d
q[n]
Impulse modulator
gT(t)
Delay matches delay through 90o phase shifter
Delay required but often omitted in diagrams

6. Baseband Digital QAM Transmitter
i[n]
gT(t) +
q[n]
Serial/ parallel converter 1
Bits
Map to 2-D
constellation J
Pulse shapers (FIR filters)
Index
Impulse modulator
s(t)
Local
Oscillator
90o
Delay
100% discrete time until D/A converter
i[n] L
gT[m]
s[m]
cos(0 m)
Bits
Index
s(t)
Serial/ parallel converter
Map to 2-D
constellation
Pulse shapers (FIR filters)
sin(0 m) +
D/A 1 J
L samples/symbol (upsampling factor)
q[n] L
gT[m]

7. Average Power Analysisd -d
-3 d
3 d
Assume each symbol is equally likely
Assume energy in pulse shape is 1
4-PAM constellation
Amplitudes are in set { -3d, -d, d, 3d }
Total power 9 d2 + d2 + d2 + 9 d2 = 20 d2
Average power per symbol 5 d2
Peak Power per symbol 9 d2
4-QAM constellation points
Points are in set { -d – jd, -d + jd, d + jd, d – jd }
Total power 2d2 + 2d2 + 2d2 + 2d2 = 8d2
Average power per symbol 2d2
Peak power per symbol 2 d2
4-level PAM Constellation
4-level QAM Constellation I Q d -d

8. The 16-Point Rectangular QAM Constellation
As we mentioned in the slide before, the levels for the PAM were {-3,-1,1,3}
Here we still have the same levels however we have two dimensions.
As you can see gray coding still applies as well. So the difference between two adjacent point is a bit only. (show an example).

9. Performance Analysis of QAM
If we sample matched filter outputs at correct time instances, nTsym, without any ISI, received signal
Transmitted signal
where i,k  { -1, 0, 1, 2 } for 16-QAM
Noise
For error probability analysis, assume noise terms independent and each term is Gaussian random variable ~ N(0; 2/Tsym)
4-level QAM Constellation I Q d -d

10. 4-PAM vs 4-QAM
Source: Appendix P in the Course Reader (EE445S)

11. 4-PAM vs 4-QAM
Perspective 1: Take a vertical slice (at fixed SNR = 14dB) Source: Appendix P in the Course Reader (EE445S)

12. 4-PAM vs 4-QAM