Transcript Quadrature Amplitude Modulation (QAM) Receiver Prof. Brian L. Evans

EE445S Real-Time Digital Signal Processing Lab
Fall 2016
Quadrature Amplitude Modulation
(QAM) Receiver
Prof. Brian L. Evans
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
Lecture 16
http://www.ece.utexas.edu/~bevans/courses/realtime
Outline
• Introduction
• Automatic gain control
• Carrier detection
• Channel equalization
• Symbol clock recovery
• QAM demodulation
• QAM transmitter demonstration
16 - 2
Introduction
• Channel impairments
Linear and nonlinear distortion of transmitted signal
Additive noise (often assumed to be Gaussian)
• Mismatch in transmitter/receiver analog front ends
• Receiver subsystems to compensate for impairments
Fading
Additive noise
Linear distortion
Carrier mismatch
Symbol timing mismatch
Automatic gain control (AGC)
Matched filters
Channel equalizer
Carrier recovery
Symbol clock recovery
16 - 3
Baseband QAM
Transmitter
i[m]
i[n]
Index
Bits
1
Serial/
parallel
converter
s[m]
r1(t)
J
Carrier recovery
is not shown
cos(c m)
sin(c m)
+
s(t)
D/A
q[m]
q[n]
c(t)
Carrier
Detect
AGC
r(t)
r[m]
fs
gT[m]
L
A/D
Downconverted
signal r1(t)
Pulse shapers
(FIR filters)
Map to 2-D
constellation
L samples/symbol
m sample index
n symbol index
Receiver
gT[m]
L
Channel
Equalizer
Symbol
Clock
Recovery
QAM Demodulation iˆ[ m]
X
LPF
iˆ[n]
L
2 cos(c m)
qˆ[ m ]
X
-2 sin(c m)
LPF
qˆ[ n ]
L
16 - 4
Automatic Gain Control
c(t)
• Scales input voltage to A/D converter
Increase/decrease gain for low/high r1(t)
r1(t)
AGC
r(t)
r[m]
A/D
• Consider A/D converter with 8-bit signed output
When gain c(t) is zero, A/D output is 0
When gain c(t) is infinity, A/D output is -128 or 127
f-128, f0, f127 represent how frequent outputs -128, 0, 127 occur
fi = ci / N where ci is count of times i occurs in last N samples
Update #1: c(t) = (1 + 2 f0 – f-128 – f127) c(t – t)
2 f0 + e
2c0 + e N
c(t - t ) =
c(t - t )
Update #2: c(t) =
f-128 + f127 + e
c-128 + c127 + e N
Constant e > 0 prevents division by zero
16 - 5
Carrier Detection
• Detect energy of received signal (always running)
p[m]  c p[m  1]  (1  c) r 2 [m]
c is a constant where 0 < c < 1 and r[m] is received signal
Let x[m] = r2[m]. What is the transfer function?
What values of c to use?
• If receiver is not currently receiving a signal
If energy detector output is larger than a large threshold,
assume receiving transmission
• If receiver is currently receiving signal, then it
detects when transmission has stopped
If energy detector output is smaller than a smaller threshold,
assume transmission has stopped
16 - 6
Channel Equalizer
• Mitigates linear distortion in channel
• When placed after A/D converter
Time domain: shortens channel impulse response
Frequency domain: compensates channel distortion over entire
discrete-time frequency band instead of transmission band
• Ideal channel
z-D
g
Cascade of delay D and gain g
Impulse response: impulse delayed by D with amplitude g
Frequency response: allpass and linear phase (no distortion)
Undo effects by discarding D samples and scaling by 1/g
16 - 7
Channel Equalizer
• IIR equalizer
Ignore noise nm
Set error em to zero
H(z) W(z) = g z-D
W(z) = g z-D / H(z)
Issues?
• FIR equalizer
Discrete-Time Baseband System
nm
Channel
Equalizer
ym
xm
rm e m
w
+
+
h
+
Training
-
sequence
Receiver
generates
xm
Ideal Channel
z-D
g
Adapt equalizer coefficients when transmitter sends training
sequence to reduce measure of error, e.g. square of em
16 - 8
Adaptive FIR Channel Equalizer
• Simplest case: w[m] = d[m] + w1 d[m-1]
Two real-valued coefficients w/ first coefficient fixed at one
• Derive update equation for w1 during training
nm
Channel
ym Equalizerrm em e[m]  r[m]  s[m]
xm
w
s[m]  g x[m  D]
+
+
h
+Training
r[m]  y[m]  w1 y[m  1]
sequence
Ideal Channel
Receiver
J LMS [m]
s
w
[
m

1
]

w
[
m
]

m
m
generates
1
1
w1 w  w [ m ]
-D
g
z
x
m
1
1 2
e [ m]
2
w1[m  1]  w1[m]  m e[m] y[m  1]
Using least mean squares (LMS) J LMS [m] 
Step size 0 < m < 1
1
Symbol Clock Recovery
• Two single-pole bandpass filters in parallel
One tuned to upper Nyquist frequency u = c + 0.5 sym
Other tuned to lower Nyquist frequency l = c – 0.5 sym
Bandwidth is B/2 (100 Hz for 2400 baud modem)
Pole
locations?
• A recovery method
Multiply upper bandpass filter output with conjugate of lower
bandpass filter output and take the imaginary value
Sample at symbol rate to estimate timing error t See Reader
v[n]  sin(  sym t )   sym t when  sym t  1 handout M
Smooth timing error estimate to compute phase advancement
p[n]   p[n  1]   v[n]
Lowpass
16 - 10
IIR filter
Baseband QAM Demodulation
• Recovers baseband in-phase/quadrature signals
• Assumes perfect AGC, equalizer, symbol recovery
• QAM modulation followed by lowpass filtering
iˆ[ m]
Receiver fmax = 2 fc + B and fs > 2 fmax
• Lowpass filter has other roles
Matched filter
Anti-aliasing filter
• Matched filters
X
LPF
x[m]
2 cos(c m)
qˆ[ m ]
X
LPF
-2 sin(c m)
Maximize SNR at downsampler output
Hence minimize symbol error at downsampler output
16 - 11
Baseband QAM Demodulation
• QAM baseband signal x[m]  i[m] cos(c m)  q[m] sin( c m)
• QAM demodulation
Modulate and lowpass filter to obtain baseband signals
iˆ[m]  2 x[m] cos(c m)  2i[m] cos 2 (ct )  2q[m] sin( c m) cos(c m)
 i[m]  i[m] cos(2c m)  q[m] sin( 2c m)
baseband
high frequency component centered at 2 c
qˆ[m]  2 x[m] sin( c m)  2i[m] cos(c m) sin( c m)  2q[m] sin 2 (c m)
 q[m]  i[m] sin( 2c m)  q[m] cos( 2c m)
baseband
high frequency component centered at 2 c
1
cos 2   (1  cos 2 )
2
2 cos sin   sin 2
1
sin 2   (1  cos 2 )
2
16 - 12
Single Carrier Transceiver Design
• Design/implement transceiver
Design different algorithms for each subsystem
Translate algorithms into real-time software
Test implementations using signal generators & oscilloscopes
Laboratory
1 introduction
2 sinusoidal generation
3(a) finite impulse response filter
3(b) infinite impulse response filter
Transceiver Subsystems
block diagram of transmitter
sinusoidal mod/demodulation
pulse shaping, 90o phase shift
transmit and receive filters,
carrier detection, clock recovery
4 pseudo-noise generation
training sequences
5 pulse amplitude mod/demodulation training during modem startup
6 quadrature amplitude mod (QAM)
data transmission
7 digital audio effects
not applicable
QAM Transmitter Demo
Lab 4
http://www.ece.utexas.edu/~bevans/courses/realtime/demonstration
Rate
Control
Reference design in LabVIEW
Lab 6
QAM
Encoder
Lab 2
Bandpass
Signal
Lab 3
Tx Filters
0-14
LabVIEW demo by Zukang Shen (UT Austin)
QAM Transmitter Demo
LabVIEW
control
panel
QAM
baseband
signal
Eye
diagram
LabVIEW demo by Zukang Shen (UT Austin)
0-15
Got Anything Faster?
• Multicarrier modulation divides broadband
(wideband) channel into narrowband subchannels
magnitude
Uses Fourier series computed by fast Fourier transform (FFT)
Standardized for ADSL (1995) & VDSL (2003) wired modems
Standardized for IEEE 802.11a/g wireless LAN
Standardized for IEEE 802.16d/e (Wimax) and cellular (3G/4G)
channel
carrier
subchannel
frequency
Each ADSL/VDSL subchannel is 4.3 kHz wide (about
width of voiceband channel) and carries a QAM signal
16 - 16