DMG-12/00
Digital Communications Basics
Dan M. Goebel
4/23/2002
April 23, 2002
Page 1
Digital Communications System
Block Diagram
DMG-12/00
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
April 23, 2002
Page 2
Digital “Bandpass” Modulation
DMG-12/00
PSK
FSK
ASK
APK/QAM
Figure of Merit = Eb/No = Energy per bit divided by noise power density
(digital systems equivalent for Signal to Noise Ratio (SNR))
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
April 23, 2002
Page 3
Digital Data Rate
DMG-12/00
• The data rate (bits per second) is given by the energy per bit
(Eb = the energy in the digital pulse)
times the rate at which bits are sent
(“bit rate” for binary pulses, or “symbol rate” if each bit represents a word)
Average Signal Power Level = Eb * R
• The data rate is increased by increasing the rate at which bits or
symbols are sent, which effectively increases the duty of the signal
• At a given Eb, increasing the rate increases the required signal power
Higher digital data rates require higher signal power
April 23, 2002
Page 4
Maximum Digital Data Rate
DMG-12/00
• Maximum channel capacity is given by Shannon’s Law:
E
C (bps) = B log2 (1 + SNR) = B log2 (1 + b B )
No R
where B = bandwidth, R = symbol rate
• Maximum bit rate = n (bits/sec/Hz) = log2 M
(M is the number of constellation points)
• Maximum data rate is the bit rate times the bandwidth = n*B
M
2
4
8
16
32
n
1
2
3
4
5
Type (f)
BPSK
QPSK
8PSK
16PSK
----
Type (QAM)
----4QAM
8QAM
16QAM
32QAM
Example: B=2 MHz, SNR=20 dB
C = 13.3 Mbs (Shannon)
Data rate = 4 Mbs if use QPSK
= 10 Mbs if use 32QAM
(must increase B to get higher rates)
April 23, 2002
Page 5
Digital Signal Detection
“constellation plots”
DMG-12/00
Quadrature
(imaginary)
Q
In phase
(real)
am
Q
de
u
t
i
pl
f
I
I
BPSK
QPSK
16QAM
M=2 states
n= 1 bit/sec/Hz
M=4 states
n= 2 bit/sec/Hz
M=16 states
n= 4 bit/sec/Hz
Must be able to distinguish each point, which leads to “bit errors”
April 23, 2002
Page 6
The Useful Digital Data Rate
Determined by Error Probability
Bit Error Rate (BER)
DMG-12/00
• For high data rates
and low bit error rates:
High bandwidth
High SNR (Eb/No)
64QAM
32QAM
High-order modulation schemes
16QAM
BPSK/QPSK
8PSK
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
April 23, 2002
Page 7
Constellation Plot Example
DMG-12/00
Bit errors in red
Eb/N0 = 11 dB
Eb/N0 = 6 dB
Eb/N0 = 2 dB
Low signal to noise ratio leads to discrimination errors
April 23, 2002
Page 8
Cause of Performance Degradation
in Digital Communications Systems
DMG-12/00
• Signal loss (Eb term)
– due to absorption, scattering, reflection, refraction, pointing, etc.
• Inter-Symbol Interference (N0 term)
– due primarily to frequency dependent effects (in channel or amps)
• Noise and interference (N0 term)
–
–
–
–
April 23, 2002
intermodulation distortion
interfering signals (co-channel and adjacent channel interference)
amplifier noise sources (shot, flicker, thermal)
atmospheric and galactic sources
Page 9
Constellation Impairments
DMG-12/00
Quadrature
(imaginary)
Gaussian
Noise
In phase
(real)
Amplitude
Distortion
Input
Phase
Distortion
April 23, 2002
IMD
Page 10
Error Probability versus Phase Jitter
DMG-12/00
10-4
Probability of Error
10-5
10-6
10-7
10-8
10-9
0 0.5 1 1.5 2 2.5 3 3.5
0 0.5 1 1.5 2 2.5 3 3.5
QAM constellation
RMS Phase Jitter (deg)
RMS Phase Jitter (deg)
with AWGN
and phase jitter
Average power
constrained
Peak power
constrained
Note: amplifier AM/PM produces phase noise from amplitude changes in channel
April 23, 2002
Page 11
Reducing Impairments for Bit Error Rate
DMG-12/00
10-2
BER with a
saturated amplifier
Bit Error Rate
10-4
Saturated QPSK
amplifier produces
large impairments
Backoff 3 dB
BER with a
backed off
amplifier
10-6
Amplifier linearity
reduces impairments,
so backoff improves
the bit-error rate
BER = 10 -7
10-8
10-10
BER = 2x10 -8
6
8
10
12
14
16
18
20
Energy per bit/Noise density in dB (Eb/No)
April 23, 2002
Page 12
Trends in Digital Communications
DMG-12/00
• QPSK Systems were “standard”
– constant amplitude: amps. run near saturation for high efficiency
– common in satellite communications (DirecTV and Satellite Radio)
• Want higher data rates (High Definition TV, Internet, etc.)
– utilize 8PSK (compatible with QPSK hardware, 2x data rate)
– utilize QAM or other higher order modulation schemes
– amplifiers run with varying amplitude and phase
• May need spread spectrum (CDMA, OFDM)
– mobile system fade/reflection tolerant
– effectively thousands of channels (frequencies) in band
– high peak to average ratio is very hard on amplifiers (clipping)
April 23, 2002
Page 13
High Peak-to-Average Operation
DMG-12/00
100
Gaussian Fit
y=40exp(-(x+1)^2/14)
CCDF for OFDM
Data
Gaussian Fit
Time (%)
10
1
>1% of the time the
amplifier is saturated
0.1
CDMA is similar,
requiring >9 dB OBO
to avoid clipping
0.01
amplifier
saturation
0.001
-15
-10
-5
0
5
10
15
Output Power (dB above RMS rated)
April 23, 2002
Page 14
Telecommunications Example
DMG-12/00
• Intermodulation Distortion is critical
– adjacent channel power level is strongly regulated
Carriers
3rd-order
distortion
(2f1 -f2)
C/3IM (dBc)
f1
f2
(2f2 -f1)
adjacent
channel
power
April 23, 2002
Page 15
Reducing Intermodulation Distortion
DMG-12/00
Run “backed off”
from saturation
50
Saturation
60
6 dB backoff (DARS)
55
Linear
regime
9 dB backoff (PCS)
50
45
2-Tone C/3IM (dBc)
Output Power (dBm)
65
40
35
30
25
0
0
5
10
15
20
25
30
Input Drive Power (dBm)
35
20
12
11
10
9
8
7
6
Backoff from Saturation (dB)
5
4
Backoff reduces the adjacent
channel power level
April 23, 2002
Page 16
Amplifier Design For Digital Comm.
DMG-12/00
• Low intermodulation distortion (IMD) requires large backoff
Psat 

*
C/3IM = 2 10 log   + 3OI


 Po 


Output
Backoff
Third-order
Intercept Point
• Need good third order interception point for low IMD
• Options:
– Design for efficiency and accept large back off
– Design for minimum AM/PM
– Design for C/3IM (gain, power and phase together)
*D.M. Goebel, R.Liou, W. Menninger, “Development of linear TWT amplifiers for Telecommunications Applications”,
IEEE Transactions on Electron Devices, 48, 74-81 (2001).
April 23, 2002
Page 17
3rd Order Interception Point
DMG-12/00
70
3rd Order Intercept = 67 dB
Conventional
figure of merit for
linearity
60
Output Power (dBm)
50
Higher 3OI gives
lower IMD at a
given operating
point
Sat. Power = 58.9dB
40
30
20
1-Tone AM/AM data
1-Tone Linear Fit
2-Tone AM/AM data
2-Tone Linear Fit
10
0
10
April 23, 2002
15
20
25
30
Input Power (dBm)
35
40
Page 18
TWT Amplifier Designed for
Linearity
DMG-12/00
Conventional
design produced
≈40˚ phase shift at
saturation
TWT designed to
minimize AM/PM
to reduce phase
shift to <10˚ at sat.
Resulted in slight
gain expansion
and non-uniform
AM/AM curve
April 23, 2002
Page 19
Improve Amplifier Performance
Predistorter-linearizer
DMG-12/00
• Utilize predistorter to improve transfer curve characteristics and
overall linearity
• Many types available
–
–
–
–
April 23, 2002
Passive
Active
Harmonic
Digital
Page 20
Passive Predistorter-linearizer
DMG-12/00
Amplitude
(2 dB/division)
Optimized to match
TWT design #3 with
low phase change
≈9 dB expansion
Phase
(2 deg/division)
≈7 degrees correction
April 23, 2002
Page 21
Predistorted Amplifier Performance
DMG-12/00
C/3IM (dBc)
Gain or Power
Phase (degrees)
Input Power (dBm)
Transfer Curves
April 23, 2002
Strongest
improvement
near saturation
(5 to 7 dB)
Outut Power (dBm)
C/3IM versus output power
Page 22
Predistorted Amplifier Optimization
DMG-12/00
• Need to match TWT characteristics to predistorter
characteristics
• For a passive predistorter with parabolic diode-type transfer
curves, the “optimized” TWT (design #4) produced only 5-to-7
dB improvement in the 2-tone C/3IM
– Could not match “diode-like” predistorter characteristics to the
TWT’s shallow AM/PM transfer curve and inflecting AM/AM curve
• The more conventional TWT design of design #5 produced over
15 dB improvement in 2-tone C/3IM with the predistorter
– Conventional “parabolic” transfer curves matched well
April 23, 2002
Page 23
Telecommunications Feed-forward
Linearizer
DMG-12/00
Multi-Channel Power Amplifier
(with feed-forward circuit)
Pre-distorter
Power
Amplifier
Input
Signal
Output
Delay
line
Delay
line
TWT only
TWT#4
TWT#5
Feed-Forward
-----5 dB
>15 dB
28 dB
35 dB
30 dB
Correction
Amp
Total
30 dB
30 dB
30 dB
65 dBc
70 dBc
>75 dBc
*FCC requires ≥70 dBc
April 23, 2002
Page 24
Conclusions
DMG-12/00
• Digital Communication is headed for higher data rates
– Higher bandwidth and higher order modulation schemes
– Requires higher power levels and/or lower noise amplifiers
• Digital Communications systems are sensitive to impairments
– Energy per bit (power level) important for low error rates (BER)
– Linearity important for detection accuracy = BER
– Intermodulation distortion for inter-symbol interference and adjacent
channel power
• Communications amplifiers must be designed for these points
– Trade off between backoff level and linearity to reduce impairments
– Predistorter/linearizer helps, but it must be optimized with the amp
April 23, 2002
Page 25