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DMG-12/00
Page 2April 23, 2002
Digital Communications System Block Diagram
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
DMG-12/00
Page 3April 23, 2002
Digital “Bandpass” Modulation
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
Figure of Merit = Eb/No = Energy per bit divided by noise power density(digital systems equivalent for Signal to Noise Ratio (SNR))
PSK
FSK
ASK
APK/QAM
DMG-12/00
Page 4April 23, 2002
Digital Data Rate
• 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
DMG-12/00
Page 5April 23, 2002
Maximum Digital Data Rate
• Maximum channel capacity is given by Shannon’s Law:
C (bps) = B log2 (1 + SNR) = B log2 (1 + ) 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
Eb
No
BR
M n Type () Type (QAM)2 1 BPSK -----4 2 QPSK 4QAM8 3 8PSK 8QAM16 4 16PSK 16QAM32 5 ---- 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)
DMG-12/00
Page 6April 23, 2002
Digital Signal Detection“constellation plots”
BPSKM=2 states
n= 1 bit/sec/Hz
In phase(real)
Quadrature(imaginary) Q
I
Q
I
QPSKM=4 states
n= 2 bit/sec/Hz
16QAMM=16 states
n= 4 bit/sec/Hz
φamplitude
Must be able to distinguish each point, which leads to “bit errors”
DMG-12/00
Page 7April 23, 2002
The Useful Digital Data Rate Determined by Error Probability
Bit Error Rate (BER)
From: B.Sklar Digital Communications, Prentice Hall, NJ 2001
• For high data ratesand low bit error rates:
High bandwidth
High SNR (Eb/No)
High-order modulation schemes
BPSK/QPSK 8PSK16QAM
32QAM64QAM
DMG-12/00
Page 8April 23, 2002
Constellation Plot Example
Eb/N0 = 11 dB Eb/N0 = 2 dBEb/N0 = 6 dB
Bit errors in red
Low signal to noise ratio leads to discrimination errors
DMG-12/00
Page 9April 23, 2002
Cause of Performance Degradation in Digital Communications Systems
• 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)– intermodulation distortion
– interfering signals (co-channel and adjacent channel interference)
– amplifier noise sources (shot, flicker, thermal)
– atmospheric and galactic sources
DMG-12/00
Page 10April 23, 2002
Constellation Impairments
In phase(real)
Quadrature(imaginary)
IMDPhaseDistortion
AmplitudeDistortion
GaussianNoise
Input
DMG-12/00
Page 11April 23, 2002
Error Probability versus Phase Jitter
QAM constellationwith AWGN
and phase jitterAverage power
constrainedPeak power constrained
Note: amplifier AM/PM produces phase noise from amplitude changes in channel
DMG-12/00
Page 12April 23, 2002
Reducing Impairments for Bit Error Rate
Saturated QPSK amplifier produces large impairments
Amplifier linearity reduces impairments, so backoff improves the bit-error rate
DMG-12/00
Page 13April 23, 2002
Trends in Digital Communications
• 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)
DMG-12/00
Page 14April 23, 2002
High Peak-to-Average Operation
0.001
0.01
0.1
1
10
100
-15 -10 -5 0 5 10 15
DataGaussian Fit
Time (%)
Output Power (dB above RMS rated)
Gaussian Fity=40exp(-(x+1)^2/14)
CCDF for OFDM
amplifiersaturation
>1% of the time the amplifier is saturated
CDMA is similar, requiring >9 dB OBO to avoid clipping
DMG-12/00
Page 15April 23, 2002
Telecommunications Example
• Intermodulation Distortion is critical– adjacent channel power level is strongly regulated
Carriers
3rd-orderdistortion
C/3IM (dBc)
(2f -f ) f f1 2 1 2 (2f -f )12
2 MHz/div
3rd-orderIMD
5th-orderIMD
Carriers
1.9 GHz
Video Ave.50 sweeps
adjacent channel power
DMG-12/00
Page 16April 23, 2002
Reducing Intermodulation Distortion
Backoff reduces the adjacent channel power level
20
25
30
35
40
45
50
456789101112
2-Tone C/3IM (dBc)
Backoff from Saturation (dB)
Run “backed off” from saturation
DMG-12/00
Page 17April 23, 2002
Amplifier Design For Digital Comm.
• Low intermodulation distortion (IMD) requires large backoff
• 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)
C/3IM = 2 10 logPsat
Po
⎛
⎝ ⎜ ⎞
⎠ ⎟ + 3OI
⎡
⎣ ⎢ ⎤
⎦ ⎥
OutputBackoff
Third-orderIntercept Point
*
*D.M. Goebel, R.Liou, W. Menninger, “Development of linear TWT amplifiers for Telecommunications Applications”, IEEE Transactions on Electron Devices, 48, 74-81 (2001).
DMG-12/00
Page 18April 23, 2002
3rd Order Interception Point
Conventional figure of merit for linearity
Higher 3OI gives lower IMD at a given operating point
0
10
20
30
40
50
60
70
10 15 20 25 30 35 40
1-Tone AM/AM data1-Tone Linear Fit2-Tone AM/AM data2-Tone Linear Fit
Output Power (dBm)
Input Power (dBm)
3rd Order Intercept = 67 dB
Sat. Power = 58.9dB
DMG-12/00
Page 19April 23, 2002
TWT Amplifier Designed for Linearity
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
DMG-12/00
Page 20April 23, 2002
Improve Amplifier PerformancePredistorter-linearizer
• Utilize predistorter to improve transfer curve characteristics and overall linearity
• Many types available– Passive
– Active
– Harmonic
– Digital
DMG-12/00
Page 21April 23, 2002
Passive Predistorter-linearizer
Amplitude(2 dB/division)
≈9 dB expansion
Phase(2 deg/division)
≈7 degrees correction
Optimized to match TWT design #3 withlow phase change
DMG-12/00
Page 22April 23, 2002
Predistorted Amplifier Performance
Strongest improvement near saturation(5 to 7 dB)
Transfer Curves C/3IM versus output power
Input Power (dBm) Outut Power (dBm)
Gai
n o
r P
ower
C/3
IM (
dBc)
Pha
se (degrees)
DMG-12/00
Page 23April 23, 2002
Predistorted Amplifier Optimization
• 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
DMG-12/00
Page 24April 23, 2002
Telecommunications Feed-forward
Linearizer
TWT only ------ 28 dB 30 dB 65 dBc
TWT#4 5 dB 35 dB 30 dB 70 dBc
TWT#5 >15 dB 30 dB 30 dB >75 dBc
Multi-Channel Power Amplifier(with feed-forward circuit)
InputSignal
Output
PowerAmplifier
CorrectionAmp
Delayline
Delayline
Pre-distorter Feed-Forward
Total
*FCC requires ≥70 dBc
DMG-12/00
Page 25April 23, 2002
Conclusions
• 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