1. DMG-12/00 Page 1 April 23, 2002 Digital Communications Basics Dan M. Goebel 4/23/2002

2. DMG-12/00 Page 2 April 23, 2002 Digital Communications System Block Diagram From: B.Sklar Digital Communications, Prentice Hall, NJ 2001

3. DMG-12/00 Page 3 April 23, 2002 Digital “Bandpass” Modulation From: B.Sklar Digital Communications, Prentice Hall, NJ 2001 Figure of Merit = E b /N o = Energy per bit divided by noise power density (digital systems equivalent for Signal to Noise Ratio (SNR)) PSK FSK ASK APK/QAM

4. DMG-12/00 Page 4 April 23, 2002 Digital Data Rate The data rate (bits per second) is given by the energy per bit (E b = 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 = E b * 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 E b, increasing the rate increases the required signal power Higher digital data rates require higher signal power

5. DMG-12/00 Page 5 April 23, 2002 Maximum Digital Data Rate Maximum channel capacity is given by Shannon’s Law: C (bps) = B log 2 (1 + SNR) = B log 2 (1 + ) where B = bandwidth, R = symbol rate Maximum bit rate = n (bits/sec/Hz) = log 2 M (M is the number of constellation points) Maximum data rate is the bit rate times the bandwidth = n*B EbEb NoNo B R MnType (  )Type (QAM) 21BPSK----- 42QPSK4QAM 838PSK8QAM 16416PSK16QAM 325----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)

6. DMG-12/00 Page 6 April 23, 2002 Digital Signal Detection “constellation plots” Must be able to distinguish each point, which leads to “bit errors”

7. DMG-12/00 Page 7 April 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 rates and low bit error rates: High bandwidth High SNR (E b /N o ) High-order modulation schemes BPSK/QPSK8PSK 16QAM 32QAM 64QAM

8. DMG-12/00 Page 8 April 23, 2002 Constellation Plot Example E b /N 0 = 11 dBE b /N 0 = 2 dBE b /N 0 = 6 dB Bit errors in red Low signal to noise ratio leads to discrimination errors

9. DMG-12/00 Page 9 April 23, 2002 Cause of Performance Degradation in Digital Communications Systems Signal loss (E b term) –due to absorption, scattering, reflection, refraction, pointing, etc. Inter-Symbol Interference (N 0 term) –due primarily to frequency dependent effects (in channel or amps) Noise and interference (N 0 term) –intermodulation distortion –interfering signals (co-channel and adjacent channel interference) –amplifier noise sources (shot, flicker, thermal) –atmospheric and galactic sources

10. DMG-12/00 Page 10 April 23, 2002 Constellation Impairments

11. DMG-12/00 Page 11 April 23, 2002 Error Probability versus Phase Jitter QAM constellation with AWGN and phase jitter Average power constrained Peak power constrained Note: amplifier AM/PM produces phase noise from amplitude changes in channel

12. DMG-12/00 Page 12 April 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

13. DMG-12/00 Page 13 April 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)

14. DMG-12/00 Page 14 April 23, 2002 High Peak-to-Average Operation CCDF for OFDM amplifier saturation >1% of the time the amplifier is saturated CDMA is similar, requiring >9 dB OBO to avoid clipping

15. DMG-12/00 Page 15 April 23, 2002 Telecommunications Example Intermodulation Distortion is critical –adjacent channel power level is strongly regulated adjacent channel power

16. DMG-12/00 Page 16 April 23, 2002 Reducing Intermodulation Distortion Backoff reduces the adjacent channel power level Run “backed off” from saturation

17. DMG-12/00 Page 17 April 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) Output Backoff Third-order Intercept 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).

18. DMG-12/00 Page 18 April 23, 2002 3rd Order Interception Point Conventional figure of merit for linearity Higher 3OI gives lower IMD at a given operating point

19. DMG-12/00 Page 19 April 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

20. DMG-12/00 Page 20 April 23, 2002 Improve Amplifier Performance Predistorter-linearizer Utilize predistorter to improve transfer curve characteristics and overall linearity Many types available –Passive –Active –Harmonic –Digital

21. DMG-12/00 Page 21 April 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 with low phase change

22. DMG-12/00 Page 22 April 23, 2002 Predistorted Amplifier Performance Strongest improvement near saturation (5 to 7 dB) Transfer CurvesC/3IM versus output power Input Power (dBm)Outut Power (dBm) Gain or Power C/3IM (dBc) Phase (degrees)

23. DMG-12/00 Page 23 April 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

24. DMG-12/00 Page 24 April 23, 2002 Telecommunications Feed-forward Linearizer TWT only ------28 dB30 dB 65 dBc TWT#4 5 dB35 dB30 dB 70 dBc TWT#5>15 dB30 dB30 dB>75 dBc Multi-Channel Power Amplifier (with feed-forward circuit) Total *FCC requires ≥70 dBc

25. DMG-12/00 Page 25 April 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