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

DMG-12/00

April 23, 2002

Digital Communications Basics

Dan M. Goebel

4/23/2002

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Digital Communications System Block Diagram

From: B.Sklar Digital Communications, Prentice Hall, NJ 2001

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Digital “Bandpass” Modulation


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

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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

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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)

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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”

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The Useful Digital Data Rate Determined by Error Probability

Bit Error Rate (BER)


• For high data ratesand low bit error rates:

High bandwidth

High SNR (Eb/No)

High-order modulation schemes

BPSK/QPSK 8PSK16QAM

32QAM64QAM

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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

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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

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Constellation Impairments

In phase(real)

Quadrature(imaginary)

IMDPhaseDistortion

AmplitudeDistortion

GaussianNoise

Input

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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

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Reducing Impairments for Bit Error Rate

Saturated QPSK amplifier produces large impairments

Amplifier linearity reduces impairments, so backoff improves the bit-error rate

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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)

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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

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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

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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

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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).

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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

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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

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Improve Amplifier PerformancePredistorter-linearizer

• Utilize predistorter to improve transfer curve characteristics and overall linearity

• Many types available– Passive

– Active

– Harmonic

– Digital

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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

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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)

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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

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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

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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

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

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