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Digital Transmission Fundamentals

& Digital Modulation Comparisons

Prof. Dr. Said E. El-Khamy,

Life Fellow IEEE

Email: elkhamy@ieee.org

Digital Networks

• Digital transmission enables networks to support many services

E-mail

Telephone

TV

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Digitization of Analog Signal

• Sample analog signal in time and amplitude • Find closest approximation

D/2

3D/2

5D/2

7D/2

-D/2

-3D/2

-5D/2

-7D/2

Original signal

Sample value

Approximation

Rs = Bit rate = # bits/sample x # samples/second

3 b

its /

sam

ple

Bit Rate of Digitized Signal

• Bandwidth Ws Hertz: how fast the signal changes – Higher bandwidth → more frequent samples

– Nyquist sampling rate = Minimum sampling rate fNQST=fsmin= 2 x Ws

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Example: Voice & Audio

Telephone voice

Ws = 4 kHz →

8000 samples/sec

8 bits/sample

Rs=8 x 8000 = 64 kbps

Cellular phones use more powerful compression algorithms: 8-12 kbps

CD Audio

Ws = 22 kHz →

44000 samples/sec

16 bits/sample

Rs=16 x 44000= 704 kbps per audio channel

MP3 uses more powerful compression algorithms: 50 kbps per audio channel

Digital Video Signals

Type Method Format Original Compressed

Video

Confer-

ence

H.261 176x144 or

352x288 pix

@10-30 fr/sec

2-36

Mbps

64-1544 kbps

Full

Motion

MPEG2 720x480 pix

@30 fr/sec

249

Mbps

2-6 Mbps

HDTV MPEG2 1920x1080 pix

@30 fr/sec

1.6

Gbps

19-38 Mbps

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Bit Rates of Digital Transmission Systems

System Bit Rate Observations

Telephone

twisted pair

33.6-56 kbps 4 kHz telephone channel

Ethernet

twisted pair

10 Mbps, 100 Mbps,

1 Gbps

100 meters of unshielded

twisted copper wire pair

Cable modem 500 kbps-4 Mbps Shared CATV return channel

ADSL 64-640 kbps in, 1.536-

6.144 Mbps out

Coexists with analog

telephone signal

2.4 GHz radio 2-11 Mbps IEEE 802.11 wireless LAN

28 GHz radio 1.5-45 Mbps 5 km multipoint radio

Optical fiber 2.5-10 Gbps 1 wavelength

Optical fiber >1600 Gbps Many wavelengths

Pulse Transmission Rate Nyquist Rate

• Objective: Maximize pulse rate through a channel, that is, make T as small as possible

Channel

t t

If input is a narrow pulse, then typical output is a spread-out pulse with ringing

Question: How frequently can these pulses be transmitted without interfering with each other?

Answer: 2 x B pulses/second

where B is the bandwidth of the channel

T

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Multilevel Pulse Transmission Assume channel of bandwidth B, and transmit 2B pulses/sec

(without interference)

If pulses amplitudes are either -A or +A (i.e. binary transmission with m=2), then each pulse conveys 1 bit, so

Rb= Bit Rate = 1 bit/pulse x 2B pulses/sec = 2B bps

If amplitudes are from {-A, -A/3, +A/3, +A}, then bit rate is 2 x 2B bps

By going to M = 2m amplitude levels (M’ary transmission), we achieve

Bit Rate = m bits/pulse x 2B pulses/sec = 2mB bps. i.e.

Rb = 2 log2(M) B bps

In the absence of noise, the bit rate can be increased without limit by increasing m

Noise & Reliable Communications

• All physical systems have noise – Electrons always vibrate at non-zero temperature

– Motion of electrons induces noise

• Presence of noise limits accuracy of measurement of received signal amplitude

• Errors occur if signal separation is comparable to noise level

• Bit Error Rate (BER) increases with decreasing signal-to-noise ratio

• Noise places a limit on how many amplitude levels can be used in pulse transmission

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Examples of Channels

Channel Bandwidth Bit Rates

Telephone voice

channel

3 kHz 33 kbps

Copper pair 1 MHz 1-6 Mbps

Coaxial cable 500 MHz

(6 MHz channels)

30 Mbps/

channel

5 GHz radio

(IEEE 802.11)

300 MHz

(11 channels)

54 Mbps /

channel

Optical fiber Many TeraHertz 40 Gbps /

wavelength

Shannon Capacity Theorem

• Consider a band-limited communication system of bandwidth B and in the presence of white noise of PSD No.

• The noise power is equal to N = NoB.

Capacity of Additive White Gaussian Noise Channels (AWGN) of Limited Bandwidth

Chanel Capacity: The maximum data rate that can be reliably transmitted over a communication channel is known as the channel capacity.

Rmax=C bits/sec

C/B is known as the Spectral (or Bandwidth) Efficiency with units bits/sec/Hz

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Example

• Find the Shannon channel capacity for a telephone channel with Wc = 3400 Hz and SNR = 10000 (40 dB)

C = 3400 log2 (1 + 10000) = 3400 log10 (10001)/log102 = 45200 bps Note that SNR = 10000 corresponds to SNR (dB) = 10 log10(10000) = 40 dB

Capacity of Digital systems

If R = C then:

The Shannon limit can be now analyzed from the bandwidth efficiency equation

There is an equivalent expression for the signal-to-noise ratio described in terms of the average bit energy Eb and the transmission rate R.

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This value is usually called the Shannon limit. This is a performance bound on the value of the ratio Eb/N0, using a rather sophisticated coding technique, and for which the channel bandwidth and the code length n are very large. This means that if the ratio Eb/N0 is kept slightly higher than this value, it is possible to have error free transmission by means of the use of such a sophisticated coding technique. Note that

Shannon Bound

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A Review of Digital Modulation Fundamentals

Coherent and Non-Coherent Techniques

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In wireless communications, it is important to select

MODEM based on the following requirements

High Spectral Efficiency

High Power Efficiency

High Fading Immunity

These factors are affected by baseband pulse shape and

phase transition characteristics of the signal. Practical Modulation Schemes

• FM : AMPS

• MSK : CT2

• GMSK : GSM, DCS 1800, CT3, DECT

• QPSK : NADC (CDMA) - base transmitter

• OQPSK : NADC (CDMA) - mobile transmitter

• 4-DQPSK : NADC (TDMA), PDC (Japan), PHP (Japan)

• MPSK : (some wireless LANs - EDGE)

MSK,GMSK GSM

PSK CABLE MODEMS

QPSK,PI/4 DPSKMOQPSK SATELLITE,CDMA,IS 95

FSK,GFSK TELEPHONE CALLER ID

8PSK EDGE,MONITORING

BROADBAND VIDEO

SYSTEMS

16 QAM MICROWAVE DIGITAL

RADIO,MODEMS

32 QAM TERRISTAL MICROWAVE

OFDM ADSL,SDSL,VDSL,WIMAX,WIF

I(A,G,N)

More Systems

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Probability of Error Curve for BASK/BFSK and BPSK

M-ary Signaling/Modulation

In binary data transmission, send only one of two possible signals during each bit interval Tb .

In M-ary data transmission, send one of M possible signals during each symbol interval Ts .

The transmitter considers k bits at a times.It produces one of M signals where M = 2k .Each of the M signals is called a symbol.

Thus, we have M-ary ASK, M-ary FSK, M-ary PSK digital modulation schemes.

M-ary schemes are more bandwidth efficient, but more susceptible to noise.

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• Quadrature Phase Shift Keying (QPSK) has twice the bandwidth efficiency of BPSK since 2 bits are transmitted in a single modulation symbol.

Carrier phases

{0, /2, , 3/2}

Carrier phases

{/4, 3/4, 5/4, 7/4}

I

Q

I

Q

Quadrature Phase Shift Keying (QPSK)

4-PSK signal constellation diagrams

M-ary Quadrature Amplitude Modulation (M-QAM)

An M-ary quadrature shift keying (M-QAM) signal can be defined by

for i = 0, 1, ..., M - 1.

4-QAM signal constellation diagram 16-QAM signal constellation diagram

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Digital Modulation Comparisons

COMPARISON OF MODULATION TYPES: 1- Bandwidth Efficiency

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Bandwidth Efficiency Comparisons

Modulation

Format

Bandwidth

efficiency C/B

Log2(C/B)

16 PSK 4 2

16 QAM 4 2

8 PSK 3 1.6

4 PSK 2 1

4 QAM 2 1

BFSK 1 0

BPSK 1 0

2. Error Performance and Power Efficiency Comparison

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Symbol Error Probability of M-PSK

Symbol Error Probability of M-QAM

Symbol Error Probability of M-FSK

M’ary Modulation Error Probabilities

MATLAB SIMULATIONS

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MPSK

ber = berawgn(EbNo,'psk',M)

MQAM

ber = berawgn(EbNo,'qam',M)

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Non coherent MFSK

ber = berawgn(EbNo,'fsk',M)

3. Digital Modulation Comparison based on Shannon Capacity

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• GSM- Digital Cellular – Data Rate = 270kb/s, bandwidth = 200kHz

– Bandwidth Efficiency = 270/200 =1.35bits/sec/Hz

– Modulation: Gaussian Minimum Shift Keying (FSK with

orthogonal frequencies). – “Gaussian” refers to filter response.

• IS-54 North American Digital Cellular – Data Rate = 48kb/s, bandwidth = 30kHz

– Bandwidth Efficiency = 48/30 =1.6bits/sec/Hz

– Modulation: p/4 DPSK

Spectral Efficiencies in practical Systems

References 1. B. Sklar, Digital Communications – Fundamentals and Application,

Prentice-Hall, Englewood Cliffs, NJ, 1988.

3. A. Bateman, Digital Communications – Design for the Real World,

Addison-Wesley, 1988

4. J. G. Proakis, Digital Communications, 3rd Edition, McGraw-Hill, 1994.

5. J. G. Proakis and Masoud Salehi, Communication Systems Engineering, Prentice-Hall, 1994

6. Shannon, C. E., “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, July and October 1948. 7. Carlson, B., Communication Systems: An Introduction to Signals and Noise in Electrical Communication, 3rd Edition, McGraw-Hill, New York, 1986.