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Analog/Digital Modulation Analog Modulation

The input is continuous signal Used in first generation mobile radio systems

such as AMPS in USA.

Digital Modulation

The input is time sequence of symbols or pulses. Are used in current and future mobile radio

systems

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Performance Metrics In analog communications we want,

Digital communication systems: Data rate (R bps) Limited by Channel Capacity Probability of error

Without noise, there are no bit errors Bit Error Rate (BER): Number of bit errors that occur for

a given number of bits transmitted.

What’s BER if Pe=10-6 and 107 bits are transmitted?

)()(ˆ tmtm

3

Frequency versus Amplitude Modulation

Frequency Modulation (FM) Most popular analog modulation technique Amplitude of the carrier signal is kept constant (constant

envelope signal), the frequency of carrier is changed according to the amplitude of the modulating message signal; hence info is carried in the phase or frequency of the carrier.

Has better noise immunity: atmospheric or impulse noise cause rapid fluctuations in the amplitude of the

received signal Performs better in multipath environment

Small-scale fading cause amplitude fluctuations as we have seen earlier. Can trade bandwidth occupancy for improved noise performance.

Increasing the bandwith occupied increases the SNR ratio. The relationship between received power and quality is non-

linear. Rapid increase in quality for an increase in received power. Resistant to co-channel interference (capture effect).

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Digital Modulation

• Cost effective because of advances in digital technology (VHDL, DSP, FPGA…)

• Advantages/disadvantages vs analog

- Better noise immunity

- Robustness to channel impairments

- Ability to multiplex information

- Error control: detect & correct corrupt bits

- Able to encrypt data

- Flexible software modulation & demodulation

- Requires complex signal conditioning

modulating signal (message) represented as pulses; n bits represented by m finite states ; n = log2m

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Factors that Influence Choice of Digital Modulation Techniques A desired modulation scheme

Should provide low bit-error rates at low SNR Power efficiency

Should occupy minimum RF channel bandwidth Bandwidth efficiency

Should perform well in multi-path and fading conditions Should be easy and cost-effective to implement

Depending on the demands of a particular system or application, tradeoffs are made when selecting a digital modulation scheme.

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Tradeoff between BW Efficiency and Power Efficiency

Adding error control codes Improves the power efficiency

Reduces the required received power for a particular bit error rate

Decreases the bandwidth efficiency Increases the bandwidth occupancy

M-ary keying modulation Increases the bandwidth efficiency Decreases the power efficiency

More power is required at the receiver

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Power Efficiency of Modulation

Power efficiency is the ability of the modulation technique to preserve fidelity of the message at low power levels.

Usually in order to obtain good fidelity, the signal power needs to be increased.

Tradeoff between fidelity and signal power Power efficiency describes how efficiently this tradeoff is made

PER

N

Ebp :Efficiency Power certain for input receiver the at required

0

Eb: signal energy per bit N0: noise power spectral densityPER: probability of error

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Bandwidth Efficiency of Modulation Ability of a modulation scheme to

accommodate data within a limited bandwidth. Bandwidth efficiency reflect how efficiently the

allocated bandwidth is utilized

bps/Hz :Efficiency BandwidthB

RB

R: the data rate (bps)B: bandwidth occupied by the modulated RF signal

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Noiseless Channels and Nyquist Theorem

For a noiseless channel, Nyquist theorem gives the relationship between the channel bandwidth and maximum data rate that can be transmitted over this channel.

mBC 2log2

Nyquist Theorem

C: channel capacity (bps)B: RF bandwidthm: number of finite states in a symbol of transmitted signal

Example: A noiseless channel with 3kHz bandwidth can only transmit a maximum of 6Kbps if the symbols are binary symbols.

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Nyquist minimum bandwidth requirement

The theoretical minimum bandwidth needed for baseband transmission of Rs symbols per second is

Rs/2 hertz ?

t

)/sinc()( Ttth 1

0 T T2TT2

T2

1

T2

1

T

)( fH

f0

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Shannon’s Bound for noisy channels

There is a fundamental upper bound on achievable bandwidth efficiency.

Shannon’s theorem gives the relationship between the channel bandwidth and the maximum data rate that can be transmitted over a noisy channel .

)1(log2max N

S

B

CB

Shannon’s Theorem

C: channel capacity (maximum data-rate) (bps)B or W : RF bandwidthS/N: signal-to-noise ratio (no unit)

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Shannon limit … Shannon theorem puts a limit on

transmission data rate, not on error probability:

Theoretically possible to transmit information at any rate Rb , where Rb C with an arbitrary small error probability by using a sufficiently complicated coding scheme.

For an information rate Rb > C , it is not possible to find a code that can achieve an arbitrary small error probability.

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Shannon limit …C

/W [

bits

/s/H

z]

SNR [dB]

Practical region

Unattainableregion

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Shannon limit …

There exists a limiting value of below which there can be no error-free communication at any information rate.

By increasing the bandwidth alone, the capacity cannot be increased to any desired value.

W

C

N

E

W

C b

02 1log

WNN

CES

N

SWC

b

0

2 1log

[dB] 6.1693.0log

1

:get we,0or As

20

eN

EW

CW

b

0/ NEb

Shannon limit

15

Shannon limit …

[dB] / 0NEb

W/C [Hz/bits/s] Practical region

Unattainableregion

-1.6 [dB]

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Bandwidth efficiency plane

R<C

Practical region

R>CUnattainable region

R/W

[bi

ts/s

/Hz]

Bandwidth limited

Power limited

R=C

Shannon limit510BP

MPSKMQAMMFSK

M=2

M=4

M=8

M=16

M=64

M=256

M=2M=4

M=8

M=16

[dB] / 0NEb

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Error probability plane(example for coherent MPSK and MFSK)

[dB] / 0NEb [dB] / 0NEb

Bit

erro

r pr

obab

ility

M-PSK M-FSK

k=1,2

k=3

k=4

k=5

k=5

k=4

k=2

k=1

bandwidth-efficient power-efficient

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M-ary signaling Bandwidth efficiency:

Assuming Nyquist (ideal rectangular) filtering at baseband, the required passband bandwidth is:

M-PSK and M-QAM (bandwidth-limited systems) Bandwidth efficiency increases as M increases.

MFSK (power-limited systems) Bandwidth efficiency decreases as M increases.

][bits/s/Hz 1log2

bs

b

WTWT

M

W

R

[Hz] /1 ss RTW

][bits/s/Hz log/ 2 MWRb

][bits/s/Hz /log/ 2 MMWRb

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Power and bandwidth limited systems

Two major communication resources: Transmit power and channel bandwidth

In many communication systems, one of these resources is more precious than the other. Hence, systems can be classified as:

Power-limited systems: save power at the expense of bandwidth (for example by using coding schemes)

Bandwidth-limited systems: save bandwidth at the expense of power (for example by using spectrally efficient modulation

schemes)

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Goals in designing a DCS Goals:

Maximizing the transmission bit rate Minimizing probability of bit error Minimizing the required power Minimizing required system

bandwidth Maximizing system utilization Minimize system complexity

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Limitations in designing a DCS

The Nyquist theoretical minimum bandwidth requirement

The Shannon-Hartley capacity theorem (and the Shannon limit)

Government regulations Technological limitations Other system requirements (e.g satellite

orbits)