1 analog/digital modulation analog modulation the input is continuous signal used in first...
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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
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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
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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)