lecture 10 performance of communication system: bit error rate … · 2016-10-19 · bandwidth: pam...

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EE4900/EE6720 Digital Communications Suketu Naik

EE4900/EE6720: Digital Communications

Lecture 10

Performance of

Communication System:

Bit Error Rate (BER)

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Block Diagrams of Communication System

Digital Communication System

Informatio

n (sound,

video, text,

data, …)

Transducer &

A/D ConverterModulator

Source

Encoder

Channel

Encoder

Tx RF

System

Output

Signal

D/A Converter

and/or output

transducer

DemodulatorSource

Decoder

Channel

Decoder

Rx RF

System

Channel

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Performance Metrics: Power and Bandwidth

Baseband Modulation is done before the information

(bits) is sent out using a carrier signal

Carrier signal is received (and down-converted to the

baseband signal)

Baseband signal is demodulated and information is

recovered

How do we know the performance of a modulation

scheme?

Bandwidth: measured from power spectral density of

the baseband signal, proportional to the bit rate

Power: Measured from probability of bit error (Bit

Error Rate or BER)

Trade-off between Bandwidth and Power

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Bandwidth

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Bandwidth: PAM

To find Bandwidth, we first need the Fourier transform

of the pulse shape p(t) in continuous-time domain

Pulse shapes: NRZ, RZ, MAN, HS, SRRC

PAM Modulator

Bandwidth

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Bandwidth: QAM

To find Bandwidth, we first need the Fourier transform

of the pulse shape p(t) in continuous-time domain

Pulse shapes: NRZ, RZ, MAN, HS, SRRC

Direct Digital Synthesizer

QAM Modulator BandwidthSame Bandwidth

(shifted by Ω0)

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Bandwidth: Pulse Shapes

NRZ, RZ, MAN, and HS pulses

NRZ

HS

MAN

RZ

Frequency at which

10log10|P(f)|2<-60dB

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Continuous-time SRRC

α = Roll-off factor: indicates excess BW

α = 0: 0% excess BW

α = 0.5: 50% excess BW

α = 1: 100% excess BW

tSmaller α = Smaller

lobes in Frequency

Domain

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Discrete-time SRRCLp=3

Lp=6

Lp=12

When you truncate the pulse in

time-domain it creates side-lobes

in freq. domain

Lp=# of Symbols used to create

the SRRC pulse

Goal: -40 dB side-lobe level

Lp vs α to achieve -40 dB

attenuation in freq. domain

Decreasing α

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Bandwidth for PAM and QAM

Bandwidth is determined from Power Spectral Density

(PSD) of PAM pulse:

Eq. 6.1: PSD equation

Eq. 6.2: BW of NRZ, RZ, MAN, and HS pulses

Eq. 6.3: BW of SRRC pulse

Bandwidth is determined from Power Spectral Density

(PSD) of QAM pulse:

Eq. 6.29: PSD equation

Eq. 6.30 : BW of NRZ, RZ, MAN, and HS pulses

Eq. 6.31: BW of SRRC pulse

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Probability of Bit Error

and Power

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Probability of Bit Error for PAM

The received baseband signal (after down-converting from the

carrier signal) is demodulated and detected (decoded)

The 1-D decision regions determine the amplitudes of the

approximated received signal

The probability of error is computed from the conditional

probabilities of error and applying the total probability theorem

Discrete-time PAM DemodulatorProbability of Error is computed

based on the decision regions

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Probability of Bit Error for 4-PAM

Decision Regions for 4-PAM (M=4)

Probability of Symbol Error, P(E), given that original

symbols were transmitted: Eq. 6.22, Eq. 6.23

Probability of Bit Error, Pb: Eq. 6.25, Eq. 6.26

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PDF for Matched Filter Output for 4-PAM

Received symbols will be shaped by randomness

introduced by noise which is defined by Gaussian R.V.

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Probability of Bit Error for M-ary PAM

Probability of Symbol Error, P(E): Eq. 6.27

Probability of Bit Error, Pb: Eq. 6.28

Probability of

Bit Error

Average Bit Energy over Noise Level

Eb/No: “ebno”

(rhymes with elbow)

is the required power

4

8

M=4

M=2

M=8

Pb is also known as

Bit Error Rate (BER)

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BER Plot for PAM

Eb/No

4

8

M=4

M=2

M=8

BER

How do we interpret the BER curves?

1) Find number of error bits given a certain power (Eb/No)

2) For constant power, BER increases as M increases

3) For constant BER, Power increases as M increases

Example: Pb=10-6 **

2-PAM: Eb/No=10.6 dB

4-PAM: Eb/No= 14.6 dB

8-PAM: Eb/No= 19.2 dB

** 10-6 or one in million bits is a standard

Trade-off between M

(faster transmission)

and BER

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BER Plot for PAM

Eb/No

4

8

M=4

M=2

M=8

BER

What about bandwidth?For Pb=10-6 and Rb=1 kbits/s : 2-PAM: Eb/No= 10.6 dB, BW=750 Hz

4-PAM: Eb/No= 14.6 dB, BW=375 Hz

8-PAM: Eb/No= 19.2 dB, BW=250 Hz

Bigger the M (# of

bits per symbol),

Smaller the BW,

Bigger the Power

BW

Decreases

Bigger M = Faster

Transmission

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Probability of Bit Error for QAM

The received baseband signal (after down-converting from the

carrier signal) is demodulated into I & Q signals

The 2-D decision regions determine the amplitudes of the

approximated I & Q signals

The probability of error is computed from the conditional

probabilities of error and applying the total probability theorem

Discrete-time QAM DemodulatorProbability of Error is computed

based on the decision regions

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Probability of Bit Error for 16-QAM

Decision Regions for 16-PAM (M=16)

Probability of Symbol Error, P(E), given that original symbols

were transmitted: Eq. 6.61, Eq. 6.62

Probability of Bit Error, Pb: Eq. 6.63

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Probability of Bit Error for M-ary QAM For MPSK, Probability of Bit Error, Pb: Eq. 6.72

For square MQAM, Probability of Bit Error, Pb: Ex. 6.5

For irregular MQAM, Probability of Bit Error, Pb: Eq. 6.91

Probability of

Bit Error

Average Bit Energy over Noise Level

M=64

(6 bits/symbol)

M=16

(4 bits/symbol)

M=256

(8 bits/symbol)

M=4

(2 bits/symbol)

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BER Plot for MPSK**

Which one is better?

** Recall that MPSK is a special case of MQAM

M=4

(2 bits/symbol)

M=8

(3 bits/symbol)

M=16

(4 bits/symbol)

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BER Plot


4-PAM

Y-QAM

QPSK

M=4, 2 bits/symbol

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BER Plot


M=8, 3 bits

CCITT V.29 (9600 bps modem)

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Measured BER Plot

How to measure BER for an actual comm. system?

1) Compare transmitted bits with received bits (from the received

symbols) and find BER. Repeat for different power levels

2) Example:

Tx: [1 0 0 1 0 1 0 0 1 1]

Rx: [1 1 0 0 0 1 0 0 1 1]

BER= Number of error bits/

Total number of bits

BER= 2/10=0.2=20%

Interpretation:

2 out of 10 bits are erroneous

20% chance of getting errors

Example: Measured BER performances of

IMDD-OOFDM** systems

** intensity-modulated and direct-detection optical OFDM

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BER Meters

Use BER Test Meters

Tektronix BitAlyzer® Bit

Error Rate Tester BA

Reach Technologies

BER Tester

Cool Low-cost

and Home-made

BER Tester

(Senior/M.S.

Project)

Example: NI’s PXI-6552 box

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Usefulness of BER

Performance Metric

Determine the integrity of the communication system

Key parameter that is used in assessing digital comm. systems

that transmit data from one location to another

Determine what degrades the digital signal: noise, interference,

changes to the propagation path, phase jitter, etc.

How to improve the communication system?

A: Reduce BER by reducing BW, increasing transmitter

power, decreasing data speed, etc.

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Usefulness of BER

Link Budget

System design: Find Eb/No (C/No) in terms of transmitter power,

distance, antenna gain, noise level, losses, etc.

Link budget equation: Eq. 6.126

Example: 3G uplink in suburban environment

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Matlab/Simulink Exercise

1) Find bandwidth of SRRC pulse

2) Find BER of either of the comm. system in Assignment 5

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Assignment 6 [10]

Simulate and generate BER plot for either of the comm.

system in Assignment 5 [10]

Submit the following:

1) BER plot:

Compare ideal BER (Formula based) with your system

Example

lecture 10 performance of communication system: bit error rate … · 2016-10-19 · bandwidth: pam...

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