Introduction to Digital Communications System

Wireless Information Transmission System Lab.

National Sun Yat-sen UniversityInstitute of Communications Engineering

Introduction to Digital Communications System

2

Recommended BooksDigital Communications / Fourth Edition (textbook)-- John G. Proakis, McGraw HillCommunication Systems / 4th Edition-- Simon Haykin, John Wiley & Sons, Inc.Digital Communications – Fundamentals and Applications / 2nd Edition-- Bernard Sklar, Prentice HallPrinciples of Communications / Fifth Edition-- Rodger E. Ziemer and William H. Tranter, John Wiley & Sons, Inc.Modern Digital and Analog Communication Systems-- B.P. Lathi, Holt, Rinehart and Winston, Inc.

3

Example of Communications System

Switch

TransmissionEquipment

LocalLoop

regenerator

T1/E1 Facilities

Switch


LocalLoop

regenerator

T1/E1 Facilities MUX

SONETSDH

Public Switched Telephone Network (PSTN)

A/D Conversion(Digitization)



Central Office

Central Office

Central Office

T1/E1 Facilities

Switch


LocalLoop

regenerator

T1/E1 Facilities

MobileSwitching

Center

MobileSwitching

Center

BaseStation

BaseStation

4

Basic Digital Communication Nomenclature

Textual Message: information comprised of a sequence of characters.Binary Digit (Bit): the fundamental information unit for all digital systems.Symbol (mi where i=1,2,…M): for transmission of the bit stream; groups of k bits are combined to form new symbol from a finite set of M such symbols; M=2k.Digital Waveform: voltage or current waveform representing a digital symbol.Data Rate: Symbol transmission is associated with a symbol duration T. Data rate R=k/T [bps].Baud Rate: number of symbols transmitted per second [baud].

5

Nomenclature Examples

6

Messages, Characters, and Symbols

7

Typical Digital Communications System

Information Bits

)(ˆ tsi

Format SourceEncoding Encryption Channel

Encoding Multiplexing Modulation FrequencySpreading

MultipleAccess

TXRFPA

BitStream

DigitalWaveformSynchronization

CHANNEL

Source Bits Channel Bits

Channel BitsSource Bits

)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources

To Other Destinations

Optional

Essential

Interleaving

Format SourceDecoding Decryption Channel

Decoding Demultiplexing Demodulation FrequencyDespreading

MultipleAccess

RXRFIF

Deinterleaving



Format

9


Information Bits

)(ˆ tsi



MultipleAccess

TXRFPA

BitStream


CHANNEL



)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources


Optional

Essential

Interleaving



MultipleAccess

RXRFIF

Deinterleaving

10

Formatting and Baseband Transmission

11

Sampling Theorem

12

Sampling Theorem

Sampling Theorem: A bandlimited signal having no spectral components above fm hertz can be determined uniquely by values sampled at uniform intervals of Tsseconds, where

In sample-and-hold operation, a switch and storage mechanism form a sequence of samples of the continuous input waveform. The output of the sampling process is called pulse amplitude modulation (PAM).

mS f

T21

≤mS ff 2 rate samplingor ≥

13

Sampling Theorem

∑∞

−∞=

−=∗=n

SS

S nffXT

fXfXfX )(1)()()( δ

14

Spectra for Various Sampling Rates

15

Natural Sampling

16

Pulse Code Modulation (PCM)

PCM is the name given to the class of baseband signals obtained from the quantized PAM signals by encoding each quantized sample into a digital word.

The source information is sampled and quantized to one of L levels; then each quantized sample is digitally encoded into an ℓ-bit (ℓ=log2L) codeword.

17

Example of Constructing PCM Sequence

18

Uniform and Non-uniform Quantization

19

Statistical Distribution of Single-Talker Speech Amplitudes

50% of the time, speech voltage is less than ¼ RMS.Only 15% of the time, voltage exceeds RMS.Typical voice signal dynamic range is 40 dB.

20

Problems with Linear Quantization

Fact: Unacceptable S/N for small signals.Solution:

Increasing quantization levels – price is too high.Applying nonlinear quantization – achieved by first distorting the original signal with a logarithmic compression characteristic and then using a uniform quantizer.

At the receiver, an inverse compression characteristic, called expansion, is applied so that the overall transmission is not distorted. The processing pair is referred to as companding.

21

Implementation of Non-linear Quantizer

22

Companding CharacteristicsIn North America: μ-law compression:

In Europe: A-law compression:⎩⎨⎧

<−≥+

=

⋅+

+=

0for 10for 1

sgn

where

sgn)1(log

)]/(1[log maxmax

xx

x

xxx

yye

e

μμ

⎪⎪⎩

⎪⎪⎨

⎧

≤<⋅+

+

≤<⋅+=

11 sgnlog1

)]/([log1

10 sgnlog1

)/(

max

maxmax

max

maxmax

xx

Ax

AxxA

y

Axx

xA

xxAy

y

e

e

e

23

Compression CharacteristicsStandard values of μ is 255 and A is 87.6.



Source Coding

25


Information Bits

)(ˆ tsi



MultipleAccess

TXRFPA

BitStream


CHANNEL



)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources


Optional

Essential

Interleaving



MultipleAccess

RXRFIF

Deinterleaving

26

Source Coding

Source coding deals with the task of forming efficient descriptions of information sources.For discrete sources, the ability to form reduced data rate descriptions is related to the information content and the statistical correlation among the source symbols.For analog sources, the ability to form reduced data rate descriptions, subject to a fixed fidelity criterion I related to the amplitude distribution and the temporal correlation of the source waveforms.

27

Huffman Coding

The Huffman code is source code whose average word length approaches the fundamental limit set by the entropy of a discrete memoryless source.

The Huffman code is optimum in the sense that no other uniquely decodable set of code-words has smaller average code-word length for a given discrete memoryless source.

28

Huffman Encoding Algorithm

1. The source symbols are listed in order of decreasing probability. The two source symbols of lowest probability are assigned a 0 and a 1.

2. These two source symbols are regarded as being combined into a new source symbol with probability equal to the sum of the two original probabilities. The probability of the new symbol is placed in the list in accordance with its value.

3. The procedure is repeated until we are left with a final list of source statistics of only two for which a 0 and a 1 are assigned.

4. The code for each (original) source symbol is found by working backward and tracing the sequence of 0s and 1s assigned to that symbol as well as its successors.

29

Example of Huffman CodingSymbol

S0S1S2S3S4

Probability0.40.20.20.10.1

Code Word001011010011

Symbol

S0S1S2S3S4

Stage 1

0.40.20.20.10.1

Stage 2

0.40.20.20.2

Stage 3

0.40.40.2

Stage 4

0.60.4

0

1

0

1

0

1

0

1

30

Properties of Huffman Code

Huffman encoding process is not unique.Code words for different Huffman encoding process can have different lengths. However, the average code-word length is the same.When a combined symbol is moved as high as possible, the resulting Huffman code has a significantly smaller variance than when it is moved as low as possible.Huffman code is a prefix code.

A prefix code is defined as a code in which no code-word is the prefix of any other code-word.

31

Bit Compression Technologies for Voice

Differential PCM (DPCM)Adaptive DPCM

Delta Modulation (DM)Adaptive DM (ADM)

Speech Encoding

.

.

.

32

Differential PCM (DPCM)

33

Delta Modulation (DM)

Delta modulation is a one-bit DPCM.Advantage: bit compression.Disadvantage: slope overload.

34

Speech Coding Objective

Reduce the number of bits needed to be transmitted, therefore lowering the bandwidth required.

35

Speech PropertiesVoiced Sound

Arises in generation of vowels and latter portion of some consonants.Displays long-term repetitive pattern corresponding to the duration of a pitch intervalPulse-like waveform.

Unvoiced SoundArises in pronunciation of certain consonants such as “s”, “f”, “p”, “j”, “x”, …, etc.Noise-like waveform.

36

Categories of Speech EncodingWaveform Encoding

Treats voice as analog signal and does not use properties of speech:

Source Model Coding or VocodingTreats properties of speech to preserve word information

Hybrid or parametric methodsCombines waveform and vocoding

37

Linear Predictive Coder (LPC)

38

Multi-Pulse Linear Predictive Coder(MP-LPC)

39

Regular Pulse Excited Long Term Prediction Coder (RPE-LPT)

40

Code-Excited Linear Predictive (CELP)

41

Speech Coder Complexity

42

Speech Processing for GSM

Composition of the 13 kbps signal:36 bits for filter parameters every 20 ms.9 bits for LTP every 5 ms.47 bits for RPE every 5 ms.

Thus, in a 20 ms (2080-bit block, or 260 sample) interval, we need a total of36+9*20/5+47*20/5=260 bits.Data Rate = 260/(20 ms) = 13 kbps.

43

Speech Processing for IS-54

Composition of the 7.95 kbps signal:43 bits for filter parameters every 20 ms.7 bits for LTP every 5 ms.88 bits for codebook every 20 ms.

Thus, in a 20 ms (2080-bit block, or 260 samples) interval, we need a total of:43+7*20/5+88=159 bits.Data Rate = 159/(20ms) = 7.95 kbps.



Channel Coding

45


Information Bits

)(ˆ tsi



MultipleAccess

TXRFPA

BitStream


CHANNEL



)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources

To Other DestinationsOptional

Essential

Interleaving



MultipleAccess

RXRFIF

Deinterleaving

46

Channel Coding

Error detecting coding: Capability of detecting errors so that re-transmission or dropping can be done.

Cyclic Redundancy Code (CRC)

Error Correcting Coding: Capability of detecting and correcting errors.

Block Codes: BCH codes, RS codes, … etc.Convolutional codes.Turbo codes.Low Density Parity Check (LDPC) Code

47

CRC in WCDMA

gCRC24(D) = D 24 + D 23 + D 6 + D 5 + D + 1;

gCRC16(D) = D 16 + D 12 + D 5 + 1;

gCRC12(D) = D 12 + D 11 + D 3 + D 2 + D + 1;

gCRC8(D) = D 8 + D 7 + D 4 + D 3 + D + 1.

48

Channel Coding Adopted in WCDMA

No coding

1/3Turbo coding

1/3, 1/2CPCH, DCH, DSCH,

FACH

RACH

PCH 1/2Convolutionalcoding

BCH

Coding rateCoding schemeType of TrCH

49

Convolutional Coding in WCDMA

Output 0G0 = 557 (octal)

InputD D D D D D D D




InputD D D D D D D D


(a) Rate 1/2 convolutional coder

(b) Rate 1/3 convolutional coder

50

Turbo Coder in WCDMA

xk

xk

zk

Turbo codeinternal interleaver

x’k

z’k

D

DDD

DD

Input

OutputInput

Output

x’k

1st constituent encoder

2nd constituent encoder



Interleaving

52


Information Bits

)(ˆ tsi



MultipleAccess

TXRFPA

BitStream


CHANNEL



)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources


Optional

Essential

Interleaving



MultipleAccess

RXRFIF

Deinterleaving

53

Bursty Error in Fading Channel

54

Interleaving Mechanism (1/2)

BitInterleaver

x y

y

j x n-bitShift registers

x

Write Clock Read Clock

Bit Stream before entering bit interleaver:x=(a11 a12 … a1n a21 a22 … a2n … aj1 aj2 … ajn)

55

Interleaving Mechanism (2/2)

Conceptually, the WRITE clock places the bit stream x by the row while the REA clock takes the bit stream y by the column:

Bit stream at the output of the bit interleaver:⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

jnjj

n

n

aaa

aaaaaa

.....................

...

...

21

22221

11211

( )jnnnjj aaaaaaaaay ............ 212221212111=

56

Burst Error Protection with Interleaver



Modulation

58


Information Bits

)(ˆ tsi



MultipleAccess

TXRFPA

BitStream


CHANNEL



)(tsiDigitalInput

im

DigitalOutput

im̂

Information Sink

From Other Sources


Optional

Essential

Interleaving



MultipleAccess

RXRFIF

Deinterleaving

59

ModulationDigital Modulation: digital symbols are transformed into waveforms that are compatible with the characteristics of the channel.

In baseband modulation, these waveforms are pulses.

In bandpass modulation, the desired information signal modulates a sinusoid called a carrier. For radio transmission, the carrier is converted in an electromagnetic (EM) wave.

60

Digital Modulations

Basic digital modulated signal:

v(t) = A(t) cos (ωt + θ)

Where A(t) = Amplitude; ω = Frequency; θ = Phase;

61

Basic Digital Modulations

62

Extended Modulated Signals – M-FSKExample: 16-FSK

Every 4 bits is encoded as: 16,,2,1 )cos( …=⋅ jtA jω

Gray Coding.

63

Extended Modulated Signals – M-PSK

Example: 16-PSKEvery 4 bits is encoded as: sin( ) 1, 2, ,16jA t jω θ⋅ + = …

Dotted lines are decision boundaries.

Gray Coding.

64

Extended Modulated Signals – 16-QAM

Every 4 bits is represented by one point in the signal constellation.Every point has its unique “amplitude” and “phase”.

65

Quadrature Phase Shift Keying (QPSK)

66

Spectrum of QPSK Signals

( ) ( )( )

( )( )

2 2sin sinc s c s

QPSK bc c

f f T f f TP f E

f f T f f Tπ π

π π

⎡ ⎤⎛ ⎞ ⎛ ⎞− − −⎢ ⎥= +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟− − −⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

67

Offset QPSK (OQPSK)For QPSK, the occasional phase shift of πradians can cause the signal envelope to pass through zero for just an instant.The amplification of the zero-crossings brings back the filtered sidelobes since the fidelity of the signal at small voltage levels is lost in transmission.To prevent the regeneration of sidelobes and spectral widening, it is imperative that QPSK signals that use pulse shaping be amplified only using linear amplifiers, which are less efficient.A modified form of QPSK, called offset QPSK (OQPSK) or staggered QPSK is less susceptible to these deleterious effects and supports more efficient amplification.OQPSK ensures there are fewer baseband signal transitions.Spectrum of an OQPSK signal is identical to that of QPSK.

68

Offset QPSK (OQPSK)The time offset waveforms that are applied to the in-phase and quadrature arms of an OQPSK modulator. Notice that a half-symbol offset is used.

69

π/4-DQPSK

70

Inter-Symbol Interference (ISI)

71

Inter Symbol Interference (ISI)

Inter-Symbol Interference (ISI) arises because of imperfections in the overall frequency response of the system. When a short pulse of duration Tb seconds is transmitted through a band-limited system, the frequency components constituting the input pulse are differentially attenuated and differentially delayed by the system. Consequently, the pulse appearing at the output of the system is dispersed over an interval longer than Tb seconds, thereby resulting in inter-symbol interference.Even in the absence of noise, imperfect filtering and system bandwidth constraints lead to ISI.

72

Nyquist Channels for Zero ISIThe Nyquist channel is not physically realizable since it dictates a rectangular bandwidth characteristic and an infinite time delay.Detection process would be very sensitive to small timing errors.Solution: Raised Cosine Filter.

73

Raised Cosine Filter

0

0

0

0

0

0

0

02

:Factor Off-Roll

:Bandwidth Excess21

for 2for

2for

0

)2

4(cos

1

)(

WWWr

WWT

W

WfWfWW

WWf

WWWWf

fH

−=

−

=

><<−

−<

⎪⎪⎩

⎪⎪⎨

⎧

−−+

=π

74

Raised Cosine Filter Characteristics

75

Raised Cosine Filter Characteristics

76

Equalization

In practical systems, the frequency response of the channel is not known to allow for a receiver design that will compensate for the ISI.The filter for handling ISI at the receiver contains various parameters that are adjusted with the channel characteristics.The process of correcting the channel-induced distortion is called equalization.

77

Equalization

78

Introduction to RAKE Receiver

Multiple versions of the transmitted signal are seen at the receiver through the propagation channels.Very low correlation between successive chips is in CDMA spreading codes.If these multi-path components are delayed in time by more than a chip duration, they appear like uncorrelated noise at a CDMA receiver.

Equalization is NOT necessary

Combine Coherently

79

Introduction to RAKE Receiver

To utilize the advantages of diversity techniques, channel parameters are necessary to be estimated.

Arrival time of each path, Amplitude, and Phase.

Maximal Ratio Combiner (MRC): The combiner that achieves the best performance is one in which each output is multiplied by the corresponding complex-valued (conjugate) channel gain. The effect of this multiplication is to compensate for the phase shift in the channel and to weight the signal by a factor that is proportional to the signal strength.

80

Maximum Ratio Combining (MRC)

MRC: Gi=Aie-jqi

Coherent Combining

Channel Estimation

Best Performance

G1

Receiver

G2 GL

81


1

22 2,

12

21

22 2

,1

22

,1 1 ,

Received Envelope:

Total Noise Power:

SNR: 2 2

Since

L

L l ll

L

n l n ll

L

l llL

L Ln

l n ll

L Ll

l l l n ll l n l

r G r

σ G

G rrSNR

G

rG r G

σ

σ σ

σσ

=

=

=

=

= =

= ⋅

=

⋅= =

⋅ ⋅ ⋅

⎛ ⎞⋅ = ⎜ ⎟⎜ ⎟

⎝ ⎠

∑

∑

∑

∑

∑ ∑

82


*

,

*

,

112,

2

1

2,

2

1 1

2

,

2,

1 1

2

,

2,

2

1

@ branches all from SNRs of SumSNROutput

:holdequality With

21

21

:Inequality sChebychev'

ll

ln

llnl

L

ll

L

l ln

lL

llnl

L

l

L

l ln

llnl

L

L

l

L

l ln

llnl

L

lll

rG

rkG

SNRr

G

rGSNR

rGrG

∝=⇒

=

==

⋅

≤

⋅≤⋅

∑∑∑

∑ ∑

∑ ∑∑

==

=

= =

= ==

σσ

σσ

σσ

σσ

83

Advantages of RAKE Receiver

Consider a receiver with only one finger:Once the output of a single correlator is corrupted by fading, large bit error is expected.

Consider a RAKE receiverIf the output of a single correlator is corrupted by fading, the others may NOT be.Diversity is provided by combining the outputs

Overcome fadingImprove CDMA reception

Introduction to Digital Communications System

Documents

Transcript of Introduction to Digital Communications System