Signal Encoding Techniques

Lecture Learning Outcomes

Be able to understand, appreciate and differentiate the different signal encoding criteria available.

Class ContentsSignal Encoding Criteria

Digital Data, Analogue Signals• ASK• FSK• PSK• QAMAnalogue Data, Analogue Signals• AM• Angle ModulationAnalogue Data, Digital Signals• PCM• Delta Modulation

Signal Encoding CriteriaEncoding is referred in general to the process of conversionOf analogue or digital data into analogue or digital signals

Signal Encoding Criteria

Wireless communications relevant techniques:

Digital to Analogue Conversion Analogue to Analogue Conversion Digital to Digital Conversion

Most important factor in determining how successful was the interpretation of the signal:

SNR or Eb/N0

Data Rate (R) Bandwidth (B)

Signal Encoding Criteria

Term Units Definition

Data Element Bits A single binary one or zero

Data Rate Bits per second (bps) The rate at which data elements are transmitted

Signal Element Digital: a voltage pulse of constant amplitude.

Analogue: a pulse of constant frequency, phase and amplitude

That part of a signal that occupies the shortest interval of a signalling code.

Signalling Rate or Modulation Rate

Signal elements per second (bauds)

The rate at which signal elements are transmitted.

Digital Data to Analogue Signals

Amplitude Shift-Keying

Frequency Shift-Keying

Phase Shift-Keying

Quadrature and Amplitude Modulation

The principle of operation compromises the representation of a digital data stream using an analogue signal

Amplitude Shift-Keying (ASK)

0binary 0

1binary)2cos()(

tfAts c

Transmitted signal for 1 bit time

Frequency Shift-Keying (FSK)

Transmitted signal for 1 bit time

0binary)2cos(

1binary)2cos()(

2

1

tfA

tfAts

Also known as Binary FSK (BFSK)

Multilevel FSK (MFSK)

Signal more bandwidth efficient, but more susceptible to error.

More than 2 frequencies are used to represent multiple levels of thesignal.

Each signal element represent more than 1 bit

MFSK for 1 element:

element signalper bits ofnumber L

2elements signaldifferent ofnumber

frequency difference

frequencycarrier

)12(

1)2cos()(MFSK

L

M

f

f

fMiff

MitfAts

d

c

dci

i

Phase Shift-Keying (PSK)

Transmitted signal for 1 bit time

Phase of the carrier shifted 1800. Also known as binary PSK (BPSK)

0binary)2cos(

1binary)2cos(

)2cos(

)2cos()( BPSK

tfA

tfA

tfA

tfAts

c

c

c

c

Differential Phase Shift-Keying (PSK)

Transmitted signal for 1 bit time

Alternative form of PSK. For a binary 0, the phase is the same asIn the previous bit. For a binary 1, the phase changes 1800.

Quadrature Phase Shift-Keying (QPSK)

• When the phase shifts occurs at 900 it is called QPSK

• Each signal element is represented by 2 bits.

1042cos

00432cos

01432cos

1142cos

)(

tfA

tfA

tfA

tfA

ts

c

c

c

c

Quadrature Phase Shift-Keying (QPSK)

the amplitudes of the binary 1 and 0 are scaled and represented by

21 and 21 respectively

tfttftts cc 2sin)(Q2

12cos)(I

2

1)(

Multilevel Phase Shift-Keying (QPSK)

The use of multiple levels can be extended taking more than 2Bits at a time and decreasing the phase angle used.

Further, each angle taken can have more than one amplitude.

Example:

a standard 9600 bps modem uses 12 phase angles, four of which have two amplitude values for a total of 16 different signal elements

Lets assume a bit stream of 1s and 0s at a data rate of R=1/tb. The encoded signal contains (L=4) bits in each signal element using M=16 different combinations of amplitude and phase. The modulation rate can be seen to be R/4, because each change of signal element communicates 4 bits. Therefore, the line signalling speed is 2400 bauds, but the data rate is 9600 bps

Multilevel Phase Shift-Keying (QPSK)

Data Rate and Modulation Rate

M2log

R

L

RD

D = modulation rate in baudsR = data rate in bpsM = number of different signal elements = 2L

L = number of bits per signal element

Quadrature Amplitude Modulation (QAM)

tfttftts cc 2sin)(d2cos)(d)( 21

QAM is a combination of ASK and PSK. It is based on the fact thattwo signals can be transmitted simultaneously on the same carrier frequency, by using two copies of the carrier frequency, one shifted 90 with respect to the other

Analogue Data to Analogue Signals

Reasons to do Analogue Modulation of Analogue Signals

Higher frequency needed for effective transmission

Modulation permits frequency division multiplexing, which is an important technique used to transmit signals simultaneously over the same communications channel.

Modulation is the process of combining an input signal m(t)And a carrier frequency fc to produce a signal s(t) whose Bandwidth is usually centred in fc

Amplitude Modulation (AM)

The amplitude of the carrier signal is altered using as guide the modulating (baseband) signal (m(t)). This signal is of lower frequency than the carrier.

tftxnts ca 2cos)](1[)(

Where cos(2. .p f.t) is the carrier frequency and x(t) is the input signal, both normalized to unity amplitude.

The parameter na is known as the modulation index, is the ratio of

the amplitude of the input signal to the carrier.

Amplitude Modulation (AM)

Time Domain Frequency Domain

Amplitude Modulation (AM)

21

2a

ct

nPP

Power Relationship in AM:

where Pt is the transmitted power in s(t), Pc is the transmitted power

in the carrier.

The ideal would be that most of the signal power is used to transmit information (that is na as big as possible), however, na must remain

below 1 to avoid loss of information.

Angle Modulation

Frequency modulation (FM) and phase modulation (PM) are special casesfor angle modulation

Modulated Signal:

)()2(cos)( ttfAts cC

For phase modulation, the phase is proportional to the modulating signal:

index modulation phase thewhere

)()(

isn

tmnt

p

p

Angle Modulation (AM)

For frequency modulation (FM), the time derivative of the phase is proportional to the modulating signal:

index modulation frequency the is where

)()()( '

f

f

n

tmntdt

td

Bandwidth Comparison:

AM: BT=2.B

Angle modulation includes a term of the form cos( (f t)), which is non linearAnd will produce a wide range of frequencies.

Bandwidth for Angle Modulation

In practice, a good approximation to the bandwidth in angle modulation is known as the Carson’s rule

FMforB2B

PMfor

B12

mf

mp

T

Anf

An

B

Both FM and PM require greater bandwidth than AM

Digital Data to Digital Signals

The digital signal can be transmitted using NRZ-L. In this case the process has gone from analogue data to a digital signal.

The signal can be encoded as a digital signal using a code different from NRZ-L. This process requires an extra step

The digital data can be converted into an analogue signal using one of the modulation techniques previously discussed (ASK,FSK,etc.)

This process should be written as the conversion of analogueData into digital data. This process is known as digitalization.

Once data have been digitalized, the 3 most common things that happens next are:

Digital Data to Digital Signals

The device used for converting analogue data into digital signals is called CODEC. The two principal CODEC techniques are:

Pulse Code Modulation

Delta Modulation

Pulse Code Modulation

It is based on the sampling theorem which states:

“If a signal f(t) is sampled at regular intervals of time and at a rate higher than twice the highest signal frequency, then the samples contain all the information of the original signal. The function f(t) may be reconstructed from these samples by the use of a low-pass filter”.

The samples taken from the analogue signal are analogue samples called pulse amplitude modulation (PAM), to convert them to digital; each of these samples should be assigned a binary code.

Pulse Code Modulation

A 8 D 8

B 15 E 6

C 12 F 6

Sample Quantization Level Assigned

Using 16 levels in the sampling process, a digital binary signal coded in 4 bits is needed to represent all the possible sample levels.

Pulse Code Modulation

Sample Binary Code

Sample Binary Code

Sample BinaryCode

Sample Binary Code

0 0000 4 0100 8 1000 12 1100

1 0001 5 0101 9 1001 13 1101

2 0010 6 0110 10 1010 14 1110

3 0011 7 0111 11 1011 15 1111

The resulting PCM bit stream for the above example is:

100011111100100001100110

Pulse Code Modulation• Typically, the PCM scheme is refined using a technique known as nonlinear encoding, which means that the quantization levels are not equally spaced.

• The main problem with equal spacing is that the mean absolute error for each sample is the same, regardless of signal level. Consequently, lower amplitude values are relatively more distorted.

• The same effect (as non-linear encoding) can be achieved by using uniform quantization but companding (compressing-expanding) the input analogue signal.

• Companding is a process that compresses the intensity range of a signal by imparting more gain to weak signals than to strong signals on input. At output, the reverse operation is performed.

• Non-linear encoding can significantly improve the PCM SNR ratio. For voice signals, improvements of 24 to 30 dB have been achieved.

Delta Modulation

It is an alternative technique to PCM. It is easier to implement than PCM

In DM, an analogue signal is approximated by a staircase function that moves up or down by one quantization level (d) at each sampling interval TS.

At each sampling time, the function moves up or down a constant amount d. Thus, the output of the delta modulation can be represented as a single binary digit for each sample.

Delta Modulation

With this technique, a bit stream is produced by approximating the derivative of an analogue signal rather than its amplitude.

A binary 1 is produced is the staircase function is to go up in the next interval, and a 0 is generated otherwise:

Delta Modulation

The two important parameters in delta modulation are:

The size of the step assigned to each binary digit ()

The sampling rate.

Delta Modulation

There are two types of error:

Quantization Noise: occurs when the analogue waveform is changing very slowly. This noise increases as increases.

Slope Overload Noise: occurs when the analogue signal is changing so fast that the staircase function can not follow. This noise is increased as is decreased.

must be chosen to produce a balance between the two noise figures.

The principal advantage of DM over PCM is its simplicity in implementation. However, PCM exhibits better SNR characteristics at the same data rate.