digital modulation

Digital Modulation in

Communications Systems –

An Introduction

Application Note 1298

®

This application note introduces the concepts of digital modulation used in

many communications systems today. Emphasis is placed on explaining

the tradeoffs that are made to optimize efficiencies in system design.

Most communications systems fall into one of three categories: bandwidth

efficient, power efficient, or cost efficient. Bandwidth efficiency describes

the ability of a modulation scheme to accommodate data within a limited

bandwidth. Power efficiency describes the ability of the system to reliably

send information at the lowest practical power level. In most systems,

there is a high priority on bandwidth efficiency. The parameter to be

optimized depends on the demands of the particular system, as can be

seen in the following two examples.

For designers of digital terrestrial microwave radios, their highest priority

is good bandwidth efficiency with low bit-error-rate. They have plenty of

power available and are not concerned with power efficiency. They are

not especially concerned with receiver cost or complexity because they do

not have to build large numbers of them.

On the other hand, designers of hand-held cellular phones put a high

priority on power efficiency because these phones need to run on a battery.

Cost is also a high priority because cellular phones must be low-cost to

encourage more users. Accordingly, these systems sacrifice some bandwidth

efficiency to get power and cost efficiency.

Every time one of these efficiency parameters (bandwidth, power or cost)

is increased, another one decreases, or becomes more complex or does not

perform well in a poor environment. Cost is a dominant system priority.

Low-cost radios will always be in demand. In the past, it was possible to

make a radio low-cost by sacrificing power and bandwidth efficiency. This

is no longer possible. The radio spectrum is very valuable and operators

who do not use the spectrum efficiently could lose their existing licenses or

lose out in the competition for new ones. These are the tradeoffs that must

be considered in digital RF communications design.

This application note covers

• the reasons for the move to digital modulation;

• how information is modulated onto in-phase (I) and quadrature (Q)

signals;

• different types of digital modulation;

• filtering techniques to conserve bandwidth;

• ways of looking at digitally modulated signals;

• multiplexing techniques used to share the transmission channel;

• how a digital transmitter and receiver work;

• measurements on digital RF communications systems;

• an overview table with key specifications for the major digital

communications systems; and

• a glossary of terms used in digital RF communications.

These concepts form the building blocks of any communications system.

If you understand the building blocks, then you will be able to understand

how any communications system, present or future, works.

2

Introduction

1. Why digital modulation?

1.1 Trading off simplicity and bandwidth

1.2 Industry trends

2. Using I/Q modulation (amplitude and phase control) to

convey information

2.1 Transmitting information

2.2 Signal characteristics that can be modified

2.3 Polar display - magnitude and phase represented together

2.4 Signal changes or modifications in polar form

2.5 I/Q formats

2.6 I and Q in a radio transmitter

2.7 I and Q in a radio receiver

2.8 Why use I and Q?

3. Digital Modulation types and relative efficiencies

3.1 Applications

3.1.1 Bit rate and symbol rate

3.1.2 Spectrum (bandwidth) requirements

3.1.3 Symbol clock

3.2 Phase Shift Keying (PSK)

3.3 Frequency Shift Keying (FSK)

3.4 Minimum Shift Keying (MSK)

3.5 Quadrature Amplitude Modulation (QAM)

3.6 Theoretical bandwidth efficiency limits

3.7 Spectral efficiency examples in practical radios

3.8 I/Q offset modulation

3.9 Differential modulation

3.10 Constant amplitude modulation

4. Filtering

4.1 Nyquist or raised cosine filter

4.2 Transmitter-receiver matched filters

4.3 Gaussian filter

4.4 Filter bandwidth parameter alpha

4.5 Filter bandwidth effects

4.6 Chebyshev equiripple FIR (finite impulse response) filter

4.7 Spectral efficiency versus power consumption

5. Different ways of looking at a digitally modulated signal

5.1 Power and frequency view

5.2 Constellation diagrams

5.3 Eye diagrams

5.4 Trellis diagrams

6. Sharing the channel

6.1 Multiplexing - frequency

6.2 Multiplexing - time

6.3 Multiplexing - code

6.4 Multiplexing - geography

6.5 Combining multiplexing modes

6.6 Penetration versus efficiency

7. How digital transmitters and receivers work

7.1 A digital communications transmitter

7.2 A digital communications receiver

3

Table of contents

8. Measurements on digital RF communications systems

8.1 Power measurements

8.1.1 Adjacent Channel Power

8.2 Frequency measurements

8.2.1 Occupied bandwidth

8.3 Timing measurements

8.4 Modulation accuracy

8.5 Understanding Error Vector Magnitude (EVM)

8.6 Troubleshooting with error vector measurements

8.7 Magnitude versus phase error

8.8 I/Q phase error versus time

8.9 Error Vector Magnitude versus time

8.10 Error spectrum (EVM versus frequency)

9. Summary

10. Overview of communications systems

11. Glossary of terms

4

Table of contents

The move to digital modulation provides more information capacity,

compatibility with digital data services, higher data security, better

quality communications, and quicker system availability. Developers of

communications systems face these constraints:

• available bandwidth

• permissible power

• inherent noise level of the system

The RF spectrum must be shared, yet every day there are more users for

that spectrum as demand for communications services increases. Digital

modulation schemes have greater capacity to convey large amounts of

information than analog modulation schemes.

1.1 Trading off simplicity and bandwidth

There is a fundamental tradeoff in communication systems. Simple

hardware can be used in transmitters and receivers to communicate

information. However, this uses a lot of spectrum which limits the number

of users. Alternatively, more complex transmitters and receivers can be

used to transmit the same information over less bandwidth. The transition

to more and more spectrally efficient transmission techniques requires

more and more complex hardware. Complex hardware is difficult to design,

test, and build. This tradeoff exists whether communication is over air or

wire, analog or digital.

5

1. Why digital

modulation?

Complex

Hardware Less Spectrum

Simple

Hardware

Simple

Hardware

Fi 1

Complex

Hardware

More Spectrum

Figure 1.

The Fundamental

Trade-off

1.2 Industry trends

Over the past few years a major transition has occurred from simple analog

Amplitude Modulation (AM) and Frequency/Phase Modulation (FM/PM) to

new digital modulation techniques. Examples of digital modulation include

• QPSK (Quadrature Phase Shift Keying)

• FSK (Frequency Shift Keying)

• MSK (Minimum Shift Keying)

• QAM (Quadrature Amplitude Modulation)

Another layer of complexity in many new systems is multiplexing. Two

principal types of multiplexing (or “multiple access”) are TDMA (Time

Division Multiple Access) and CDMA (Code Division Multiple Access).

These are two different ways to add diversity to signals allowing different

signals to be separated from one another.

6

QAM, FSK,

QPSK

Vector Signals

AM, FM

Scalar Signals

TDMA, CDMA

Time-Variant

Signals

Required Measurement Capability

Signal/System Complexity

Figure 2.

Trends in the Industry

2.1 Transmitting information

To transmit a signal over the air, there are three main steps:

1. A pure carrier is generated at the transmitter.

2. The carrier is modulated with the information to be transmitted.

Any reliably detectable change in signal characteristics can carry

information.

3. At the receiver the signal modifications or changes are detected

and demodulated.

2.2 Signal characteristics that can be modified

There are only three characteristics of a signal that can be changed over

time: amplitude, phase or frequency. However, phase and frequency are

just different ways to view or measure the same signal change.

In AM, the amplitude of a high-frequency carrier signal is varied in

proportion to the instantaneous amplitude of the modulating message

signal.

Frequency Modulation (FM) is the most popular analog modulation

technique used in mobile communications systems. In FM, the amplitude

of the modulating carrier is kept constant while its frequency is varied

by the modulating message signal.

Amplitude and phase can be modulated simultaneously and separately,

but this is difficult to generate, and especially difficult to detect. Instead,

in practical systems the signal is separated into another set of independent

components: I (In-phase) and Q (Quadrature). These components are

orthogonal and do not interfere with each other.

7

2. Using I/Q modulation

to convey information.

Modify a

Signal

"Modulate"

Detect the Modifications

"Demodulate"

Any reliably detectable change in

signal characteristics can carry information

Amplitude

Frequency

or

Phase

Both Amplitude

and Phase

Figure 3.

Transmitting

Information...

(Analog or Digital)

Figure 4.

Signal Characteristics

to Modify

2.3 Polar display - magnitude and phase represented together

A simple way to view amplitude and phase is with the polar diagram. The

carrier becomes a frequency and phase reference and the signal is interpreted

relative to the carrier. The signal can be expressed in polar form as a

magnitude and a phase. The phase is relative to a reference signal, the carrier

in most communication systems. The magnitude is either an absolute or

relative value. Both are used in digital communication systems. Polar

diagrams are the basis of many displays used in digital communications,

although it is common to describe the signal vector by its rectangular

coordinates of I (In-phase) and Q (Quadrature).

2.4 Signal changes or modifications in polar form

This figure shows different forms of modulation in polar form. Magnitude

is represented as the distance from the center and phase is represented

as the angle.

Amplitude modulation (AM) changes only the magnitude of the signal.

Phase modulation (PM) changes only the phase of the signal. Amplitude

and phase modulation can be used together. Frequency modulation (FM)

looks similar to phase modulation, though frequency is the controlled

parameter, rather than relative phase.

8

Phase

Mag

0 deg

Phase

Mag

0 deg

Magnitude Change

Phase

0 deg

Phase Change

Magnitude & Phase Change Frequency Change

0 deg

0 deg

Figure 5.

Polar Display -

Magnitude and Phase

Represented Together

Figure 6.

Signal Changes or

Modifications

One example of the difficulties in RF design can be illustrated with

simple amplitude modulation. Generating AM with no associated angular

modulation should result in a straight line on a polar display. This line

should run from the origin to some peak radius or amplitude value. In

practice, however, the line is not straight. The amplitude modulation itself

often can cause a small amount of unwanted phase modulation. The result

is a curved line. It could also be a loop if there is any hysteresis in the

system transfer function. Some amount of this distortion is inevitable in

any system where modulation causes amplitude changes. Therefore, the

degree of effective amplitude modulation in a system will affect some

distortion parameters.

2.5 I/Q formats

In digital communications, modulation is often expressed in terms of I and

Q. This is a rectangular representation of the polar diagram. On a polar

diagram, the I axis lies on the zero degree phase reference, and the Q axis

is rotated by 90 degrees. The signal vector’s projection onto the I axis is its

“I” component and the projection onto the Q axis is its “Q” component.

9

{ {

0 deg

"I"

"Q"

Q-Value

I-Value

Project signal

to "I" and "Q" axes

Polar to Rectangular Conversion

Figure 7.

“I-Q” Format

2.6 I and Q in a radio transmitter

I/Q diagrams are particularly useful because they mirror the way most

digital communications signals are created using an I/Q modulator. In the

transmitter, I and Q signals are mixed with the same local oscillator (LO).

A 90 degree phase shifter is placed in one of the LO paths. Signals that are

separated by 90 degrees are also known as being orthogonal to each other

or in quadrature. Signals that are in quadrature do not interfere with

each other. They are two independent components of the signal. When

recombined, they are summed to a composite output signal. There are

two independent signals in I and Q that can be sent and received with

simple circuits. This simplifies the design of digital radios. The main

advantage of I/Q modulation is the symmetric ease of combining independent

signal components into a single composite signal and later splitting such a

composite signal into its independent component parts.

2.7 I and Q in a radio receiver

The composite signal with magnitude and phase (or I and Q) information

arrives at the receiver input. The input signal is mixed with the local

oscillator signal at the carrier frequency in two forms. One is at an arbitrary

zero phase. The other has a 90 degree phase shift. The composite input

signal (in terms of magnitude and phase) is thus broken into an in-phase,

I, and a quadrature, Q, component. These two components of the signal are

independent and orthogonal. One can be changed without affecting the other.

Normally, information cannot be plotted in a polar format and reinterpreted

as rectangular values without doing a polar-to-rectangular conversion.

This conversion is exactly what is done by the in-phase and quadrature

mixing processes in a digital radio. A local oscillator, phase shifter, and

two mixers can perform the conversion accurately and efficiently.

10

90 deg

Phase Shift

Local Osc.

(Carrier Freq.)

Q

I

Composite

Output

Signal S

Local Osc.

(Carrier Freq.)

Quadrature Component

In-Phase Component

Composite

Input

Signal

90 deg

Phase Shift

Figure 8.

I and Q in a Practical

Radio Transmitter

Figure 9.

I and Q in a Radio

Receiver

2.8 Why use I and Q?

Digital modulation is easy to accomplish with I/Q modulators. Most digital

modulation maps the data to a number of discrete points on the I/Q plane.

These are known as constellation points. As the signal moves from one

point to another, simultaneous amplitude and phase modulation usually

results. To accomplish this with an amplitude modulator and a phase

modulator is difficult and complex. It is also impossible with a conventional

phase modulator. The signal may, in principal, circle the origin in one

direction forever, necessitating infinite phase shifting capability.

Alternatively, simultaneous AM and Phase Modulation is easy with an

I/Q modulator. The I and Q control signals are bounded, but infinite phase

wrap is possible by properly phasing the I and Q signals.

11

This section covers the main digital modulation formats, their main

applications, relative spectral efficiencies and some variations of the main

modulation types as used in practical systems. Fortunately, there are a

limited number of modulation types which form the building blocks of

any system.

3.1 Applications

This table covers the applications for different modulation formats in both

wireless communications and video.

Although this note focuses on wireless communications, video applications

have also been included in the table for completeness and because of their

similarity to other wireless communications.

3.1.1 Bit rate and symbol rate

To understand and compare different modulation format efficiencies, it is

important to first understand the difference between bit rate and symbol

rate. The signal bandwidth for the communications channel needed depends

on the symbol rate, not on the bit rate.

Symbol rate =

bit rate

the number of bits transmitted with each symbol

12

3. Digital modulation

types and relative

efficiencies

Modulation format Application

MSK, GMSK GSM, CDPD

BPSK Deep space telemetry, cable modems

QPSK, ¹/4 DQPSK Satellite, CDMA, NADC, TETRA, PHS, PDC, LMDS, DVB-S, cable (return

path), cable modems, TFTS

OQPSK CDMA, satellite

FSK, GFSK DECT, paging, RAM mobile data, AMPS, CT2, ERMES, land mobile,

public safety

8, 16 VSB North American digital TV (ATV), broadcast, cable

8PSK Satellite, aircraft, telemetry pilots for monitoring broadband video systems

16 QAM Microwave digital radio, modems, DVB-C, DVB-T

32 QAM Terrestrial microwave, DVB-T

64 QAM DVB-C, modems, broadband set top boxes, MMDS

256 QAM Modems, DVB-C (Europe), Digital Video (US)

Bit rate is the frequency of a system bit stream. Take, for example, a radio

with an 8 bit sampler, sampling at 10 kHz for voice. The bit rate, the basic

bit stream rate in the radio, would be eight bits multiplied by 10K samples

per second, or 80 Kbits per second. (For the moment we will ignore the

extra bits required for synchronization, error correction, etc.).

Figure 10 is an example of a state diagram of a Quadrature Phase Shift

Keying (QPSK) signal. The states can be mapped to zeros and ones. This is

a common mapping, but it is not the only one. Any mapping can be used.

The symbol rate is the bit rate divided by the number of bits that can be

transmitted with each symbol. If one bit is transmitted per symbol, as with

BPSK, then the symbol rate would be the same as the bit rate of 80 Kbits

per second. If two bits are transmitted per symbol, as in QPSK, then the

symbol rate would be half of the bit rate or 40 Kbits per second. Symbol

rate is sometimes called baud rate. Note that baud rate is not the same as

bit rate. These terms are often confused. If more bits can be sent with each

symbol, then the same amount of data can be sent in a narrower spectrum.

This is why modulation formats that are more complex and use a higher

number of states can send the same information over a narrower piece of

the RF spectrum.

3.1.2 Spectrum (bandwidth) requirements

An example of how symbol rate influences spectrum requirements can be

seen in eight-state Phase Shift Keying (8PSK). It is a variation of PSK.

There are eight possible states that the signal can transition to at any

time. The phase of the signal can take any of eight values at any symbol

time. Since 23 = 8, there are three bits per symbol. This means the symbol

rate is one third of the bit rate. This is relatively easy to decode.

13

01 00

11 10

QPSK

Two Bits Per Symbol

QPSK

State Diagram

BPSK

One Bit Per Symbol

Symbol Rate = Bit Rate

8PSK

Three Bits Per Symbol

Symbol Rate = 1/3 Bit Rate

Figure 10.

Bit Rate and Symbol

Rate

Figure 11.

Spectrum

Requirements

3.1.3 Symbol clock

The symbol clock represents the frequency and exact timing of the

transmission of the individual symbols. At the symbol clock transitions,

the transmitted carrier is at the correct I/Q (or magnitude/phase) value to

represent a specific symbol (a specific point in the constellation).

3.2 Phase Shift Keying

One of the simplest forms of digital modulation is binary or Bi-Phase

Shift Keying (BPSK). One application where this is used is for deep space

telemetry. The phase of a constant amplitude carrier signal moves between

zero and 180 degrees. On an I and Q diagram, the I state has two different

values. There are two possible locations in the state diagram, so a binary

one or zero can be sent. The symbol rate is one bit per symbol.

A more common type of phase modulation is Quadrature Phase Shift Keying

(QPSK). It is used extensively in applications including CDMA (Code

Division Multiple Access) cellular service, wireless local loop, Iridium

(a voice/data satellite system) and DVB-S (Digital Video Broadcasting -

Satellite). Quadrature means that the signal shifts between phase states

which are separated by 90 degrees. The signal shifts in increments of 90

degrees from 45 to 135, –45, or –135 degrees. These points are chosen as

they can be easily implemented using an I/Q modulator. Only two I values

and two Q values are needed and this gives two bits per symbol. There are

four states because 22 = 4. It is therefore a more bandwidth-efficient type

of modulation than BPSK, potentially twice as efficient.

14

BPSK

One Bit Per Symbol

QPSK

Two Bits Per Symbol

Figure 12.

Phase Shift Keying

3.3 Frequency Shift Keying

Frequency modulation and phase modulation are closely related. A static

frequency shift of +1 Hz means that the phase is constantly advancing at

the rate of 360 degrees per second (2 ¹ rad/sec), relative to the phase of the

unshifted signal.

FSK (Frequency Shift Keying) is used in many applications including

cordless and paging systems. Some of the cordless systems include DECT

(Digital Enhanced Cordless Telephone) and CT2 (Cordless Telephone 2).

In FSK, the frequency of the carrier is changed as a function of the

modulating signal (data) being transmitted. Amplitude remains unchanged.

In binary FSK (BFSK or 2FSK), a “1” is represented by one frequency and

a “0” is represented by another frequency.

3.4 Minimum Shift Keying

Since a frequency shift produces an advancing or retarding phase, frequency

shifts can be detected by sampling phase at each symbol period. Phase

shifts of (2N + 1) ¹/2 radians are easily detected with an I/Q demodulator.

At even numbered symbols, the polarity of the I channel conveys the

transmitted data, while at odd numbered symbols the polarity of the Q

channel conveys the data. This orthogonality between I and Q simplifies

detection algorithms and hence reduces power consumption in a mobile

receiver. The minimum frequency shift which yields orthogonality of I and Q

is that which results in a phase shift of ± ¹/2 radians per symbol (90 degrees

per symbol). FSK with this deviation is called MSK (Minimum Shift

Keying). The deviation must be accurate in order to generate repeatable

90 degree phase shifts. MSK is used in the GSM (Global System for

Mobile Communications) cellular standard. A phase shift of +90 degrees

represents a data bit equal to “1”, while –90 degrees represents a “0”. The

peak-to-peak frequency shift of an MSK signal is equal to one-half of the

bit rate.

FSK and MSK produce constant envelope carrier signals, which have no

amplitude variations. This is a desirable characteristic for improving the

power efficiency of transmitters. Amplitude variations can exercise

nonlinearities in an amplifier’s amplitude-transfer function, generating

spectral regrowth, a component of adjacent channel power. Therefore,

more efficient amplifiers (which tend to be less linear) can be used with

constant-envelope signals, reducing power consumption.

15

MSK

Q vs. I

FSK

Freq. vs. Time

One Bit Per Symbol One Bit Per Symbol

Figure 13.

Frequency Shift

Keying

MSK has a narrower spectrum than wider deviation forms of FSK. The

width of the spectrum is also influenced by the waveforms causing the

frequency shift. If those waveforms have fast transitions or a high slew rate,

then the spectrum of the transmitter will be broad. In practice, the

waveforms are filtered with a Gaussian filter, resulting in a narrow

spectrum. In addition, the Gaussian filter has no time-domain overshoot,

which would broaden the spectrum by increasing the peak deviation.

MSK with a Gaussian filter is termed GMSK (Gaussian MSK).

3.5 Quadrature Amplitude Modulation

Another member of the digital modulation family is Quadrature Amplitude

Modulation (QAM). QAM is used in applications including microwave

digital radio, DVB-C (Digital Video Broadcasting - Cable) and modems.

In 16-state Quadrature Amplitude Modulation (16QAM), there are four I

values and four Q values. This results in a total of 16 possible states for the

signal. It can transition from any state to any other state at every symbol

time. Since 16 = 24, four bits per symbol can be sent. This consists of two

bits for I and two bits for Q. The symbol rate is one fourth of the bit rate.

So this modulation format produces a more spectrally efficient transmission.

It is more efficient than BPSK, QPSK or 8PSK. Note that QPSK is the

same as 4QAM.

Another variation is 32QAM. In this case there are six I values and six Q

values resulting in a total of 36 possible states (6x6=36). This is too many

states for a power of two (the closest power of two is 32). So the four corner

symbol states, which take the most power to transmit, are omitted. This

reduces the amount of peak power the transmitter has to generate. Since

25 = 32, there are five bits per symbol and the symbol rate is one fifth of

the bit rate.

The current practical limits are approximately 256QAM, though work is

underway to extend the limits to 512 or 1024 QAM. A 256QAM system

uses 16 I-values and 16 Q-values giving 256 possible states. Since 28 = 256,

each symbol can represent eight bits. A 256QAM signal that can send

eight bits per symbol is very spectrally efficient. However, the symbols

are very close together and are thus more subject to errors due to noise

and distortion. Such a signal may have to be transmitted with extra power

(to effectively spread the symbols out more) and this reduces power

efficiency as compared to simpler schemes.

16

16QAM

Four Bits Per Symbol

Symbol Rate = 1/4 Bit Rate

I

Q

32QAM

Five Bits Per Symbol

Symbol Rate = 1/5 Bit Rate

Vector Diagram Constellation Diagram

Fig. 14

Figure 14.

Quadrature

Amplitude Modulation

Compare the bandwidth efficiency when using 256QAM versus BPSK

modulation in the radio example in section 3.1.1 (which uses an eight-bit

sampler sampling at 10 kHz for voice). BPSK uses 80 Ksymbols-per-second

sending 1 bit per symbol. A system using 256QAM sends eight bits per

symbol so the symbol rate would be 10 Ksymbols per second. A 256QAM

system enables the same amount of information to be sent as BPSK using

only one eighth of the bandwidth. It is eight times more bandwidth

efficient. However, there is a tradeoff. The radio becomes more complex

and is more susceptible to errors caused by noise and distortion. Error

rates of higher-order QAM systems such as this degrade more rapidly than

QPSK as noise or interference is introduced. A measure of this degradation

would be a higher Bit Error Rate (BER).

In any digital modulation system, if the input signal is distorted or severely

attenuated the receiver will eventually lose symbol lock completely. If

the receiver can no longer recover the symbol clock, it cannot demodulate

the signal or recover any information. With less degradation, the symbol

clock can be recovered, but it is noisy, and the symbol locations themselves

are noisy. In some cases, a symbol will fall far enough away from its

intended position that it will cross over to an adjacent position. The I and

Q level detectors used in the demodulator would misinterpret such a

symbol as being in the wrong location, causing bit errors. QPSK is not as

efficient, but the states are much farther apart and the system can

tolerate a lot more noise before suffering symbol errors. QPSK has no

intermediate states between the four corner-symbol locations so there is

less opportunity for the demodulator to misinterpret symbols. QPSK

requires less transmitter power than QAM to achieve the same bit error

rate.

3.6 Theoretical bandwidth efficiency limits

Bandwidth efficiency describes how efficiently the allocated bandwidth is

utilized or the ability of a modulation scheme to accommodate data, within

a limited bandwidth. This table shows the theoretical bandwidth efficiency

limits for the main modulation types. Note that these figures cannot

actually be achieved in practical radios since they require perfect

modulators, demodulators, filter and transmission paths.

If the radio had a perfect (rectangular in the frequency domain) filter, then

the occupied bandwidth could be made equal to the symbol rate.

Techniques for maximizing spectral efficiency include the following:

• Relate the data rate to the frequency shift (as in GSM).

• Use premodulation filtering to reduce the occupied bandwidth.

Raised cosine filters, as used in NADC, PDC, and PHS give the

best spectral efficiency.

• Restrict the types of transitions.

17

Modulation Theoretical bandwidth

format efficiency limits

MSK 1 bit/second/Hz

BPSK 1 bit/second/Hz

QPSK 2 bits/second/Hz

8PSK 3 bits/second/Hz

16 QAM 4 bits/second/Hz

32 QAM 5 bits/second/Hz

64 QAM 6 bits/second/Hz

256 QAM 8 bits/second/Hz

3.7 Spectral efficiency examples in practical radios

The following examples indicate spectral efficiencies that are achieved in

some practical radio systems.

The TDMA version of the North American Digital Cellular (NADC) system,

achieves a 48 Kbits-per-second data rate over a 30 kHz bandwidth or

1.6 bits per second per Hz. It is a ¹/4 DQPSK based system and transmits

two bits per symbol. The theoretical efficiency would be two bits per second

per Hz and in practice it is 1.6 bits per second per Hz.

Another example is a microwave digital radio using 16QAM. This kind

of signal is more susceptible to noise and distortion than something

simpler such as QPSK. This type of signal is usually sent over a direct

line-of-sight microwave link or over a wire where there is very little noise and

interference. In this microwave-digital-radio example the bit rate is 140 Mbits

per second over a very wide bandwidth of 52.5 MHz. The spectral efficiency

is 2.7 bits per second per Hz. To implement this, it takes a very clear

line-of-sight transmission path and a precise and optimized high-power

transceiver.

18

Effects of going through

the origin

Take, for example, a QPSK signal where

the normalized value changes from 1, 1

to –1, –1. When changing simultaneously

from I and Q values of +1 to I and Q

values of –1, the signal trajectory goes

through the origin (the I/Q value of 0,0).

The origin represents 0 carrier magnitude.

A value of 0 magnitude indicates

that the carrier amplitude is 0 for a

moment.

Not all transitions in QPSK result in a

trajectory that goes through the origin.

If I changes value but Q does not (or

vice-versa) the carrier amplitude

changes a little, but it does not go

through zero. Therefore some symbol

transitions will result in a small amplitude

variation, while others will result

in a very large amplitude variation. The

clock-recovery circuit in the receiver

must deal with this amplitude variation

uncertainty if it uses amplitude variations

to align the receiver clock with the

transmitter clock.

Spectral regrowth does not automatically

result from these trajectories that pass

through or near the origin. If the amplifier

and associated circuits are perfectly

linear, the spectrum (spectral occupancy

or occupied bandwidth) will be unchanged.

The problem lies in nonlinearities

in the circuits.

A signal which changes amplitude over

a very large range will exercise these

nonlinearities to the fullest extent. These

nonlinearities will cause distortion

products. In continuously-modulated

systems they will cause “spectral regrowth”

or wider modulation sidebands

(a phenomenon related to intermodulation

distortion). Another term which is

sometimes used in this context is “spectral

splatter”. However this is a term

that is more correctly used in association

with the increase in the bandwidth

of a signal caused by pulsing on and off.

Digital modulation types - variations

The modulation types outlined in sections 3.2 to 3.4 form the building blocks

for many systems. There are three main variations on these basic building

blocks that are used in communications systems: I/Q offset modulation,

differential modulation, and constant envelope modulation.

3.8 I/Q offset modulation

The first variation is offset modulation. One example of this is Offset

QPSK (OQPSK). This is used in the cellular CDMA (Code Division

Multiple Access) system for the reverse (mobile to base) link.

In QPSK, the I and Q bit streams are switched at the same time. The

symbol clocks, or the I and Q digital signal clocks, are synchronized. In

Offset QPSK (OQPSK), the I and Q bit streams are offset in their relative

alignment by one bit period (one half of a symbol period). This is shown

in the diagram. Since the transitions of I and Q are offset, at any given

time only one of the two bit streams can change values. This creates a

dramatically different constellation, even though there are still just two

I/Q values. This has power efficiency advantages. In OQPSK the signal

trajectories are modified by the symbol clock offset so that the carrier

amplitude does not go through or near zero (the center of the constellation).

The spectral efficiency is the same with two I states and two Q states. The

reduced amplitude variations (perhaps 3 dB for OQPSK, versus 30 to 40 dB

for QPSK) allow a more power-efficient, less linear RF power amplifier

to be used.

19

QPSK

Offset

QPSK

Q

I

Q

I

Eye Constellation

Figure 15.

I-Q “Offset”

Modulation

3.9 Differential modulation

The second variation is differential modulation as used in differential

QPSK (DQPSK) and differential 16QAM (D16QAM). Differential means

that the information is not carried by the absolute state, it is carried by

the transition between states. In some cases there are also restrictions on

allowable transitions. This occurs in ¹/4 DQPSK where the carrier

trajectory does not go through the origin. A DQPSK transmission system

can transition from any symbol position to any other symbol position.

The ¹/4 DQPSK modulation format is widely used in many applications

including

• cellular

-NADC- IS-54 (North American digital cellular)

-PDC (Pacific Digital Cellular)

• cordless

-PHS (personal handyphone system)

• trunked radio

-TETRA (Trans European Trunked Radio)

The ¹/4 DQPSK modulation format uses two QPSK constellations offset

by 45 degrees (¹/4 radians). Transitions must occur from one constellation

to the other. This guarantees that there is always a change in phase at

each symbol, making clock recovery easier. The data is encoded in the

magnitude and direction of the phase shift, not in the absolute position

on the constellation. One advantage of ¹/4 DQPSK is that the signal

trajectory does not pass through the origin, thus simplifying transmitter

design. Another is that ¹/4 DQPSK, with root raised cosine filtering,

has better spectral efficiency than GMSK, the other common cellular

modulation type.

20

QPSK ¹/4 DQPSK

Both formats are 2 bits/symbol

Figure 16.

“Differential”

Modulation

3.10 Constant amplitude modulation

The third variation is constant-envelope modulation. GSM uses a variation

of constant amplitude modulation format called 0.3 GMSK (Gaussian

Minimum Shift Keying).

In constant-envelope modulation the amplitude of the carrier is constant,

regardless of the variation in the modulating signal. It is a power-efficient

scheme that allows efficient class-C amplifiers to be used without

introducing degradation in the spectral occupancy of the transmitted

signal. However, constant-envelope modulation techniques occupy a larger

bandwidth than schemes which are linear. In linear schemes, the amplitude

of the transmitted signal varies with the modulating digital signal as in

BPSK or QPSK. In systems where bandwidth efficiency is more important

than power efficiency, constant envelope modulation is not as well suited.

MSK (covered in section 3.4) is a special type of FSK where the peak-to-peak

frequency deviation is equal to half the bit rate.

GMSK is a derivative of MSK where the bandwidth required is further

reduced by passing the modulating waveform through a Gaussian filter.

The Gaussian filter minimizes the instantaneous frequency variations over

time. GMSK is a spectrally efficient modulation scheme and is particularly

useful in mobile radio systems. It has a constant envelope, spectral

efficiency, good BER performance and is self-synchronizing.

21

MSK (GSM)

Amplitude (Envelope) Varies

From Zero to Nominal Value

QPSK

Amplitude (Envelope) Does

Not Vary At All

Fig. 17

Figure 17.

Constant Amplitude

Modulation

Filtering allows the transmitted bandwidth to be significantly reduced

without losing the content of the digital data. This improves the spectral

efficiency of the signal.

There are many different varieties of filtering. The most common are

• raised cosine

• square-root raised cosine

• Gaussian filters

Any fast transition in a signal, whether it be amplitude, phase or

frequency will require a wide occupied bandwidth. Any technique that

helps to slow down these transitions will narrow the occupied bandwidth.

Filtering serves to smooth these transitions (in I and Q). Filtering

reduces interference because it reduces the tendency of one signal or one

transmitter to interfere with another in a Frequency-Division-Multiple-

Access (FDMA) system. On the receiver end, reduced bandwidth improves

sensitivity because more noise and interference are rejected.

Some tradeoffs must be made. One is that some types of filtering cause

the trajectory of the signal (the path of transitions between the states) to

overshoot in many cases. This overshoot can occur in certain types of filters

such as Nyquist. This overshoot path represents carrier power and phase.

For the carrier to take on these values it requires more output power

from the transmitter amplifiers. It requires more power than would be

necessary to transmit the actual symbol itself. Carrier power cannot be

clipped or limited (to reduce or eliminate the overshoot) without causing

the spectrum to spread out again. Since narrowing the spectral occupancy

was the reason the filtering was inserted in the first place, it becomes a

very fine balancing act.

Other tradeoffs are that filtering makes the radios more complex and can

make them larger, especially if performed in an analog fashion. Filtering

can also create Inter-Symbol Interference (ISI). This occurs when the

signal is filtered enough so that the symbols blur together and each symbol

affects those around it. This is determined by the time-domain response,

or impulse response of the filter.

4.1 Nyquist or raised cosine filter

This graph shows the impulse or time-domain response of a raised cosine

filter, one class of Nyquist filter. Nyquist filters have the property that

their impulse response rings at the symbol rate. The filter is chosen to ring,

or have the impulse response of the filter cross through zero, at the symbol

clock frequency.

22

4. Filtering

0

0.5

1

-10 -5 0 5 10

h

i

t

i

One symbol

Figure 18.

Nyquit or Raised

Cosine Filter

The time response of the filter goes through zero with a period that exactly

corresponds to the symbol spacing. Adjacent symbols do not interfere with

each other at the symbol times because the response equals zero at all

symbol times except the center (desired) one. Nyquist filters heavily filter

the signal without blurring the symbols together at the symbol times.

This is important for transmitting information without errors caused by

Inter-Symbol Interference. Note that Inter-Symbol Interference does exist

at all times except the symbol (decision) times. Usually the filter is split,

half being in the transmit path and half in the receiver path. In this case

root Nyquist filters (commonly called root raised cosine) are used in each

part, so that their combined response is that of a Nyquist filter.

4.2 Transmitter-receiver matched filters

Sometimes filtering is desired at both the transmitter and receiver. Filtering

in the transmitter reduces the adjacent-channel-power radiation of the

transmitter, and thus its potential for interfering with other transmitters.

Filtering at the receiver reduces the effects of broadband noise and also

interference from other transmitters in nearby channels.

To get zero Inter-Symbol Interference (ISI), both filters are designed until

the combined result of the filters and the rest of the system is a full Nyquist

filter. Potential differences can cause problems in manufacturing because

the transmitter and receiver are often manufactured by different companies.

The receiver may be a small hand-held model and the transmitter may be

a large cellular base station. If the design is performed correctly the results

are the best data rate, the most efficient radio, and reduced effects of

interference and noise. This is why root-Nyquist filters are used in

receivers and transmitters as à Nyquist x à Nyquist = Nyquist. Matched

filters are not used in Gaussian filtering.

4.3 Gaussian filter

In contrast, a GSM signal will have a small blurring of symbols on each

of the four states because the Gaussian filter used in GSM does not have

zero Inter-Symbol Interference. The phase states vary somewhat causing

a blurring of the symbols as shown in figure 17. Wireless system

architects must decide just how much of the Inter-Symbol Interference can

be tolerated in a system and combine that with noise and interference.

23

Actual Data

Root Raised

Cosine Filter

DAC

Detected Bits

Root Raised

Cosine Filter

Transmitter

Receiver

Demodulator

Modulator

Figure 19.

Transmitter-Receiver

Matched Filters

Gaussian filters are used in GSM because of their advantages in carrier

power, occupied bandwidth and symbol-clock recovery. The Gaussian filter

is a Gaussian shape in both the time and frequency domains, and it does

not ring like the raised cosine filters do. Its effects in the time domain are

relatively short and each symbol interacts significantly (or causes ISI) with

only the preceding and succeeding symbols. This reduces the tendency for

particular sequences of symbols to interact which makes amplifiers easier

to build and more efficient.

4.4 Filter bandwidth parameter alpha

The sharpness of a raised cosine filter is described by alpha (a). Alpha

gives a direct measure of the occupied bandwidth of the system and is

calculated as

occupied bandwidth = symbol rate X (1 + a).

If the filter had a perfect (brick wall) characteristic with sharp transitions

and an alpha of zero, the occupied bandwidth would be

for a = 0, occupied bandwidth = symbol rate X (1 + 0) = symbol rate.

24

Hz

Ch1

Spectrum

LogMag

10

dB/div

GHz

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

a = 0.3

a = 0.5

a = 0

a = 1.0

Fs : Symbol Rate

Figure 20.

Gaussian Filter

Figure 21.

Filter Bandwidth

Parameters “a”

In a perfect world, the occupied bandwidth would be the same as the symbol

rate, but this is not practical. An alpha of zero is impossible to implement.

Alpha is sometimes called the “excess bandwidth factor” as it indicates the

amount of occupied bandwidth that will be required in excess of the ideal

occupied bandwidth (which would be the same as the symbol rate).

At the other extreme, take a broader filter with an alpha of one, which is

easier to implement. The occupied bandwidth will be

for a = 1, occupied bandwidth = symbol rate X (1 + 1) = 2 X symbol rate.

An alpha of one uses twice as much bandwidth as an alpha of zero. In

practice, it is possible to implement an alpha below 0.2 and make good,

compact, practical radios. Typical values range from 0.35 to 0.5, though

some video systems use an alpha as low as 0.11. The corresponding term for

a Gaussian filter is BT (bandwidth time product). Occupied bandwidth

cannot be stated in terms of BT because a Gaussian filter’s frequency

response does not go identically to zero, as does a raised cosine. Common

values for BT are 0.3 to 0.5.

4.5 Filter bandwidth effects

Different filter bandwidths show different effects. For example, look at a

QPSK signal and examine how different values of alpha effect the vector

diagram. If the radio has no transmitter filter as shown on the left of the

graph, the transitions between states are instantaneous. No filtering

means an alpha of infinity.

Transmitting this signal would require infinite bandwidth. The center

figure is an example of a signal at an alpha of 0.75. The figure on the right

shows the signal at an alpha of 0.375. The filters with alphas of 0.75 and

0.375 smooth the transitions and narrow the frequency spectrum required.

Different filter alphas also affect transmitted power. In the case of the

unfiltered signal, with an alpha of infinity, the maximum or peak power of

the carrier is the same as the nominal power at the symbol states. No extra

power is required due to the filtering.

25

QPSK Vector Diagrams

No Filtering a = 0.75 a = 0.375

Figure 22.

Effect of Different

Filter Bandwidth

Take an example of a ¹/4 DQPSK signal as used in NADC (IS-54). If an

alpha of 1.0 is used, the transitions between the states are more gradual

than for an alpha of infinity. Less power is needed to handle those

transitions. Using an alpha of 0.5, the transmitted bandwidth decreases

from 2 times the symbol rate to 1.5 times the symbol rate. This results in

a 25% improvement in occupied bandwidth. The smaller alpha takes

more peak power because of the overshoot in the filter’s step response.

This produces trajectories which loop beyond the outer limits of the

constellation.

At an alpha of 0.2, about the minimum of most radios today, there is a need

for significant excess power beyond that needed to transmit the symbol

values themselves. A typical value of excess power needed at an alpha of

0.2 for QPSK with Nyquist filtering would be approximately 5dB. This is

more than three times as much peak power because of the filter used to

limit the occupied bandwidth.

These principles apply to QPSK, offset QPSK, DQPSK, and the varieties

of QAM such as 16QAM, 32QAM, 64QAM, and 256QAM. Not all signals

will behave in exactly the same way, and exceptions include FSK, MSK and

any others with constant-envelope modulation. The power of these signals

is not affected by the filter shape.

4.6 Chebyshev equiripple FIR (finite impulse respone) filter

A Chebyshev equiripple FIR (finite impulse response) filter is used for

baseband filtering in IS-95 CDMA. With a channel spacing of 1.25 MHz

and a symbol rate of 1.2288 MHz in IS-95 CDMA, it is vital to reduce

leakage to adjacent RF channels. This is accomplished by using a filter

with a very sharp shape factor using an alpha value of only 0.113. A FIR

filter means that the filter’s impulse response exists for only a finite

number of samples. Equiripple means that there is a “rippled” magnitude

frequency-respone envelope of equal maxima and minima in the pass- and

stopbands. This FIR filter uses a much lower order than a Nyquist filter to

implement the required shape factor. The IS-95 FIR filter does not have

zero Inter Symbol Interference (ISI). However, ISI in CDMA is not as

important as in other formats since the correlation of 64 chips at a time is

used to make a symbol decision. This “coding gain” tends to average out the

ISI and minimize its effect.

26

Figure 23.

Chebyshev Equiripple

FIR Filter

4.7 Competing goals of spectral efficiency

and power consumption

As with any natural resource, it makes no sense to waste the RF spectrum

by using channel bands that are too wide. Therefore narrower filters are

used to reduce the occupied bandwidth of the transmission. Narrower

filters with sufficient accuracy and repeatability are more difficult to build.

Smaller values of alpha increase ISI because more symbols can contribute.

This tightens the requirements on clock accuracy. These narrower filters

also result in more overshoot and therefore more peak carrier power. The

power amplifier must then accommodate the higher peak power without

distortion. The bigger amplifier causes more heat and electrical interference

to be produced since the RF current in the power amplifier will interfere

with other circuits. Larger, heavier batteries will be required. The

alternative is to have shorter talk time and smaller batteries. Constant

envelope modulation, as used in GMSK, can use class-C amplifiers which

are the most efficient. In summary, spectral efficiency is highly desirable,

but there are penalties in cost, size, weight, complexity, talk time, and

reliability.

27

There are a number of different ways to view a signal. This simplified

example is an RF pager signal at a center frequency of 930.004 MHz. This

pager uses two-level FSK and the carrier shifts back and forth between two

frequencies that are 8 kHz apart (930.000 MHz and 930.008 MHz). This

frequency spacing is small in proportion to the center frequency of

930.004 MHz. This is shown in figure 24 (a). The difference in period

between a signal at 930 MHz and one at 930 MHz plus 8 kHz is very small.

Even with a high performance oscilloscope, using the latest in high-speed

digital techniques, the change in period cannot be observed or measured.

In a pager receiver the signals are first downconverted to an IF or baseband

frequency. In this example, the 930.004 MHz FSK-modulated signal

is mixed with another signal at 930.002 MHz. The FSK modulation causes

the transmitted signal to switch between 930.000 MHz and 930.008 MHz.

The result is a baseband signal that alternates between two frequencies,

–2 kHZ and +6 kHz. The demodulated signal shifts between –2 kHz and

+6 kHz. The difference can be easily detected.

This is sometimes referred to as “zoom” time or IF time. To be more specific,

it is a band-converted signal at IF or baseband. IF time is important as it

is how the signal looks in the IF portion of a receiver. This is how the IF of

the radio detects the different bits that are present. The frequency domain

representation is shown in figure 24 (c). Most pagers use a two-level,

Frequency-Shift-Keying (FSK) scheme. FSK is used in this instance

because it is less affected by multipath propagation, attenuation and

interference, common in urban environments. It is possible to demodulate

it even deep inside modern steel/concrete buildings, where attenuation,

noise and interference would otherwise make reliable demodulation

difficult.

28

5. Different ways of

looking at a digitallymodulated

signal time

and frequency domain

view

Time-Domain

Baseband

Time-Domain

"Zoom"

Freq.-Domain

Narrowband

24 (a)

24 (c)

24 (b)

8 kHz

Figure 24.

Time and Frequency

Domain View

5.1 Power and frequency view

There are many different ways of looking at a digitally-modulated signal.

To examine how transmitters turn on and off, a power-versus-time

measurement is very useful for examining the power level changes involved

in pulsed or bursted carriers. For example, very fast power changes will

result in frequency spreading or spectral regrowth. This is also known as

frequency “splatter”. Very slow power changes waste valuable transmit

time, as the transmitter cannot send data when it is not fully on. Turning

on too slowly can also cause high bit error rates at the beginning of the

burst. In addition, peak and average power levels must be well understood,

since asking for excessive power from an amplifier can lead to compression

or clipping. These phenomena distort the modulated signal and usually

lead to spectral regrowth as well.

5.2 Constellation diagrams

As discussed, the rectangular I/Q diagram is a polar diagram of magnitude

and phase. A two-dimensional diagram of the carrier magnitude and phase

(a standard polar plot) can be represented differently by superimposing

rectangular axes on the same data and interpreting the carrier in terms

of in-phase (I) and quadrature-phase (Q) components. It would be possible

to perform AM and PM on a carrier at the same time and send data this

way; it is easier for circuit design and signal processing to generate and

detect a rectangular, linear set of values (one set for I and an independent

set for Q).

The example shown is a ¹/4 Differential Quadrature Phase Shift Keying

(¹/4 DQPSK) signal as described in the North American Digital Cellular

(NADC) TDMA standard. This example is a 157-symbol DQPSK burst.

29

Frequency

Time

Amplitude

Time

Power vs.

Time

Freq. vs.

Time

DQPSK, 157 Symbols

and "Trajectory"

Constellation Diagram

DQPSK, 157 Symbol

Constellation with Noise

Polar Diagram

Q

I

Figure 25.

Power and Frequency

View

Figure 26.

Constellation Diagram

The polar diagram shows several symbols at a time. That is, it shows

the instantaneous value of the carrier at any point on the continuous

line between and including symbol times, represented as I/Q or

magnitude/phase values.

The constellation diagram shows a repetitive “snapshot” of that same

burst, with values shown only at the decision points. The constellation

diagram displays phase errors, as well as amplitude errors, at the decision

points. The transitions between the decision points affects transmitted

bandwidth. This display shows the path the carrier is taking but does not

explicitly show errors at the decision points. Constellation diagrams

provide insight into varying power levels,the effects of filtering, and

phenomena such as Inter-Symbol Interference.

The relationship between constellation points and bits per symbol is

M=2n where M = number of constellation points

n = bits/symbol

or n= log2 (M)

This holds when transitions are allowed from any constellation point to

any other.

5.3 Eye diagrams

Another way to view a digitally modulated signal is with an eye diagram.

Separate eye diagrams can be generated, one for the I-channel data and

another for the Q-channel data. Eye diagrams display I and Q magnitude

versus time in an infinite persistence mode, with retraces. The I and Q

transitions are shown separately and an “eye” (or eyes) is formed at the

symbol decision times. QPSK has four distinct I/Q states, one in each

quadrant. There are only two levels for I and two levels for Q. This forms

a single eye for each I and Q. Other schemes use more levels and create

more nodes in time through which the traces pass. The lower example is a

16QAM signal which has four levels forming three distinct “eyes”. The eye

is open at each symbol. A “good” signal has wide open eyes with compact

crossover points.

30

I-Mag Q-Mag

Time

QPSK

16QAM

I-Mag

Time

Figure 27.

I and Q Eye Diagrams

5.4 Trellis diagrams

This figure is called a “trellis” diagram, because it resembles a garden

trellis. The trellis diagram shows time on the X-axis and phase on the

Y-axis. This allows the examination of the phase transitions with different

symbols. In this case it is for a GSM system. If a long series of binary ones

were sent, the result would be a series of positive phase transitions of, in

the example of GSM, 90 degrees per symbol. If a long series of binary zeros

were sent, there would be a constant declining phase of 90 degrees per

symbol. Typically there would be intermediate transmissions with random

data. When troubleshooting, trellis diagrams are useful in isolating

missing transitions, missing codes, or a blind spot in the I/Q modulator

or mapping algorithm.

31

Phase

Time

GMSK Signal

(GSM) Phase

vs.

Time

Figure 28.

Trellis Diagram

The RF spectrum is a finite resource and is shared between users using

multiplexing (sometimes called channelization). Multiplexing is used to

separate different users of the spectrum. This section covers multiplexing

frequency, time, code, and geography. Most communications systems use

a combination of these multiplexing methods.

6.1 Multiplexing - frequency

Frequency Division Multiple-Access (FDMA) splits the available frequency

band into smaller fixed frequency channels. Each transmitter or receiver

uses a separate frequency. This technique has been used since around 1900

and is still in use today. Transmitters are narrowband or frequency-limited.

A narrowband transmitter is used along with a receiver that has a narrowband

filter so that it can demodulate the desired signal and reject unwanted

signals, such as interfering signals from adjacent radios.

6.2 Multiplexing - time

Time-division multiplexing involves separating the transmitters in time so

that they can share the same frequency. The simplest type is Time Division

Duplex (TDD). This multiplexes the transmitter and receiver on the same

frequency. TDD is used, for example, in a simple two-way radio where a

button is pressed to talk and released to listen. This kind of time division

duplex, however, is very slow. Modern digital radios like CT2 and DECT

use Time Division Duplex but they multiplex hundreds of times per second.

TDMA (Time Division Multiple Access) multiplexes several transmitters or

receivers on the same frequency. TDMA is used in the GSM digital cellular

system and also in the US NADC-TDMA system.

32

6. Sharing the channel

Narrowband

Transmitter

Narrowband

Receiver

TDMA Time Division Multiple-Access

1

2

3

TDD Time Division Duplex

Amplitude

Time

T R T R

A A A

B B B

C C C

A B C

Figure 29.

Multiplexing

- Frequency

Figure 30.

Multiplexing - Time

6.3 Multiplexing - code

CDMA is an access method where multiple users are permitted to transmit

simultaneously on the same frequency. Frequency division multiplexing is

still performed but the channel is 1.23 MHz wide. In the case of US CDMA

telephones, an additional type of channelization is added, in the form of

coding.

In CDMA systems, users timeshare a higher-rate digital channel by

overlaying a higher-rate digital sequence on their transmission. A different

sequence is assigned to each terminal so that the signals can be discerned

from one another by correlating them with the overlaid sequence. This is

based on codes that are shared between the base and mobile stations.

Because of the choice of coding used, there is a limit of 64 code channels

on the forward link. The reverse link has no practical limit to the number

of codes available.

6.4 Multiplexing - geography

Another kind of multiplexing is geographical or cellular. If two

transmitter/receiver pairs are far enough apart, they can operate on

the same frequency and not interfere with each other. There are only a

few kinds of systems that do not use some sort of geographic multiplexing.

Clear-channel international broadcast stations, amateur stations, and

some military low frequency radios are about the only systems that have

no geographic boundaries and they broadcast around the world.

33

˜˜ Frequency

Amplitude

Time

F1

1

2

3

4

1

2

3

4

F1'

Figure 31.

Multiplexing

- Code

Figure 32.

Multiplexing

- Geography

6.5 Combining multiplexing modes

In most of these common communications systems, different forms of

multiplexing are generally combined. For example, GSM uses FDMA,

TDMA, FDD and geographic. DECT uses FDMA, TDD and geographic

multiplexing. For a full listing see the table in section ten.

6.6 Penetration versus efficiency

Penetration means the ability of a signal to be used in environments where

there is a lot of attenuation or noise or interference. One very common

example is the use of pagers versus cellular phones. In many cases,

pagers can receive signals even if the user is inside a metal building or a

steel-reinforced concrete structure like a modern skyscraper. Most pagers

use a two-level FSK signal where the frequency deviation is large and the

modulation rate (symbol rate) is quite slow. This makes it easy for the

receiver to detect and demodulate the signal since the frequency difference

is large (the symbol locations are widely separated) and these different

frequencies persist for a long time (a slow symbol rate).

However, the factors causing good pager signal penetration also cause

inefficient information transmission. There are typically only two symbol

locations. They are widely separated (approximately 8 kHz), and a small

number of symbols (500 to 1200) are sent each second. Compare this with

a cellular system such as GSM which sends 270,833 symbols each second.

This is not a big problem for the pager since all it needs to receive is its

unique address and perhaps a short ASCII text message.

A cellular phone signal, however, must transmit live duplex voice. This

requires a much higher bit rate and a much more efficient modulation

technique. Cellular phones use more complex modulation formats (such

as ¹/4 DQPSK and 0.3 GMSK) and faster symbol rates. Unfortunately,

this greatly reduces penetration and one way to compensate is to use more

power. More power brings in a host of other problems, as described

previously.

34

7.1 A digital communications transmitter

Here is a simplified block diagram of a digital communications transmitter.

It begins and ends with an analog signal. The first step is to convert a

continuous analog signal to a discrete digital bit stream. This is called

digitization.

The next step is to add voice coding for data compression. Then some

channel coding is added. Channel coding encodes the data in such a way

as to minimize the effects of noise and interference in the communications

channel. Channel coding adds extra bits to the input data stream and

removes redundant ones. Those extra bits are used for error correction or

sometimes to send training sequences for identification or equalization.

This can make synchronization (or finding the symbol clock) easier for the

receiver. The symbol clock represents the frequency and exact timing of

the transmission of the individual symbols. At the symbol clock transitions,

the transmitted carrier is at the correct I/Q (or magnitude/phase) value to

represent a specific symbol (a specific point in the constellation). Then the

values (I/Q or magnitude/ phase) of the transmitted carrier are changed

to represent another symbol. The interval between these two times is the

symbol clock period. The reciprocal of this is the symbol clock frequency.

The symbol clock phase is correct when the symbol clock is aligned with

the optimum instant(s) to detect the symbols.

The next step in the transmitter is filtering. Filtering is essential for

good bandwidth efficiency. Without filtering, signals would have very fast

transitions between states and therefore very wide frequency spectra —

much wider than is needed for the purpose of sending information. A single

filter is shown for simplicity, but in reality there are two filters; one each

for the I and Q channels. This creates a compact and spectrally efficient

signal that can be placed on a carrier.

The output from the channel coder is then fed into the modulator. Since

there are independent I and Q components in the radio, half of the

information can be sent on I and the other half on Q. This is one reason

digital radios work well with this type of digital signal. The I and Q

components are separate.

The rest of the transmitter looks similar to a typical RF transmitter or

microwave transmitter/receiver pair. The signal is converted up to a higher

intermediate frequency (IF), and then further upconverted to a higher

radio frequency (RF). Any undesirable signals that were produced by the

upconversion are then filtered out.

35

7. How digital

transmitters and

receivers work

A/D

I Mod I

Q Q

IF RF

Processing/

Compression/

Error Corr

Encode

Symbols

Figure 33.

A Digital Transmitter

7.2 A digital communications receiver

The receiver is similar to the transmitter but in reverse. It is more complex

to design. The incoming (RF) signal is first downconverted to (IF) and

demodulated. The ability to demodulate the signal is hampered by factors

including atmospheric noise, competing signals, and multipath or fading.

Generally, demodulation involves the following stages:

1. carrier frequency recovery (carrier lock)

2. symbol clock recovery (symbol lock)

3. signal decomposition to I and Q components

4. determining I and Q values for each symbol (“slicing”)

5. decoding and de-interleaving

6. expansion to original bit stream

7. digital-to-analog conversion, if required

In more and more systems, however, the signal starts out digital and stays

digital. It is never analog in the sense of a continuous analog signal like

audio. The main difference between the transmitter and receiver is the

issue of carrier and clock (or symbol) recovery.

Both the symbol-clock frequency and phase (or timing) must be correct

in the receiver in order to demodulate the bits successfully and recover the

transmitted information. A symbol clock could be at the right frequency

but at the wrong phase. If the symbol clock was aligned with the transitions

between symbols rather than the symbols themselves, demodulation would

be unsuccessful.

Symbol clocks are usually fixed in frequency and this frequency is accurately

known by both the transmitter and receiver. The difficulty is to get them

both aligned in phase or timing. There are a variety of techniques and

most systems employ two or more. If the signal amplitude varies during

modulation, a receiver can measure the variations. The transmitter can

send a specific synchronization signal or a predetermined bit sequence

such as 10101010101010 to “train” the receiver’s clock. In systems with a

pulsed carrier, the symbol clock can be aligned with the power turn-on of

the carrier.

In the transmitter, it is known where the RF carrier and digital data clock

are because they are being generated inside the transmitter itself. In the

receiver there is not this luxury. The receiver can approximate where the

carrier is but has no phase or timing symbol clock information. A difficult

task in receiver design is to create carrier and symbol-clock recovery

algorithms. That task can be made easier by the channel coding performed

in the transmitter.

36

AGC Demod Q

I I

Q

Adaption/

Process/

Decompress

D/A

RF IF

Decode

Bits

Figure 34.

A Digital Receiver

Complex tradeoffs in frequency, phase, timing, and modulation are

made for interference-free, multiple-user communications systems. It is

necessary to accurately measure parameters in digital RF communications

systems to make the right tradeoffs. Measurements include analyzing the

modulator and demodulator, characterizing the transmitted signal quality,

locating causes of high Bit-Error-Rate and investigating new modulation

types. Measurements on digital RF communications systems generally fall

into four categories: power, frequency, timing, and modulation accuracy.

8.1 Power measurements

Power measurements include carrier power and associated measurements

of gain of amplifiers and insertion loss of filters and attenuators. Signals

used in digital modulation are noise-like. Band-power measurements

(power integrated over a certain band of frequencies) or power spectral

density (PSD) measurements are often made. PSD measurements

normalize power to a certain bandwidth, usually 1 Hz.

8.1.1 Adjacent channel power

Adjacent channel power is a measure of interference created by one user

that effects other users in nearby channels. This test quantifies the

energy of a digitally-modulated RF signal that spills from the intended

communication channel into an adjacent channel. The measurement result

is the ratio (in dB) of the power measured in the adjacent channel to the

total transmitted power. A similar measurement is alternate channel

power which looks at the same ratio two channels away from the intended

communication channel.

37

8. Measurements on

digital RF

communications

systems

TRACE A: Ch1 IQ Ref Time

A Ofs 38.500000 sym 3.43 dB 23.465 deg

100 uV

I-Q

20 uV/div

-100 uV

Amplitude

Frequency

GSM-TDMA

Signal

t

Figure 35.

Power Measurement

Figure 36.

Power and Timing

Measurements

For pulsed systems (such as TDMA), power measurements have a time

component and may have a frequency component, also. Burst power profile

(power versus time) or turn-on and turn-off times may be measured.

Another measurement is average power when the carrier is on or averaged

over many on/off cycles.

8.2 Frequency measurements

Frequency measurements are often more complex in digital systems since

factors other than pure tones must be considered. Occupied bandwidth is an

important measurement. It ensures that operators are staying within the

bandwidth that they have been allocated. Adjacent channel power is also

used to detect the effects one user has on other users in nearby channels.

8.2.1 Occupied bandwidth

Occupied bandwidth (BW) is a measure of how much frequency spectrum

is covered by the signal in question. The units are in Hz, and measurement

of occupied BW generally implies a power percentage or ratio. Typically,

a portion of the total power in a signal to be measured is specified.

A common percentage used is 99%. A measurement of power versus

frequency (such as integrated band power) is used to add up the power to

reach the specified percentage. For example, one would say “99% of the

power in this signal is contained in a bandwidth of 30 kHz.” One could also

say “The occupied bandwidth of this signal is 30 kHz” if the desired power

ratio of 99% was known.

Typical occupied bandwidth numbers vary widely, depending on symbol

rate and filtering. The figure is about 30 kHz for the NADC ¹/4 DQPSK

signal and about 350 kHz for a GSM 0.3 GMSK signal. For digital video

signals occupied bandwidth is typically 6 to 8 MHz.

Simple frequency-counter-measurement techniques are often not accurate

or sufficient to measure center frequency. A carrier “centroid” can be

calculated which is the center of the distribution of frequency versus PSD

for a modulated signal.

38

fo

Figure 37.

Frequency

Measurements

8.3 Timing measurements

Timing measurements are made most often in pulsed or burst systems.

Measurements include pulse repetition intervals, on-time, off-time, duty

cycle, and time between bit errors. Turn-on and turn-off times also involve

power measurements.

8.4 Modulation accuracy

Modulation accuracy measurements involve measuring how close either

the constellation states or the signal trajectory is relative to a reference

(ideal) signal trajectory. The received signal is demodulated and compared

with a reference signal. The main signal is subtracted and what is left is

the difference or residual. Modulation accuracy is a residual measurement.

Modulation accuracy measurements usually involve precision

demodulation of a signal and comparison of this demodulated signal

with a (mathematically-generated) ideal or “reference” signal. The

difference between the two is the modulation error, and it can be expressed

in a variety of ways including Error Vector Magnitude (EVM), magnitude

error, phase error, I-error and Q-error. The reference signal is subtracted

from the demodulated signal, leaving a residual error signal. Residual

measurements such as this are very powerful for troubleshooting. Once the

reference signal has been subtracted, it is easier to see small errors that

may have been swamped or obscured by the modulation itself. The error

signal itself can be examined in many ways; in the time domain or (since it

is a vector quantity) in terms of its I/Q or magnitude/phase components.

A frequency transformation can also be performed and the spectral

composition of the error signal alone can be viewed.

8.5 Understanding Error Vector Magnitude

Recall first the basics of vector modulation: Digital bits are transferred

onto an RF carrier by varying the carrier’s magnitude and phase. At each

symbol-clock transition, the carrier occupies any one of several unique

locations on the I versus Q plane. Each location encodes a specific data

symbol, which consists of one or more data bits. A constellation diagram

shows the valid locations (i.e., the magnitude and phase relative to the

carrier) for all permitted symbols of which there must be 2n, given n bits

transmitted per symbol. To demodulate the incoming data, the exact

magnitude and phase of the received signal for each clock transition must

be accurately determined.

The layout of the constellation diagram and its ideal symbol locations is

determined generically by the modulation format chosen (BPSK, 16QAM,

¹/4 DQPSK, etc.). The trajectory taken by the signal from one symbol

location to another is a function of the specific system implementation,

but is readily calculated nonetheless.

At any moment, the signal’s magnitude and phase can be measured.

These values define the actual or “measured” phasor. At the same time, a

corresponding ideal or “reference” phasor can be calculated, given knowledge

of the transmitted data stream, the symbol-clock timing, baseband filtering

parameters, etc. The differences between these two phasors form the

basis for the EVM measurements.

39

Figure 38 defines EVM and several related terms. As shown, EVM is the

scalar distance between the two phasor end points, i.e. it is the magnitude

of the difference vector. Expressed another way, it is the residual noise

and distortion remaining after an ideal version of the signal has been

stripped away.

In the NADC-TDMA (IS-54) standard, EVM is defined as a percentage of

the signal voltage at the symbols. In the ¹/4 DQPSK modulation format,

these symbols all have the same voltage level, though this is not true of

all formats. IS-54 is currently the only standard that explicitly defines

EVM, so EVM could be defined differently for other modulation formats.

In a format such as 64QAM, for example, the symbols represent a variety

of voltage levels. EVM could be defined by the average voltage level of all

the symbols (a value close to the average signal level) or by the voltage of

the outermost (highest voltage) four symbols. While the error vector has a

phase value associated with it, this angle generally turns out to be random

because it is a function of both the error itself (which may or may not be

random) and the position of the data symbol on the constellation (which,

for all practical purposes, is random). A more useful angle is measured

between the actual and ideal phasors (I/Q phase error), which contains

information useful in troubleshooting signal problems. Likewise, I-Q

magnitude error shows the magnitude difference between the actual and

ideal signals. EVM, as specified in the standard, is the root-mean-square

(RMS) value of the error values at the instant of the symbol-clock

transition. Trajectory errors between symbols are ignored.

8.6 Troubleshooting with error vector measurements

Measurements of error vector magnitude and related quantities can,

when properly applied, provide much insight into the quality of a digitally

modulated signal. They can also pinpoint the causes for any problems

uncovered by identifying exactly the type of degradation present in a

signal and even help identify their sources. For more detail on using

error-vector-magnitude measurements to analyze and troubleshoot

vector-modulated signals, see product note 89400-14. The Hewlett-Packard

literature number is 5965-2898E.

40

{

I

Q

Magnitude Error

(IQ error mag)

Error Vector

Ideal (Reference) Signal

Phase Error (IQ error phase)

Measured

Signal

f

Figure 38.

EVM and Related

Quantities

EVM measurements are growing rapidly in acceptance, having already

been written into such important system standards as NADC and PHS, and

they are poised to appear in several upcoming standards including those

for digital video transmission.

8.7 Magnitude versus phase error

Different error mechanisms affect signals in different ways: in magnitude

only, phase only, or both simultaneously. Knowing the relative amounts of

each type of error can quickly confirm or rule out certain types of problems.

Thus, the first diagnostic step is to resolve EVM into its magnitude and

phase error components (see figure 38) and compare their relative sizes.

When the average phase error (in degrees) is substantially larger

than the average magnitude error (in percent), some sort of unwanted

phase modulation is the dominant error mode. This could be caused by

noise, spurious or cross-coupling problems in the frequency reference,

phase-locked loops, or other frequency-generating stages. Residual AM is

evidenced by magnitude errors that are significantly larger than the

phase angle errors.

8.8 I/Q phase error versus time

Phase error is the instantaneous angle difference between the measured

signal and the ideal reference signal. When viewed as a function of time

(or symbol), it shows the modulating waveform of any residual or interfering

PM signal. Sinewaves or other regular waveforms indicate an interfering

signal. Uniform noise is a sign of some form of phase noise (random jitter,

residual PM/FM, etc.).

41

5

deg

Phase

–5

0 Sym 99 Sym

MSK1 Phs Error 1

Figure 39.

Incidental (inband)

PM sinewave is

clearly visible even at

only three degrees

peak-to-peak.

A perfect signal will have a uniform constellation that is perfectly symmetric

about the origin. I/Q imbalance is indicated when the constellation is not

“square”, i.e. when the Q-axis height does not equal the I-axis width.

Quadrature error is seen in any “tilt” to the constellation. Quadrature

error is caused when the phase relationship between the I and Q vectors

is not exactly 90 degrees.

8.9 Error Vector Magnitude versus time

EVM is the difference between the input signal and the internally-generated

ideal reference. When viewed as a function of symbol or time, errors may

be correlated to specific points on the input waveform, such as peaks

or zero crossings. EVM is a scalar (magnitude-only) value. Error peaks

occurring with signal peaks indicate compression or clipping. Error peaks

that correlate to signal minima suggest zero-crossing nonlinearities.

An example of zero-crossing nonlinearities is in a push-pull amplifier,

where the positive and negative halves of the signal are handled by

separate transistors. It can be quite a challenge (especially in high-power

amplifiers) to precisely bias and stabilize the amplifiers such that one set

is turning off exactly as the other set is turning on, with no discontinuities.

The critical moment is zero crossing, a well-known effect in analog design.

It is also known as zero-crossing errors, distortion, or nonlinearities.

42

5

deg

Real

–5

0 Sym 99 Sym

16QAM Phs Error 1

3

%

Magnitude

0

2

Magnitude

0

32QAM Err V Tim 1

40 Sym 80 Sym

32QAM Meas Time 1

40 Sym 80 Sym

Figure 40.

Phase noise appears

random in the time

domain.

Figure 41.

EVM peaks on this

signal (upper trace)

occur every time the

signal magnitude

(lower trace)

approaches zero.

This is probably a

zero-crossing error

in an amplification

stage.

8.10 Error spectrum (EVM versus frequency)

The error spectrum is calculated from the Fast Fourier Transform (FFT)

of the EVM waveform and results in a frequency-domain display that

can show details not visible in the time domain. In most digital systems,

nonuniform noise distribution or discrete signal peaks indicate the

presence of externally-coupled interference.

For more detail on EVM measurements, see product note 89400-14

“Using Error-Vector-Magnitude Measurements to Analyze and Troubleshoot

Vector-Modulated Signals.” The Hewlett-Packard literature number is

5965-2898E.

43

30

dB%

rms

Mag (dB)

-120

825.962 MHz 826.038 MHz

PI/4 Err V Spec 1

30

dB%

rms

Mag (dB)

-120

825.962 MHz 826.038 MHz

PI/4 Err V Spec 1

Figure 42.

Interference from

adjacent (lower)

channel causes

uneven EVM spectral

distribution.

Figure 43.

Switching-powersupply

interference

appears as EVM

spur, offset from

carrier by 10kHz.

Communication system design requires the simultaneous conservation of

bandwidth, power, and cost. In the past, it was possible to make a radio

low cost by sacrificing parameters such as power and bandwidth efficiency.

This application note has presented the building blocks of any

communications system. With these concepts, you will be able to

understand how communications systems work, and make more informed

decisions regarding the tradeoffs required to optimize your system.

9. Summary

GSM900 NADC PDC CDMA

Geography Europe North America Japan North America,

Korea, Japan

Introduction 1992 1992 1993-1994 1995-1997

Frequency Range 935-960 MHz down 869-894 MHz down 810-826 MHz down 824-849 MHz (US)

890-915 MHz up 824-849 MHz up 940-956 MHz up 869-894 MHz (US)

EGSM 925-960 MHz 1777-1801 MHz down 832-834, 843-846,

880-915 MHz 1429-1453 MHz up 860-870 MHz (Japan)

887-889, 898-901,

915-925 MHz (Japan)

Data Structure TDMA TDMA TDMA CDMA

Channel per 8-16 3-6 3-6 32-64 (Dyn. adapt)

Frequency

Modulation 0.3 GMSK ¹/4 DQPSK ¹/4 DQPSK Mobile: QPSK

(1 bit/symbol) (2 bits/symbol) (2 bits/symbol) Base: OQPSK

(1 bit/symbol)

Speech CODEC RELP-LTP VSELP 8 Kbits/s VSELP 8 Kbits/s 8 Kbits/s var rate CELP

13 Kbits/s EFR 13 kbit/s var rate CELP

Mobile Output 3.7mW to 20W 2.2mW to 6W .3W to 3W 10nW to 1W

Power

Modulation 270.833 Kbits/s 48.6 Kbits/s 42 Kbits/s 9600/14,400 bps data;

Data Rate (1 bit/symbol) (2 bits/symbol) (2 bits/symbol) 1.2288 Mb/s spreading

Filter 0.3 Gaussian SQRT raised cosine SQRT raised cosine Chebychev low

a = .35 a = .50 pass (FIR)

Channel Spacing 200 kHz 30 kHz 50 kHz 1.23 MHz

25 kHz interleave

Number of 124 frequency ch. 832 frequency ch. 1600 frequency ch. 19-20 frequencies

Channels w/8 timeslots per ch. w/3 users per ch. w/3 users per ch.

(1000) (2496) (4800)

Est # of 15-20 million 35-40 million 5 million

Subscribers by (8.9 million 9/92)

year 2000

Source GSM Standard IS-54 RCR Spec IS-95 spec

Std 27B

Service Public Cellular Public Cellular Public Cellular Public Cellular

44

10. Overview of

communications

systems

DCS1800 PHS DECT TETRA

Trans European

Trunked Radio

Geography Europe Japan/China Europe/China Europe

Introduction 1993 1993 Private office 1993 1995

1995 Public

Frequency Range 1.7-1.9 GHz 1895-1918 MHz 1.897-1.913 GHz 450 MHz

1710-1785 MHz down up/down <>

1805-1880 MHz up 1.9, 1.93 GHz (China) 1.9, 1.93 GHz (China)

Data Structure TDMA TDMA/TDD TDMA/TDD TDMA

Channel per 8-16 4-8 12 4

Frequency

Modulation 0.3 GMSK ¹/4 DQPSK 0.5 GFSK ¹/4 DQPSK

(1 bit/symbol) (2 bits/symbol) ±202-403 kHz dev

(1 bit/symbol)

Speech CODEC RELP-LTP ADPCM ADPCM Includes channel

13 Kbits/s 32 Kbits/s 32 Kbits/s & speech coding

7.2 Kbits/s

Mobile Output 250mW to 2W 10mW 250mW

Power

Modulation Data 270.833 Kbits/s 384 Kbits/s 1.152 Mbit/s 19.2 Kb/s

Rate

Filter 0.3 Gaussian SQRT raised cosine 0.5 Gaussian a = 0.4 SQRT

a = .50 raised cosine

Channel Spacing 200 kHz 300 kHz 1.728 MHz 25 kHz

Number of 3000-6000 10 carrier frequencies

Channels w/12 users per

frequency (120)

Est # of Subscribers 4-13 million 6.5-13 million

by year 2000

Source prI-ETS 30 176 RCR spec Std 28 CI Spec., Part 1, Mobile Europe

prETS 300 175-2 China-First News Rev 05.2e Magazine 1/92

Release 8/15/96 China-First News

Release 8/15/96

Service Personal Cordless Telephone Wireless PBX Trunked system

Communications Personal Adj. ch. sel > 60 dB

Communications

45

10. Overview of

communications

systems

ACP Adjacent Channel Power

ADPCM Adaptive Digital Pulse Code Modulation

AM Amplitude Modulation

AMPS Advanced Mobile Phone System

B-CDMA Broadband Code Division Multiple Access

BER Bit Error Rate

BPSK Binary Phase Shift Keying

BFSK Binary Frequency Shift Keying

BW Bandwidth

CDMA Code Division Multiple Access

CDPD Cellular Digital Packet Data

COFDM Coded Orthogonal Frequency Division Multiplexing

CRC Cyclic Redundancy Check

CT2 Cordless Telephone - 2

DAB Digital Audio Broadcast

DCS 1800 Digital Communication System - 1800 MHz

DECT Digital Enhanced Cordless Telephone

DMCA Digital MultiChannel Access, similar to iDEN

DQPSK Differential Quadrature Phase Shift Keying

DSP Digital Signal Processing

DVB-C Digital Video Broadcast - Cable

DVB-S Digital Video Broadcast - Satellite

DVB-T Digital Video Broadcast - Terrestrial

EGSM Extended Frequency GSM

ERMES European Radio Message System

ETSI European Telecommunications Standards Institute

EVM Error Vector Magnitude

FDD Frequency Division Duplex

FDMA Frequency Division Multiple Access

FER Frame Error Rate

FFSK Fast Frequency Shift Keying

FFT Fast Fourier Transform

FLEX 4-level FSK-based paging standard developed by

Motorola

FM Frequency Modulation

FSK Frequency Shift Keying

GFSK Gaussian Frequency Shift Keying

Globalstar Satellite system using 48 low-earth orbiting

satellites

GSM Global System for Mobile Communication

GMSK Gaussian Minimum Shift Keying

HDTV High Definition Television

iDEN integrated Dispatch Enhanced Network (Motorola

designed system for dispatch, cellular and conference

calling)

46

11. Glossary of terms

IF Intermediate Frequency

I/Q In phase / Quadrature

Iridium Motorola voice/data 66-satellite system worldwide

ISI Intersymbol Interference

IS-54 Interim Standard for US Digital Cellular (NADC)

IS-95 Interim Standard for US Code Division Multiple

Access

IS-136 Interim Standard for NADC with Digital Control

Channels

LMDS Local Multipoint Distribution System

MFSK Minimum Frequency Shift Keying

MMDS Multichannel Multipoint Distribution System

MPSK Minimum Phase Shift Keying

MSK Minimum Shift Keying

NADC North American Digital Cellular system

OFDM Orthogonal Frequency Division Multiplexing

OQPSK Offset Quadrature Phase Shift Keying

PACS Personal Access Communications Service

PCS Personal Communications System

PCM Pulse Code Modulation

PDC Pacific Digital Cellular System (formerly JDC)

PHS Personal Handyphone System (formerly PHP)

PRBS Pseudo-Random Bit Sequence

PSD Power Spectral Density

PSK Phase Shift Keying

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying

RAM Wireless data network

RF Radio Frequency

RMS Root Mean Square

SQRT Square Root

TDD Time Division Duplex

TDMA Time Division Multiple Access

TETRA Trans European Trunked Radio

TFTS Terrestrial Flight Telephone System

VSB Vestigal Side Band

WLL Wireless Local Loop

47

11. Glossary of terms

(cont’d)

For more information about

Hewlett-Packard test and measurement

products, applications,

services, and for a current sales

office listing, visit our web site,

http://www.hp.com/go/tmdir. You

can also contact one of the following

centers and ask for a test and

measurement sales representative.

United States:

Hewlett-Packard Company

Test and Measurement Call Center

P.O. Box 4026

Englewood, CO 80155-4026

1 800 452 4844

Canada:

Hewlett-Packard Canada Ltd.

5150 Spectrum Way

Mississauga, Ontario L4W 5G1

(905) 206 4725

Europe:

Hewlett-Packard

European Marketing Centre

P.O. Box 999

1180 AZ Amstelveen

The Netherlands

(31 20) 547 9900

Japan:

Hewlett-Packard Japan Ltd.

Measurement Assistance Center

9-1, Takakura-Cho, Hachioji-Shi,

Tokyo 192, Japan

Tel: (81) 426-56-7832

Fax: (81) 426-56-7840

Latin America:

Hewlett-Packard

Latin American Region Headquarters

5200 Blue Lagoon Drive, 9th Floor

Miami, Florida 33126, U.S.A.

(305) 267 4245/4220

Australia/New Zealand:

Hewlett-Packard Australia Ltd.

31-41 Joseph Street

Blackburn, Victoria 3130, Australia

1 800 629 485

Asia Pacific:

Hewlett-Packard Asia Pacific Ltd.

17-21/F Shell Tower, Times Square,

1 Matheson Street, Causeway Bay,

Hong Kong

Tel: (852) 2599 7777

Fax: (852) 2506 9285

Data Subject to Change

Copyright © 1997

Hewlett-Packard Company

Printed in U.S.A. 7/97

5965-7160E

®