NTIA-REPORT-79-29

Methods of Improving

the Performances of

HF Digital Radio Systems

c.c. Watterson

u.s. DEPARTMENT OF COMMERCE

Juanita M. Kreps, Secretary

".

Henry Geller, Assistant Secretary

for Communications and ·Information

October 1979

PREFACE

The work described in this report was done for and with

the support of the U. S. Army Communications-Electronics

Engineering Installation Agency, Fort Huachuca, Arizona,

under Project Order Number CCC-PO-14-78.

iii

TABLE OF CONTENTS

PREFACE

LIST OF FIGURES

LIST OF TABLES

ABSTRACT

1. INTRODUCTION

2. HF DIGITAL RADIO SYSTEMS

3. TRANSMITTER

3 •1 Error Coder

3 • 2 Modulator

3 • 3 HF Transmitter

3. 4 Transmitting Antenna

4. HF CHANNEL

4. 1 Propagation Characteristics

4 • 2 Channel Model

5. RECEIVER

5.1 Receiving Antenna

5.2 HF Receiver

5 • 3 De modulator

5.4 Error Decoder

5.5 Diversity Operation

5.6 Performance Monitoring and Prediction

6. SYSTEM PERFORMANCES

6 •1 Additive Distortions

6. 2 Multiplicative Distortions

6.3 Nonlinear Distortions

7. PERFORMANCE IMPROVEMENTS

7.1 System Design

7 • 2 Syste m Operation

8. SUMMARY AND CONCLUSIONS

9. RECOMMENDATIONS

10. ACKNOWLEDGEMENTS

11. REFERENCES

v

Page

iii

vi

vii

1

1

3

9

9

10

29

31

35

35

39

46

46

47

49

68

72

74

76

77

90

108

113

113

121

122

127

127

127
LIST OF FIGURES

...Ftgur-e

4

22

27

21

25

38

30

36

17

14

1. Basic HF dig'ital r-adtosystem,

"2. Examples of amplftude aoftr-ains of complex pulses.

3. Examples of single -fi.lter complex keying values.

4. Orthonormal 'parabolic cylinder waveforms•

5. Pulse distributions infrequency and tirrie with M-ary ASK,

PSK, and APSK.

6. Pulse distributions in frequency and time with binaryFS'K~

7. Pulse .distr-Ibutdons in frequency and tdrne withbinary Cf-K,

8. Typical HFexciter.

'9. Hypothetical ionograms

10. Maximumdiffer-ential; delayver-sus relative operating

frequency for HF channels.

;1,1. Maxirnnmdiffer-entfal-de.lay versus drstance for HF channels. 38

12. HF channel model. 40

13. Path-gain spectrum. . 43

14. Hypothetical channel scatter function. 43

15. Typical HF receiver. 48

16. Portions of demodulators' for pulse train A. 50

<.,,'17. Characteristics of matched-filter system with binary PSK 53

under ideal conditions.

,18. Matrices for soft decoding ofa(25,16) block code. 70

,19. Bit-error-probability performances of matched-filter ASK, 80

PSK, FSK, and CPK systems over a slow, frequency-flat,

Rayleigh-fading channel with white thermal noise.

20. Bit-error-probability performances of matched-filter coherent 87

binary and quaternary PSK systems over slow, frequency-flat,

independently Rayleigh-fading diversity channels withindependent white thermal noise and maximal-ratio combining.

21. Bit-error-probability performances of nonmatched-filter, 89

frequency-multiplexed, time-differentially coherent, quaternary PSK systems with and without (25,16) soft error-correcting coding over a slow, frequency-flat, Rayleigh-fading channel

with white thermal noise.

vi
Figure Page

22. Perspective plot of the magnitude of the response of 93

a detector with guard time to a rectangular pulse.

23 • Contour plot of the magnitude of the response of a 94

detector with guard time to a rectangular pulse.

24. Perspective plot of the magnitude of a hypothetical detector 98

response with zero total derivatives as well as zeros at

the locations of undesired pulses in a system with frequencymultiplexed pulse trains.

25. Example of coherence multiplicative distortions in the 99

succeeding demodulator pulse samples in a single-filter

ASK,PSK, or APSKsystem with K~(t)= 1 in the absence

of additive and crosstalk multiplicative distortions.

26. Bit-error-probability performances of nonmatched-filter, 102

frequency-multiplexed, time-differentially coherent,

quaternary PSK systems over a frequency-flat, Rayleighfading channel.

27. Bit and block error-probability performances of the USC-lO, 109

ACQ-6, and MX-190 frequency-multiplexed, time-differentially coherent, quaternaryPSK modems over a two-path,

frequency-selective, Rayleigh-fading channel.

LIST OF TABLES

Table

1. Permutations of N bits

2. Keying methods for various bit-decision methods

3. Channel and equipment distortions

vii

11

58

78

lVIETHODS OF IMPROVING THE PERFORMANCES

OF HF DIGITAL RADIO SYSTEMS

Clark C. Watter-son"

The bit-error-probability performances of HF digital radio

systems with respect to channel and equipment additive , multiplicative, and nonlinear distortions are evaluated with respect

to the nine system design features that affect the performances.

The system design features are the fundamental pulse wavefor-m,

the keying method (ASK1 PSK1 APSK1 FSK, and CPK)I the

multiplexing method (frequency and concentric multiplexing ),

the type of demodulator filter (matched and nonmatched nonadaptive filters and quasi-static and dynamic adaptive f'ilter s ),

the detection method (coher-ent , partially cohe t-ent , differentially

coherent 1 and noncohe r'ent ), the transmitter power 1 the antennas,

diversity 1 and error coding. Spectral efficiency (information

rate Isignal bandwidth) is also evaluated . The be st combination

of system design features is determined.

Key Words: Adaptive fil'ter-ing , additive distortion, APSK, ASK,

bit error probability 1 bit error rate, channel modeI, coding,

coherent, CPK, dete ction, differentially coherent, digital,

distor'tion, diver-slty, error r-ate , fading, FSK1 HF, ionosphere"

keying, modem, multipath, multiplexing1 multiplicative distortion, noricoher-ent , nonlinear distortion" partially coherent"

performance" PSK, radio" spectral efficiency.

1. INTRODUCTION

For a number of decades" HF ionospheric radio has been a reasonably

simple and effective method of communicating over a very large range of

-distances: from less than 100 miles (the upper limit of the range of VHF

and UHFline-of-sight radio) to many thousands of miles (wor-Id-wide ).

HF radio has been particularly useful where cable communication is

impossible or impractical: for communication with aircraft" ships" and

other mobile units; and for communication with temporary and remote

*The author is with the Institute for Telecommunication Sciences"

National Telecommunications and Information Administration, U. S,

Department of Commerce" Boulder, Colorado 80303,.
ground stations.

In recent ye ars , the rapid development of SHF satellite radio has

provided an alternate method of communication with .mobi.le units and

remote ground stations over the same large range of distances 0 Because

SHF satellite radio can be competitive in cost and is usually superior in

performance and reliabilityI it almost certainly will.replace HF ionospheric radio as the predominant mode of long-distance communication

with mobile units and remote ground stations.

Despite its usual superiorityJ however J SHF satellite radio is greatly

inferior to HF ionospheric radio in one respect: in military communications under wartime conditions, it is (or probably will be) much more

susceptible to destruction by an enemy. For this r-eaaon, the armed

forces need to retain an efficient and reliable capability in HF ionospheric

radio as a backup to the more vulnerable SHF satellite radio. It is therefore important to improve the performance and reliability of HF ionospheric radio communication.

During the past three de cade s , the development and use of transistors

. and integrated circuits has substantially improved the weight, power

r-equir-ements , and reliability of HF radio equipment. However J little has

been done to reduce or overcome the performance degradations imposed

by multipath, fading, interfer-ence, and other types of channel distortions

characteristic of HF radio. While the general replacement of AM (amplitude modulation) with SSB (single sideband) has improved analog voice

communtcattons, essentially no improvements have been made in signal

processing techniques in digital communications: The same FSK (frequency-shift keying) and PSK (phase-shift keying) techniques introduced

some decades ago are still in universal use" and despite the development

of effective error-detecting I correcting coding te chntques, the armed

forces have made little use of this improvement in HF digital radio systems.

The performance and reliability of HF digital radio can be very substantially improved by the development and use of a number of improved

signal pr-oce saingtechnique s , The present availability of integrated circuits

2
in general and micr-opr-oce ssors in particular make the application of

such techniques very practical. With this in mind, the purpose of the

present report is to present general and detailed descriptions of HF

digital radio systems that include classifications and descriptions of

system design features, HF ionospheric channel characteristics, and

the types of channel and equipment distortions that degrade system performance; to relate the equipment design features to the various types

of channel and equipment distortions to determine the best methods of

improving system performance; and to present suitable conclusions

and recommendations.

2. HF DIGITAL RADIO SYSTEMS

The functional form of a basicHF digital radio system is illustrated

in Figure 1. The system consists of three major parts: the transmitter

on the left, the HF ionospheric channel at the top, and the receiver on the

right. In gener-alj vthetransmttter consists of an error coder, a modulator, an HF transmitter, and an antenna, while the receiver consists of

an antenna, an HFreceiver, a demodulator, and an error decoder.

Unlike the other parts of the transmitter and receiver, the error coder

and error decoder are optional; most military HF digital radio systems

at present do not use them.

Regardless of its actual format, the digital information to be transmitted can be viewed'aaa binary sequence of information brts, bl (i}, with

values of zero or one that occur at a constant rate, fl-With error coding,

the transmitter input binary information sequence,b1(I), is delivered to

an encoder. The encoder uses the information bits to generate additional

check bits in a manner determined by an encoding algorithm. The information and che ck bits are combined to form an encoder output binary

data sequence, b 2(j ), that is delivered to the modulator. The binary data

sequence, b 2(j) , has values of zero or one that occur at a constant rate,

f

2, that is greater than f1because of the introduction of~fhe check bits.

3
HF Channel

Q)

>

Q)

o

Q)

a::

Error

Decoder

z(t)

HF

Receiver

Demodulator

Output

Binary Information

Sequence

i--

I

I

J

I

L __

l

I

I

t

I

_ J

~. xlt)

HF

Transmitter

h

w(f)

Modulator

a

b2 ( j ) f2

4"'--

Error

Coder

4"'--

b1(i) f1

+

Input

BincryTnforrnction

Sequence

E

en

c:

o

...

....

Figure 1. Basic HF digital radio system,

4
When error coding is not u sed , the information bits are delivered

directly to the modulatorI as shown by the dashed line in Figure 1.

The modulator generates one or more trains of IF pulses that are

multiplexed and transmitted simultaneously over separate subchannels.

The pulses may have any shape and time spacing, but usually are adjoining rectangular pulses. Each pulse is keyed or selected by the data

sequence from a set of two or more pulse waveforms that differ in amplitude , phase , fr-equency, or other waveshape characteristics. In nearly

all aystems, the number of selectable pulse waveforms is an integral

power of two. Each keyed or selected pulse via its distinctive waveform

then carries an integral number of data bits , usually one or two.

The one or more trains of low-level keyed IF pulses , w(t) in Figure

11 are delivered by the modulator to an HF transmitter. The HF transmitter frequency translates the trains of IF pulses (which are usually

generated in the ELF band) to the desired frequency in the HF band, and

filters and amplifies the resulting trains of HF pulses to a suitably higher

power level. The higher power trains of HFpulses" X(t)1 are delivered

by the HF transmitter to the transmitting antenna which radiates them.

The radiated trains of HF pulses constitute the HF transmitted signal.

The HF transmitted signal travels to the receiving antenna by

reflection from the ionosphere. Because the HF signal generally propagates to the receiving antenna over several fading paths (involving one

or more reflections from several layers in the ionosphere)" it arrives

at the receiving antenna in a distorted form. The receiving· antenna also

receives noise and sometimes interference (unwanted signals) in the same

frequency band as the signal that constitute additional channel distortion

components. The aggregate (signal and distortion components)" y(t) in

Figure 1" is delivered by the antenna to an HF receiver that is tuned to

the signal band. The receiver amplifies the aggregate to a higher power

levei suitable for subsequent processing, it filters the aggregate to

exclude out-of-signal-band noise and interference" and it frequencytranslates the aggregate to restore nominally the signal pulse trains to

5
the intermediate frequencies at which they were generated in the modulator . The amplffiedvfflter-ed, and frequency-translated aggregate I Z(t)1

is delivered by the HF receiver to the demodulator.

In the demodulator I the trains of distorted IF signal pulses are separated by suitable band-pass filters. Each train of pulses is then sampled

(detected) at the pulse rate to obtain an estimate of the amplitude the

phase I or the amplitude and phase of each signal pulse. In gener-al, each

pulse sample differs from the true value of the signal pulse because of the

various types of signal distortion that are introduced by the channel and

equipment. Each pulse sample is delivered toa bit decider which, for

each data bit carried by the pulse , decides whether a zero or one bit was

transmitted. The data-bit decisions are delivered at. the output of the

demodulator. Regardless of the datavbit for-mat, the decisions can be A

viewed as a binary data sequerice , b2(j)~of zero or one values that occur

at a constant r ate , f

2 . Ide al.Iy, the binary data sequence at the demodulator output, b2

(j ), is identical to the binary data sequence at the modulator

input, b 2(j) in Figure 1. Pr-acti.cal.Iy, however, it differs [is an estimate

of b 2(j )] , because of binary errors introduced in the bit-decision process

by the channel and equipment distortions.

In an HF digital radio system that does not incorporate error coding, A

the binary data sequence from the demodulator, b 2(j ), is delivered directly A

as the receiver output binary information sequence, b

1

(0, as shown by

the dashed line in Figure 1. In a system that does incorporate error

coding, b2{j) is delivered to a decoder, as illustrated. The magnitudes

of the pulse samples , ·fd(j) f that are obtained in the demodulator sometimes are also delivered to the decoder. The decoder then processes ".,

b 2(j}, and sometimes Id(j}I, using a suitable decoding algorithm, to detect

and correct binary errors. The decoder delivers the receiver output

binary infor-mation sequence, 1\(i), that is an estimate of the transmitter ".,

input binary information sequence, b1(i). In general, b

1(0 differs from

b

1

(i) because ofuncorrected errors. However, b1(I) has a lower error

probability with error coding than w ithout, except at high error probabil6
ities; i.e. I the error coding improves the overall system performance.

In some duplex (two-way) systems with error detection, the receiver

via the return transmitter-receiver link may ask for a repeat of some

portion of the transmission when errors are detected.

Some HF digital radio systems use space diversity to improve the

system performance. With space diversity, the receiver in the basic

system of Figure 1 is expanded to include two or more parallel antennas

and HF receivers that drive a single demodulator designed for such

multiple inputs.

The sources of signal distortion that produce bit errors are:

Sources of Signal Distortion

(1) Transmitter

(a) Modulator

(b) HF transmitter

(2) HF channel

(3) Receiver

(a) HF receiver

(b) Demodulator

In general, each source may introduce several types of distortion.

The distortions introduced by the transmitter are usually small and not

significant. The HF channel distortions coan be substantial, however,

and are of primary importance. While the distortions introduced by the

receiver may not be larger than the distortions introduced by the transmitterI their effects on system bit-error-probability performance can

be much greater under some channel conditions, and their presence

should not be ignored. The system performance is dependent not only on

the types and magnitudes of the distortions, but is also dependent on the

system design features: the fundamental pulse waveform, the type of

keying I the multiplexing technique, the receiver filtering, the bitdecision (detection) method, the transmitter power, the"antennas, the

7
order and type of diversity" and the type of error coding.

The signal distortions introduced by the transmitter and receiver (equipment distortions) can be classified as follows:

T'ypes of Equipment Distortion

(1) Additive

(a) Noise

(I) Thermal

(it) Quantizing

(b) Interference (internal)

(2) Multiplicative

(a) Time scatter (frequency selective)

(L) Synchronization

(ii) Filtering

(b) Frequency scatter (time selective)

{i ) Doppler correction

{ii) AGe (automatic gain control)

(3) Nonlinear

Synchronization distortion and filtering distortion are classified as

time-scatter distortions because synchronization distortion is produced

by a nonoptimum allowance for or correction of the signal delay or

translation in time" while filtering distortion is produced by a nonoptimum

spreading or stretching of the signal pulses in time by the filtering. In

an analagous way" Doppler-correction distortion is produced by a nonoptimum allowance for or correction of signal Doppler shift or translation

in frequency" while AGC distortion is produced when the AGC modulates

the signal" generates sidebands" and thus spreads the signal in frequency.

'The channel distortions are classified later.

The preceding brief preliminary description of a basic HF digital

radio system is expanded with more detailed descriptions and evaluations

in the following three sections: the transmitter design features and

8
distortions in Section 3, the HF channel characteristics and distortions

in Section 4, and the receiver design features and distortions in Section

5. The effects of the system design features on system perfor-mance are

then determined in Section 6 for the various types of channel and equipment distortions. The optimum system design features are selected in

Section 7, and suitable conclusions and recommendations are presented

in Sections 8 and 9. In doing this, the goal was to be as comprehensive

as possible, so as to include all factors that have a significant effect on

HF digital system performance, but at the same time, to keep the descriptions as brief as practical for the present purpose of evaluating methods

of improving HF digital radio system performance.

3 . TRANSMITTER

3 •1 Error Coder

With error coding, the transmitter input binary information sequence,

b l(i}, is delivered to the encoder at rate f

l " The encoder combines the

information bits with additional check bits, according to some coding

algorithm, and delivers a binary data sequence, b 2{j), at rate f

2 > f

l

,

as illustrated in Figure 1, p. 4. The coding ratio,

(1 )

is one measure of the efficiency of the coding technique.

There are two major types of error codes:

Types of Error Codes

(1) Block

(2) Convolutional

In a block code I successive sets of n. adjacent information bits in

1

bl (L) are each combined with n c check bits to form a block (set) of size

9
nb = n.+ n

1 c

bits (2 )

In-each block, the n check bits are generated from then. information

c 1

bits according to the encoding algorithm, and are combined with the

unaltered information bits to form the block of n

b bits. If the information

bit sequence, b1(i ), contains,independent bits. then the successive encoded

blocks in the output data sequence, b 2(j ), are independent.

In a convolutional code, the generation of each bit in the encoder output

data sequence, b 2(j ), is determined by the previous n

c

check bits, as well

as.n, of the most recent information bits, according to the encoding algor- 1

rthm, The convolutional code then has a constraint length. • However,

unlike the block code, each data bit in b 2(j) is dependent on all preceding

data bits, even with independent information bits in b1(0. However, the

dependence decreases for an increasing number of past data bits beyond

the constraint length, ~.

Because error encoders are digital equipmerrts, the introduce no

distortion.

3 • 2 Modulator

The modulator generates one or more trains of IF pulses. .When more

than one train of pulses is used, the several trains, numbered

A = 0, ,I, 2, ••• , A-I (3 )

ar-e transmitted simultaneously oyer separate subchanneIs, using either

frequency multiplexing or concentric multiplexing. With frequency multiplexing, the pulse trains have different center frequencies, and with

concentric multiplexing, the pulse trains have a common center frequency,

as explained later. The input binary data sequence, b 2(j), is commutated

in the modulator to the A generators of the IF pulse trains. Each generatorz-e ce ive s a binary sequence. b3A(k) for the Xth generator. with a

recurrence rate that is 1/Ii t~mes the recurrence rate of b 2(j ). In the

Xth IF pulse -train generator, each successive set of N adjacent bits in

10
b 3).(k) is used in effect to select one of

different available pulse waveforms for transmission. Let

m = 0 1 1, 2, ••• , M

(4),;~

(5)"

Table 1. Permutations of N brts

m N= 1 N=2 N=3

0 0 00 000

1 1 '01 001

2 11 011

3 10 010

4 110

5 111

6 101

7 100 :

be: an integer that numbers the available pulse .wavefor-msciThen each of

the M available pulse waveforms

corresponds .to one of M pos-sible

permutations of the N bits , as

illustrated by the examples in

Table 1. Consequently, each

transmitted pulse, by means of

its distinctive waveform, carries

N bits of data. In nearlyallJiF

digital radio systems, N is an

integer (usually one or two)

and will be so considered in

thi.s report.

The A trains of IF pulse s

generated by the modulator constitute the real IF bandpass signal output

from the modulator. The real bandpass signal can be specified by

\l1(t) = Re[w(t)exp(j2nfrt)]

where f

r

is an arbitrary reference frequency, usually in or near the IF

signal band, and

w(t) = w'(t) + jw"(tJ (7 )

is the complex envelope of the signal. .The r-eal band-pass stgnalthenIs

\l1(t) = w '{t) cos( 2nf

r t ) - w"(t) sin(2nfrt.)

11

(8)
which contains two quadrature reference (carrier) components Lcosf z-rf t)

r

and sin(2Trf t ), multiplied (amplitude modulated) by two real baseband

r

functions, w'(t) and w l'(t), that are the components of the complex

envelope, wet) in (7). If wA(t) is the complex envelope of the Xth pulse

train relative to fr, then

(9)

In the remainder of the report, the signal and the channel and equipment

processing imposed on it will be described by complex-envelope functions.

All of the It pulse trains, [wA(t)}, are obtained by frequency multiplexing or concentrically multiplexing a set of A basic pulse trains,

[wA(t)}. The basic pulse trains are generated from a common set 9( M

available basic pulse waveforms, [Pm(t)}, each of which is generally

complex and, in practice, of finite duration. Let

(10)

be the mth available basic pulse waveform, where am(t) and am(t) are the

real amplitude and phase components, and P m(f), the Fourier transform

of p (t ), is centered onf = 00 Then for each basic pulse train, succes- m c,

sive sets of N bits in b

3A(k) are used to select basic pulse waveforms

from [p (t)} to form the Xth bas.ic pulse train, m

WA(t) = PmA(·o(t-tT)

.{,

(11 )

where .{, is an integer that numbers the pulses, and T is the time spacing

of adjacent pulses. The subscript m for the mth available pulse in (10) is

replaced by rnA(t) in (11) to indicate the value of m is generally different

in each basic pulse train and changes with t.

There are an infinite variety of pulse waveforms from which M basic

12
pulse waveforms, [Pm(t)}, can be chosen for use in an HF digital radio

system. The possible designs of [Pm(t)} can be classified in terms of

the pulse duration , '-p' relative to the adjacent pulse spacing, T:

Types of Pulse Waveforms

(l) Spaced ('-p < T)

(2) Adjoining ('-p= T)

(3) Overlapping ('-p > T)

Examples of the three types of pulse waveforms are illustrated by

their amplitude components in Figure 2. In the examples, the pulse

amplitude function is the same for all illustrated values of t. This is

not necessary, of course; the M members may have different amplitude

functions. For each pulse amplitude function, a (t}, there is an infinite

m

variety of phase functions that might be used .for am(t). Most past and

present HF digital radio systems use adjoining pulses with rectangular

amplitude functions and constant phase functions, primarily because

they are easiest to generate. However, other pulse functions can provide

better-over-aflaystem performance.

In the: generation of each basic pulse train, ,~\(t) in (11 ), when N

adjacent data bits in b3A(k) are used in effect to select one ofM available

pulse waveforms, p (t), for transmission, the selection can be viewed

m

as a keying process: the data bits in effect key (switch) the values of

one or more waveform parameters to change the pulse waveform, or key

(select) one of M stored waveforms 0 The possible methods of keying a

pulse can be classified as follows:

13
I

-2T

LOm).L/ )(t-1 T )

-'

-T 0 T

(a) Spoced Rectangular Pulses

2T

(b) Spaced Nonre ctonqu lor Pulses

-2T

-2T

-T 0 T

(c) Adjoining Rectang ulor Pulses

T

(d ) Adjoining Nonrectangular Pulses

-T 0 T

(e) Overlapping Nonrectangula r Pulses

2T

2T

t

t

Figure 2. Examples' of amplitudes of trains of complex pulses.

14
Keying Methods

(1) Single filter

(a) Amplitude-scale keying (ASK)

(b) Phase-shift keying (PSK)

(c) Amplitude-and-phase-sb.ift keying (APSK)

(2) Multiple filter

(a) Frequency-shift keying (FSK)

(b) Concentric-pulse keying (CPK)

The two major keying methods, single filter and multiple filter, refer

to the number of filters used in the demodulator to separate each train of

pulses from the other A-1 pulse trains' and from noise and interference

that is outside the aignal pulse train frequency band. Any of the keying

methods may be used with any of the types of pulse waveforms listed

earlier. It is convenient and desirable to view the single-filter keying

methods as fundamental, and to view the multiple-filter keying methods

as modifications of one single-filter keyingmethod i ASK., Therefore,

the single-filter keying methods will be described first, and then the

multiple-filter keying methods will be considered.

In 'the stngle-ftlterIceytng methodsr.Let

p(t) = a(t)exp[j a(t)] (12 )

be a generally complex fundamental pulse waveform, where a(t) and a(t)

are real amplitude and phase functions. Then in each single-filter keying

method, the fundamental pulse waveform" p'[t}, is modified inM different

ways to form the set of M basic pulse wavefor.ms, [Pm(t)}. With

amplitude -scale keying,

P (t ) = k p(t) = k a(t)exp[ja(t)] m m m

ASK (13 )

where k is one of M different positive real keying numbers. With ASK, m

the mth basic pulse waveform, p (t), is therefore obtained by multiplying m

15
the fundamental pulse wavefor-m, P(t)1 with a positive real numberI k I

m

that scales its amplitude component I a(t). The term "amplitude -shift

keying" is often used , but generally is incorrect because a(t) is not shifted

by the addition of k m l but is scaled by the multiplication of k

m•

When

rectangular pulses are u sed, "amplitude-shift keying" can be correctly

used if a rectangular time fun ction, k (t ), with a duration and timing m

identical to a(t)1 is added to a(t) to shift it only during the pulse per-iod,

T

p • This is not possible with nonrectangular pulse waveforms, however.

With phase-shift keying,

where

P (t)= exp(j t; )p(t) = a(t)exp[j[a(t)+K m m m]}

-1T < Km :5 1T radians

PSK (14)

(15 )

is one of M different real phase keying values. With PSK1 the mth basic

pulse wavefor-m, p (t ), is therefore obtained by multiplying the fundam

mental pulse wavefor-m, P(t)1 with a unit-magnitude complex number that

shifts its phase cornponent , a(t)1 by an amount K

m•

With amplitude-and-phase-shift keying,

where

P (t ) = KmP(t) = k a(t)exp[j[a(t)+ K J} m m m

APSK (16 )

(17)

is one of M different complex numbers 8 With A"PSK1 the mth basic pulse

wavefor-m, p (t)1 is therefore obtained by multiplying the fundamental

m

pulse wavefor-m, P(t)1 with a complex number" K I that in general scales

m

its amplitude component" att), and shifts its phase component" a(t). It

can be seen that ASK and PSK are special cases of APSK: with ASK1

Km= 0 for all m , and with PSK1 k

m=

1 for all m ,

The three single-filter keying methods are illustrated in Figure 3.

For each of the three keying met hods, the M=2N possible keying values"

16
Im(Km) Im(Km)

1(0) (1) (00) (01) (11) (10)

Re(K m) >--------< Re(Km)

o 1 0 1 2 3

N=1 N=2

(0) Amplitude - Scale Keying (ASK)

Im(Km ) Im(Km)

(01) j 1

(1) (0) (11 ) (00)

-1

Re (K m) -1

Re( Km)

N =1 (10) - j1 N=2

( b) Phase - Shift Keying (PSK)

1m( Km)

non j2

(001) j 1

(111) (011)

-2

(010) . - j 1

(000) (100)

2

N=3

Re(Km)

(c) Amplitude-and-Phase-Shift Keying (APSK)

Figure 3 e Examples of single -filter complex keying value s,

17
[Km}" are illustrated by circles in the complex plane for various values

of N" the numberofbits/pulse. The numbers in parentheses are the

permuations of the N data bits corresponding to each keying value. For

N > 1" the permutations are usually assigned to the keying values so that

the most closely spaced pairs of keying values differ in only one bit;

otherwise the system performance would be poorer. In Ffgur-e S'(a), the

N=1 example is simple on-off keying. In Figure 3(b)1 the N=1 example

is binary (bl-phas e) PSK" while the N=2 example is quaternary (fourphase) PSK. In Figure S(c ), the N =3 example makes use of twoamplitudes and four phases. The N =3 example can be extended to N =4 by

incorporating eight additional complex keying values with magnitudes of

1 and 2 at angle'sof ±45°a,nd ±135°" or also by forming a square4X4

matrix of keying values centered on K =O, For any N" the choice of

m

keying values' is arbitrary" but the best performance is usually obtained

when the spacing of the values is maximized for a gi,ven average power

of the keying values.

In the single-filter keying methods , the successive keying values in

each train of pulses form a generally complex M-ary sequence. KA(.t).

where A specifies the pulse train and tnumbers the pulses in the tr-ain,

For each value of.t~ KA(.t) may have anyone of the M value s in [Km}.

The Xth basic pul.ae t r ain, v.\(t) in (11). then becomes

WA(t) = I: KA(.t)p(t-.tT)

t

ASK1 . PSK" APSK (18)

In some PSKand APSK systems. the direct keying sequence. KA(.t).

is replaced by a phase-differential keying sequence. KA~(t). Three

types of phase-differential keying are possible : t.irnevdiffer-enttal (TD)

keying" which can be used with single or multiple fr-equericy-cmult ip'le xe d

or concentrically multiplexed pulse trains; frequency-differential (FD)

keying I which can be used only with multiple frequency-multiplexed

pulse trains : . and concentr-icvdiffer-enti al (CD) keying" which can be used • -". :;. '01~

only with multiple concentrically multiplexed pulse trains e

18
In time-differential keying, which is widely used In PSK systems,

the direct keying sequence, KA(t), is replaced by the time-differential

keying sequence,'

TD (19 )

i.e., the tth value in .thedir-e ct keying sequence, KA(t) [generated from

b3A(k)], is advanced in phase by I<A6(.t-O,the phase of the preceding

differential keying value, to generate K All(t), whichisusectto key the

tth pulse.

In frequency-differential keying and concentric-differential keying,

which are little used, the direct keying sequence, KA(t), is replaced by

the frequency-differential or concentric-differential keying sequence I

FD, CD (20)

Le., the tth value in the direct keying sequence, K/t}, is advanced in

phase by I«A-Of.\(.(J, the phase of the concurrent differential keying value

inthe adjacent (A-l)th basic pulse train, to generate KAl:l(t), which is

used to key the tth pulse in theXth basic pulse traineThe A='O pulse

tr-ain can carry no frequency-differentially keyed orconcentric-differentially keyed data" although it still might carry data that is directly or

time-differentially keyed. A distinction is made between frequencydifferential and concentric-differential keying because they result in

different system performance s under some channel conditions e

The Xth pulse train, wA(t) in (9), is obtained by frequency multiplexing

or concentrically multiplexing the pulses in the Xth basic pulse train,

wA(t) in (18). If P'l"b A specifies the multiplexing operation for' .wA(t), then

wA(t) = 2:,?IZ- A[KA(t)p(t-tT)] =

t

2: KA(t) m: A. [p(t-tT)] • (21)

t

With frequency multiplexing" the basic pulse trains are frequency

translated so that the center frequencies of their spectrums have equal

19
adjacent spacings, F 0 Given the fundamental pulse waveform, ptt), F is

chosen so that the -/\ trains of pulses in w(t) can be adequately separated

by suitable filtering in the demodulator. With frequency multiplexing,

(21) becomes

WA,(t) = L: KA,(,(,)exp[j21T[A-(A-l)!2] Ft} p(t-,(,T) (22)

t

when the spectrum of w(t) is centered on f =O.

c

With concentric multiplexing, the spectrums of the A pulse trains,

[wA,(t)L have a common center frequency, f c = O. Concentric multiplexing

can be illustrated with parabolic cylinder functions (Jahnke et al, , 1960).

Let the fundamental pulse waveform be a real Gaussian function,

(23 )

Then (21 ) becomes

WA,(t)

where

A ( x

2

) dA ( x

2

H ) .(x) = (-1) exp - -- exp --. eA 2 dxA 2

(25 )

is the Xth Hermite polynomial. Given 1\ and T, the parameter c can be

adjusted to control the overlapping of successive pulses. The A concentric

pulse waveforms for t= 0 in (24) are illustrated in Figure 4 for c= 2,

1\= 8, and KA(O)= 1. Because the l\. parabolic cylinder waveforms are an

orthonormal set, the 11. pulse trains, [w>...(t)}, can be separated by matched

filters in the demodulator.

With single -filter keying (ASK, PSK, and APSK) and frequency multiplexing, the pulses in the A trains in w(t) 'are distributed in frequency and

~ime as illustrated in Figure 5(a) for A= 4 pulse trains. Each rectangle

represents one pulse carrying N bits of data, as shown. The effective

20
c.

E

<!

3 ----.. .. ----_._-..__ ._- .

... ...

2 ~-=~~~:-::: ::: ..::: :-_~ __ ... ,........... _~_.#

. . . ..

A=O-:-:~:-=:-1 :-~-~-:- 2~3-:4:.5~6:7::::-:: :-:=:.:~-:--=

Relative Time, tiT

Figure 4. Orthonormal parabolic cylinder waveforms.

bandwidth of each pulse is F, the height of each rectangle, while the

effective duration of each pulse is T, the width of each rectangle.

Let the. spectral efficiency of the signal, wft ), be defined as the ratio

of the information rate, f

1, carried by w(t), the the bandwidth of w(t).

Then with single-filter keying and frequency multiplexing, Figure 5(a)

shows that w(t) carries f

2= 1I.N/T data bits!second in a bandwidth B=1I.F.

Therefore, the spectral efficiency with single-filter keying and frequency

multiplexing is

ASK, PSK, APSK (26)

With single -filter keying and concentric multiplexing, the pulses in

the A trains in w(t) have- a common center frequency, f =0, as described

c

in the discussion of (23)-(25). Consequently, their spectrums occupy

some central portion or all of a frequency band, B, centered on f= 0, as

21
, 2F

o

c:

Q)

::J

CT

Q)

'-u,

F

o

-F

-

N N N N N N

N N N N N N

N N N N N N

N N N N N N

T 2T 3T 4T 5T

Time, t

(a) Frequency-Multiplexed Pulse Trains

3T 4T 5T 6T

A~4

T 2T

-

I-- 4N 4N 4N 4N 4N 4N

8/2

-8/2

o

o

c: 0

Q)

;:)

CT

Q)

'- u,

Time, t

(b) Concentrically-Multiplexed Pulse Trains

Figure 5. Pulse distributions infrequency and time

with M-,aryASK" PSK" and APSK.

22
illustrated in Figure 5(b) for A= 4 pulse trains. Each rectangle represents A puls e s , concentric in frequency and t i me , that carry AN data bits ,

Figure 5(b) and (1) show that the spectral efficiency with single -filter

keying and concentric multiplexing is

'll c= ASKI PSKI APSK (27 )

The signal bandwidth with concentric multiplexing, BI may be smaller

or larger than the signal bandwidth with frequency multiplexing, l\FI for

. the same number of'bits Zpul.se , N~ the same pulse spacing, T I and the

same number of pulse trains, 1\1 because generally.different basic pulse

waveforms are used with the two multiplexing methods. HoweverI if

comparable care is given to the design of the basic pulse waveforms in

the two multiplexing methods, B~J\F in (27)~ and Tlc~ 'llf with single-filter

(ASKI PSKland APSK) keying.

It is informative and therefore desirable to view the multiple-filter

keying methods (FSK and CPK) as modifications of one single-filter

keying method: binary ASK (on-off keying). FSK can be viewed as a

modification of frequency-multiplexed binar-y ASKI and. CPK can be

viewed as a modification of concentrically multiplexed ASK. In both case s,

the binary ASK keying values, KO=0 and K 1 =1 in Figure 3(a), p. 17,

may be used with any fundamental pul.sewaveform.vptt) in (1'2)0

A single train of binary FSK pulses Is. equivalent to two dependent

(redundant) frequency-multiplexed tr-ains of binary ASK pulses, one of

which is on while the other is off; i 0 eo I the on-off keying sequence on

one binary ASK pulse train is complemented (zeros and ones interchanged)

to key the se-cond binary ASK pulse train. When adjoining rectangular

pulses are u sed , and FT is not an integerI the keying sequence on each

binary ASK pulse train in effect is adjusted by a suitable amount on each

succeeding pulse Ifphaae continuity is desired at the pulse transition

times. HoweverI this is not usually desirable with pulses other than

adjoining re ctangular pulses.

23
Figure 6(a) illustrates the frequency and time distributions of the

pulses in A= 2 trains of frequency-multiplexed binary FSK pulses. The

lowest two rows of rectangles represent the two binary ASK pulse trains

that comprise the A= 0 train of binary FSK pulses~ while the upper two

rows of rectangles represent the two binary ASK pulse trains that comprise

the A= 1 train of binary FSK pulses. The rectangles labeled 1 represent

on states (energy pre sent}, and the rectangles labeled 0 represent off

states (no energy). In each pulse interval, T in each binary FSK pulse

tr-ain, A, the selected pulse-waveform number m, is determined by which

of the two frequency-multiplexed binary ASK pulse trains is on. In effe ct ,

each on pulse carries N =1 data bit, as shown" while the off pulses each

carry zero data bits. The on-pulse density in the frequency-time domain

is one - half.

Frequency-multiplexed binary FSK" illustrated in Figure 6(a)" can be

extended to frequency-multiplexed M-ary FSK. Each train of M-ary FSK

pulses is equivalent to M dependent frequency-multiplexed trains of binary

ASK p~ses" one of which is on while the other M-1 are off for each pulse

number" t. For each pulse number" t" in each M-ary FSK pulse train"

A" the selected pulse-waveform numbe r , m, is determined by which one

of the M frequency-multiplexed binary ASK pulse trains is on. In effect"

as with binary FSK" each on pulse carries N data bits", while the off pulses

carry zero data bits. The on-pulse density in the frequency-time domain

is 11M. Therefore" the spectral efficiency with FSK and frequency multiplexing is

FSK (28)

Several trains of M-ary FSK pulses may also be concentrically multiplexed, as illustrated in Figure 6(b) for A=2 trains of binary FSK pulse

trains. Each row of rectangles represent A= 2 concentrically multiplexed

binary ASK pulse trains. The number in each rectangle specifies the

number of concentric pulses that are on in that rectangle" where the 0-1

24
2F

F

0

c

Q) 0

::J

C"

Q)

u, -F

-2F

- , -

1 1 0 0 1 0

0 0 1 1 0 1

1 1 0 1 0 0

0 0 1 0 1 1

0 T 2T 3T 4T 5T 6T

u, ..... v

II

LL.

Z

C\J

< o II

. II CD

J~

Time, t

(a) Frequency -Multiplexed Pulse Trains

---r

u,

V ... II

.-LL.

Oz

.. C\J

~<

II

CD

J

T 3T2T 4T 5T 6T

- , -

2 I 2 0 1 1 0

i

0 0 2 1 1 2

-8/2

o

8/2

0

c::

Q) 0

:::J

C"

Q)

lu;

Time, t

(b) Concentrically -Multiplexed Pulse Trains

Figure 6. Pulse distributions in frequency and time with binary FSK.

25
pattern in the two frequency-multiplexed binary FSK pulse trains in Figure

6(a) are repeated in the two concentrically multiplexed binary FSK pulse

tr-ains in Figure 6(b).Each rectangle of area BT 1M in Figure 16(b) carries

an average of AN1M data bits, so the spectral efficiency with FSK and

concentric multiplexing is

FSK (29)

If comparable care is given to the designs of the basic pul.sewaveforms

in the frequency-multiplexed and concentrically multiplexed F~K systems,

BR1 A2NF in (29), andT'lc R1 Tlf wi t h FSK.

A single train of M-ary CPK pulses is equivalent to M dependent

concentrically multiplexed trairis'ofbinar'y' ASK pulses, -one of which is,

on while the other 1\11 -1 are off for each pulse number, t. For each pulse

number, t, in each M-ary CPK pulse train, A, the selected pulse-waveform number, m, is determined. by which one of the M concentrically

multiplexed binary ASK pulse trains is on. In effect, each on pulse carries

N data bits, while the off pulses carry zero data bits• Several trains of

CPK p·ulses,like. several trains of FSK pulses, may be frequency, multiplexed or concentrically multiplexed • Frequency multiplexing of CPK

pulsetrains is illustrated in Figure 7(a) for It = 2 trains of binary CPK

pulse "trains• Thespectralefficienc:ywithCPK and frequency.multiplexing is

II - _._ ~1C~' -_.'?:-I .. '~! , ,,-,

r

.•.~c~.Nf - BT 2NFT (30)

.Concentr-ic multiplexingofCPK pulse trains is illustrated in Figure

7(bl{orA;=2 trains .of binary~rKp.ulsetrains, The spectral efficiency

withCPK and concentric multiplexing is

ArcN rcN

Tlc = BT R1 2N F T

26

CPK (31)
-r

LL "'v

II·

LL

Z

(\J

0<

.. II

AID

-±

3T 4T 5T

N=1, A=2

11

T 2T

1 1

8/2 foo------..,---~--_T_--r__-___r_--_......._

- 8/2 ....-----'-----'------'----01------'-----.....-

o

o

; 0 ........--+-----+------+-----+-----+------+-

CT

Q)

'-

IJ..

Time, t,

(a) Frequency - Multiplexed Pulse Trains

T 2T 3T 4T 5T

8/2 t-------r-----:------r----r___------.----....--

Time t t

(b) Concentrically - Multiple.xe.d Pulse Trains'

Figure 7 • Pulse distributions in' frequeneyand timewithbinaryCPK."

. 27
A comparison of the spectral efficiencies in (28 )-(31 ) for the multiplefilter keying methods (FSK and CPK) with the spectral efficiences in (26)-

(27) for the single-filter keying methods (ASK" PSK" and APSK) shows

that the single-filter keying methods have spectral efficiences that are

",2N = M times greater.

Of all of the single-filter and multiple-filter keying methods" binary

FSK with adjoining rectangular pulses is most commonly used in HF

digital communication systems" with frequency multiplexing when more than

than one train of pulses is used. Binary and quaternary PSK with

adjoining re ctangular pulses is second most commonly used" also with

frequency multiplexing when more than one train of pulses is used. Other

pulse waveforms" other keying methods" and concentric multiplexing are

less frequently or rarely used.

In nearly all applications" w(t) in effect is used to generate a real IF

signal" W(t) in (8)" p. 11" which is then delivered by the modulator to the

HF transmitter for suitable frequency translation to and amplification in

the HFband. It is possible" however" to use a double-modulation process

in whichw(t) is first used to generate ~(t) at a suitably low IF" and then

~(t)" rather than being frequency translated to the .HF band" is used in

turn to modulate the amplitude or phase of a higher IF carrier that is

frequency translated to the HF band. While such double -modulation techniques are useful and commonly used .in the UHF and SHF bands" they are

little used in HF digital communication because their performance is

poorer under HF channel conditions. Therefore" double modulation will

not be considered further in this report .

The modulator can introduce all of the types of equipment distortion

listed on p. 8 except synchronization distortion and Doppler-correction

distortion (the latter because it is assumed that any frequency error introduced by the modulator can be compensated or corrected by the Dopplercorrection circuit in the demodulator). The modulator always introduces

thermal noise ; quantizing noise is unavoidably introduced when the modulator incorporates digital processing" as most modern modulators do;

28
and internal interference (120-Hz power-supply ripple, clocking transients,

etc.) is always present. Any filters that are used in the modulator can

introduce filtering distortion, the variations in signal level imposed by

any AGC circuit introduce at least a small amount of frequency-scatter

distor-tion, and nonlinear distortion is always present 0 All of the modulator distortions are usually small enough to have negligible effect on the

system performance, however, and therefore may be Ignor-ed,

3 • 3 HF Transmitter

The one or more trains of low-level keyed IF pulses (the signal)

generated in the modulator are delivered to the HF transmitter for frequency translation and amplification. The transmitter typically consists

of a low-level HF exciter followed by an HF power amplifier of one or

more tuned stages. The exciter translates the signal to the desired

frequency in the HF band, and the power amplifier increases the signal

power to the desired amount.

A typical HF exciter is illustrated in Figure 8. It consists of an input

first-IF amplifier followed by a first frequency converter, a fixed-tuned

band-pass higher frequency second-IF amplifier, a second frequency

converter, and a tunable output band-pass HF pre-amplifier. The second

local-oscillator frequency is adjusted to obtain the desired HF transmitter signal frequency. The band-pass filtering in the second-IF amplifier and the output HF pre-amplifier suppress the unwanted sideband

generated by each frequency converter, suppress the local-oscillator

components if the balancing of the frequency converters is inadequate, and

also suppress any undesired out-of-signal-band higher order intermodulation productions generated by the converters that are not good approximations of true multipliers. The amplification provided by the HF

exciter may be controlled manually or by an AGC circuit 0

The HF power amplifier which the HF exciter drives may use nonlinear (class-C) tuned amplifier stages when the signal has an envelope

29
Input

from"

Modulator

1sf- IF

Amplifier

1st

Frequency

Converter

. 1stLocal

Oscillator

2nd

Frequency

Converter

2nd Local

Oscillator

HF

Pre-Amp

Output

to HF

Power

Amplifier

Figure 8. Typical HF exciter.

whose magnitude is constant, because, the nonlinear (harmonic) distortion

is suppressed by the band-pass filtering. The signal has a constantmagnitude envelope only when a single pulse train is used, and then only

whenPSK or FSK modulation is used with adjoining rectangular pulses.

Otherwise, the power amplifier must be essentially linear (class-A,

push-pull class-AB, or push-pull class-B stages) to minimize nonlinear

distortion of the filtered signal.

It can be seen that the HF transmitter performs three interleaved

primary functions:

HF Transmitter Functions

(1) Frequency translation

(2) Filtering

(3) Amplification

In performing these functions, theHF transmitter can introduce all of the

types of equipment distortion listed on p. 8 except quantizing noise (providedall-analog circuits are used), aynchr-ontz atton distortion, and Dopplercorrection distortion (because it is assumed that any frequency error introduced <by the local oscillators in Figure 8 can be compensated or corrected

by the Doppler-correction circuit in the demodulator). The HF transmitter

30
distortions are usually small enough to have negligible effect on the

system per'formance , however, and may therefore be ignored.

3.4. Transmitting 'Antenna

Both transmitting and receiving antennas can be characterized in

terms of the following major electrical characteristics:

Antenna Characteristics'

(1) Size (in wavelengths)

(2) Gain

(3) Bandwidth

(4) Steer-ing

The electrical size of an antenna can be specified in terms of Its

maximum dimension in wavelengths: small if less than 0.1 wavelengths, medium for 0.1 to 1. 0 wavelengths, and large if more than

1.0 wavelengths. For a given electrical size, the physical size Ls

inversely proportional to frequency. The gain of an antenna relative

to a half'-wavel.ength dipole can be rated low up to 3 dB, medium from

3 to 8 dB, and high for more than 8 dB. The bandwidth of an antenna

(with fixed tuning) can berated in terms of the ratio of its high arid low

3-dB frequencies: small'forratiosuptol.1 ,medium for ratios up to

2, and large for higher r atios, The az'imuthal electrical or mechanical

steering capabilities of an antenna can be r-ated as none, partial, or

complete (360°).

The types of antennas that are commonly used inHF transmitting

and receiving applications (Ja.stk, 1961) are:

31
Types of Antennas

(1) Dipole

(2) Whip

(3) Long wire

(4) V

(5) Rhombic

(6) Broadside (curtain)

(7) End fire (Yagi)

(8) Log periodic

(9) Wire/cap/notch (aircraft)

A dipole antenna is' typically one-half wavelength in size, horizontally

polarized, 'and easy to install. It has a broad bidirectional azimuthal

pattern with low gain. A dipoleantenna has a narrow bandwidth, is

usually not tuned, and consequently is restricted to a single narrow

frequency band in tr-anamittfngoper-atton , Mechanically steerable dipoles

are practical at frequencies above about 10 MHz" but are rarely used.

A vertical whip antenna, usually used on a vehicle" is physically

small and simple to install. It has an omnidirectional, low-gain pattern

which is usually desirable in mobile applications. However, it has a

small bandwidth, requires tuning to change frequency in the HF band, and

can be inefficient (lossy) in the lower frequency end of the HF band.

A long-wire antenna is medium to large in size and usually easy to

install. The number of radtatfon-patter-n lobes increases with the length,

with the strongest lobes of'a jstr-aight wire nearest its axis. The strongest lobe gain increases withantenna length and ranges from low to medium.

An unterminated Iong -wir-e antenna has a small bandwidth, requires tuning,

cannot be steered, and has a radiation pattern that changes with frequency.

A V antenna is formed from two straight long-wire antennas that. are

driven at the apex of the V'. T;h~angle of the V is chosen so that the major

lobes of the two long-wire legs reinforce each other. A V antenna is

medium to large in size, withia {gain that ranges from low to medium-large.

32
An unterminated V antenna has a bidirectional pattern" narrow bandwidth"

and requires tuning. A V antenna with proper resistive terminations is

unidirectional" has a medium to large bandwidth" but is not practical to

steer.

A rhombic antenna, formed by joining two V antennas at their open

ends" is driven at one end and terminated by a suitable resistance at the

other end. It is large in size, typically several wavelengths per side,

and has a unidirectional pattern. It usually has a large gain and medium

to large bandwidth, but cannot be steered.

A broadside antenna is formed in general Iroma matrix (curtain) of

driven elements, usually dipoles, in a vertical plane. The elements are

driven in phase to form a bidirectional pattern. The antenna can be

made unidirectional with greater gain-by including ar-ef'lectingcurtain,

A broadside antennaIs large in size and has a medium to high gain. It

has a narrow bandwidth, is not practical to tune, and consequently is

restricted to a single narrow frequency band of operation. Mechanical

steering is impractical, but limited electrical steering (beam slewing)

is possible •

An end-fire antenna is formed from a number ofcoplanarelements

that are· excited to form a pattern with the main lobe in the plane of the

elements.It Ismediumto large in aize • The commonest end-fire

array is the Yagi antenna, which consists of a set of parallel dipoles,

One or more of the elements are driven while the remainder (usually the

majority)areparasitically.excited by the fields of the driven elements.

The lengths of the dipole elements are tapered to form a unidirectional

pattern with medium to high gain. An end-fire antenna has a narrow

bandwidth, is not practical to tune, and consequently. is restricted to a

single narrow frequency band of operation. Electrical steering is impractical, but· complete (360°) mechanical steering is practical at

frequencies above about 10 MHz.

A log-periodic antenna is. formed from a set of paralie1 dipole,

elements whose center form a line. The electrical Si2H! and spacing of

33
adjacent elements change logarithmically along the Iine , and all of the

elements are driven. A log-periodic antenna is medium to large in size

and has a medium to high gain. The bandwidth ofa log-periodic antenna

is approximately equal to the ratio of the size of the largest element at

one end of the array to that of the smallest element at the other end 0 Its

bandwidth typically is large and can be made to cover the entire Hlr' band,

thus requiring little or no tuning. A log-periodic antenna is not electrically steer-able , but complete (360°) mechanical steering is practical if

the antenna is designed for frequencies above about 1 0 MHz.

In HF aeronautical mobile communication, the entire metal aircraft

is used as an antenna. Wire , cap, or notch coupling is used to connect

the aircraft with the transmitter or receiver. In slower air-cr-aft, wire

coupling is obtarned by driving an exter-nalwire (mounted or trailing )

against the aircraft structure • In faster (jet) aircraftI where the aerodynamic drag of an external wire is unde sirable , cap or notch coupling

can be used, Cap coupling (GrangerI 1950) is obtained by driving an

electrically insulated portion of the aircraft structure I such as a wing

tip or the vertical fin , against the remainder of the structure. Notch

coupling (T'anner, 1958) is obtained by driving the open end of a notch in

an edge of the metallic aircraft structure, such as the faring in the leading edge of the fin or the fillet in a trailing-edge wing root. The notch is

fared with nonconducting material to maintain aerodynamic efficiency.

All three types of coupl.ing, wire, cap, and notch, can be made electrically efficient (low Ioas), The notch, even though a small fraction of a

wavelength in size I is efficient because of its location in ahighrf current

density portion of the aircraft e Aircraft antenna patterns depend on the

size and shape of the aircraft relative to the HF wavelength, and consequently change with fr-equency, Aircraft antennas have low gain, narrow

bandwidth, and require tuning. Steering can be accomplished only by

turning the aircraft 0

The only equipment distortion that a transmitting antenna introduces is

filtering di.stor-tionIrnposed by its generally frequency-selective response e

34
4. HF CHANNEL

4.1 Propagation Characteristics

The ionosphere is a portion of the earth's atmosphere that is ionized

by solar radiation. It extends in altitude from about 50 km to several

hundred km and higher. The free-electron density asa .function of

altitude typically has variations called layers: the D, E, F 1, and F 2

layers. An HF .transmitted signal propagates to a receiving antenna by

reflection from one or more of the upper layers: E, F l' and F 2 (Davies,

1965). The reflections (actually refractions) are produced by the interaction between the signal field and the free electrons• In general, the

signal can propagate to the receiyervia several major modes: e.g.,

a single reflection from an F layer (a 1F mode), a double r.eflection from

an F layer with an inter-mediate reflection from the earth (a 2F mode),

a double reflection from an F layer with an intermediate upward reflection

from the E layer (anM mode), etc.

Figure 9(a) presents a hypothetical example of the delay (propagation)

times for> 1F and 2F modes as functions of frequency (an, oblique ionogram) fora quiet ionosphere (explained later). Ingeneral., each mode

contains both low and high rays which merge at the maximum frequency

for that mode • The largest of these is usually cal.ledthe MUF (maximum

usuable frequency). Both high and low rays contain ordinary and extraordinary components 'produced by the earth's magnetic field. The

propagation times of the ordinary and extraordinary components are

essentially identical for the low rays, but may be significantly different

in the high rays. For each of the magnetoionic components, dispersion

can be defined as the negative of the derivative of the propagation delay

with respect to frequency; L, e., the negative of the slope of each curve

in Figure 9(a). It can be seen then that the low rays have no significant

dispersion, except near the maximum frequency of themode , while the

high rays exhibit significant dispersion. However, over the bandwidths ;, \. ,i~ .~ \ .;5 _

35
,------------------"--->

11

2F Mode

1F Mode

Ordinary

Low Rays

Extraordinary

11

10 20

Frequency, MHz

(0) QUIET IONOSPHERE

30

10 20 30

Frequency, MHz

(b) SPREAD - F

Figure 9 0 Hypothetical ionograms 0

36
of typical HF digital systems «12 klfz ), the high-ray differential delay

from the low to the high end of the signal band is quite small compared

to the differential delays between the low and high rays and between

different major modes. Cons equently, the high-ray dispersion is not

important practically.

The propagation modes that exist for any HF radio system depend on

the time (state of the ionoaphe re ), the transmitter-receiver distance

and the operating frequency. The differential delay between the shortest

and longest propagation paths depends on both transmitter-receiver

distance and operating frequency. This dependerice , which was determined experimentally from a number of oblique ionograms (Bafley, 1959;

Salaman, 1962)~ is illustrated in Figure 10. For each transmitterreceiver distance , d , the maximum differential de Iay, ~Tm~ increases

monotonically as the operating fr-equen cy, f decreases below the

o

rna.xirnurn usuable fr-e quency, 1M• Each curve itself has a maximum,

with the maxima of the various curves forming the loci of the dashed

curve, 6r' . The maximum differential delay, 6r' , varies with

m m

transmitter-receiver distance, d , as shown in Figure 11.

The ionosphere always has a turbulent structure that affects the signal

on each propagation mode or path in two ways: it modulates the signal in

both amplitude and phase in a random f'ashion, thus generating sidebands

that scatter or spread the signal in frequency; and it scatters or spreads

the signal in time. When the turbulence .Ls relatively mild (the usual

case), the ionosphere is said to be quiet, and the major effect of the

turbulence is to scatter the signal in frequency (produce fadingl) on each

mode while producing no significant scattering in time. Each propagation

mode then is essentially discrete in time, as illustrated by the curves

in Figure 9(a). When the turbulence is more severe , a spread-F condition exists. The more severe turbulence still scatters the signal in

1 The radio signal fading produced by ionospheric turbulence is similar

to the scintillation of star light produced by tropospheric turbulence.

37
0.8 1.0

fo'/f M

•••.• J

0.6

Frequency,

...• . ..' -

0.4

..........._. ·········t __ ..

•. __-1_...... _...... •. •.•. _ .... :~. •.• -:_ .. .-.~ .--·····-4····- ........-'...+-+-.--++-+-+ .. ~~.+-t

0.2

Relative Operating

8~-·

Figure 10. Maximum differential delay versus relative operating

frequency for HF channels.

fI)

E

...

E

-....

<3

o

Q)

o

c

o

E

::::J

E

)(

o 10

Transmitter-Receiver Distance, d',Mm

100

Figure -11. Ma:6i-iirium differential delay versus distance for HF channels.

38
frequency" usually by a larger amount (a higher fading rate)" but also

scatters the signal in time by a significant or substantial amount" as

illustrated by Figure 9(b). Each propagation mode or path that is

essentially discrete in time with a quiet ionosphere in effect is replaced

under spread-F conditions by a multiplicity of faster fading paths with

different generally larger closely spaced delays (a time continuum of

paths). Spread-F conditions exist part of the time predominantly in

high-latitude and equatorial regions of the earth.

In addition to the time scattering imposed on a signal by multipath

propagation" and frequency scattering imposed by the fading on each path"

the generally increasing or decreasing heights of the ionospheric layers

(greatest near sunrise and sunset) will introduce generally different mean

Doppler shifts on the various multipath signal components. Doppler

shifts and frequency spreads range from about O. 01 Hz to 1. 0 Hz with

a quiet ionosphere" but range up to 10 Hz or more under spread-F

conditions.

4.2 ChannelModel

Themultipath, Doppler" and Jading characteristics of the ionosphere

affect the performance of an HF digital radio system in ways that can be

described and evaluated most effectively in terms of an HF channel model.

Figure 12 is a diagram of an experimen~allyvalidated HF channel model

(Watterson et al,.; 1970) for a quiet ionosphere • The transmitted signal"

x(t) in complex-envelope notation" feeds an ideal delay line and appears

at a selectable number of taps with adjustable delays. [Tpl. where p= 1

2" 3" ••• " P is an integer thatnumbers the paths. In general, one tap

or path is used for each magnetoionic component. The signal at each

tap, x(t-r ) at the pth tap, is multiplied (modulated in amplitude and

p

phase) by a complex" baseband, random" path-gain function" g (t ), The

p

delayed and modulated multipath signal components are summed in

general with noise and interference" n(t) and i(t) r-espectively, to form

39
Transmitted

Signal

Tp

I

Tapped Delay Line

Received

Signal

y (t)

Noise, nl t ) Interference, i (t)

Figure 12. HF channel model.

the received aggr-egate, y(t). The functions nft), i(t)J and y(t)J like x(t),

are complex envelope functions that are defined with respect to the same

rf reference frequency, f

r•

The channel model in Figure 12 excludes dispersion because it is not

significant over bandwidths typical of HF digital systems «12 kHz). If

dispersion were aignificant, it could be included in the model by incorporating all-pass dispersion filters in each path immediately preceding

the path-gain multiplier.

From F'igure 12 it can be seen that

P

y(t) = ~g (t)X(t-T ) + nlt) + i(t) LJ P.P

p=l

(32)

The complex, ttme-varytng, impulse response. of the channel, x(t) to y(t),

40
is

P

hh.t) = 2: gp(t)6h-Tp)

p=l

(33 )

where 6(T) is the Dirac delta function. The Fourier transform of h(,., t)

on T is the complex time-varying frequency response of the channel,

P

H(f.t) = 2:gp(t)exp(-j2iTTpf)

p=l

(34)

Because each path-gain function, g (t ), is a random process, it must

p

be described in terms of its statistical parameters. In the experimental

validation of the HF channel model, it was shown that the path-gain

functions are independent Gaussian-scattering (Rayleigh-fading) processes

with generally different mean Doppler shiftsII Specifically, it was shown

that each complex path-gain function is accurately described by

g (t) = g 0(t) e xp(j 2'IT\J t) P P P (35 )

where gO(t) is a stationary. zero-mean. circular. complex-Gaussian

process~. and v is the mean Doppler shift on the path. If

p

C (6t) = E[g*(t)g (t+ ~t)] P p P (36)

is the autocorrelation of the path-gain function, then it was shown that

its Fourier transform. the power spectrum of gp(t). is

(37 )

2 A stationary, zero-mean, circular I complex-Gaussian random process

has real and imaginary components that are independent, stationary,

zero-mean Gaussian processes with identical even power spectrums.

41
where 2CJp is defined as the frequency spread (approximately the fading

rate) on the path. Equation (37) is illustrated in Figure 13. It can be

seen that the statistical characteristics of the path-gain funct iori, g (t ), P

are completely specified by three parameters: the path power gain,

Cp(O) [or the path attenuat.ionLn decibels, Ap=--10log[Cp(O)]}; the path

Doppler shift, v

p;

and the path frequency spread, 2CJp•

Each path as described above represents one magnetoionic component

when the two magnetoionic componerits in a high ray or low ray have

significantly differ-ent de Iays, Doppler 'shifts" or frequency spr'e ad's; i , e."

when therr-dtfferentfal delay is a aignif'icant'Tr-aetion of"the reciprocal of

the bandwidth of the channel being modeled , when their differential Doppler

shift is a significant fraction of their frequency spreads" or when their

frequency spreads are signifiCafltly different. When the de Iays, Doppler

shifts, and frequency spreads of the two magnetoionic components are

nearly the same" as they typically are on daytime F-layer low-ray modes"

then a single path can represent both magnetoionic components.

The channel can be described in a similar way. The channel

correlation function is defined by

R(llf" 6t)= E [H*(f"t)H(f+Af"t + ~t)J (38)

The channel scatter function is defined as the double Fourier transform

on t.J. and ~t of R(6f,,::Cit)1 which for-the model of Figure 12 is

P

S,(T, v) ='2: 0( T ""Tp)Vp(V)

p=1

(39 )

Equation (39 ) is illustrated in Figure 14 for a hypothetical channel with

IF and 2F low-ray modes where the two magnetoionic components in each

mode have essentially identical delays" Doppler shifts" and frequency

spreads.

Because g (t ) and H(f" t ) are dimensionless" their autocor-r-elations, p

Cp(At) and R(M, ~t), are also dimensionless. Cp(O) is the power gain on

4:2
v p (7/)

Cp(O)

fi1i O"p

__________----=:~-~....._--...L--~----....;..:::=~-'V

o 'Vp

Figure 13. Path-gain spectr-um,

5crY)

Figure 14. Hypothetical channel scatter function.

43
the pth path, while R(O~ 0) is the channel power gain. Therefore, vp(\J)

and S(T \J) are power-gain density functions: v (\J) is the ratio of the

p

output signal power per unit frequency interval received over the pth

path to the channel signal input power and S(T~ \J) is the ratio of the output

signal power per unit frequency interval and per unit time interval over

all paths to the channel signal input power o Each path can be viewed as

a continuum of infinitesimal specular (nonfading) paths with a common

deIay, different frequency shifts with equal adjacent infinitesimal spacirigs ,

and random phase s, where the magnitudes of the infinitesimal specular

components are proportional to s(,- \J)~ the square root of the channel

scatter function in (39)0 Because each fading path is a Gaussian-scattering proce s s , the channel is a Gaussian-scattering process; i , e. the

signal carried by each path and the total signal carried by the channel

exhibit Rayleigh fading (the magnitude of the received signal envelope

has a Rayleigh density function).

The preceding validated channel model applies only to a quiet ionosphere (the usual case) where the propagation modes are essentially

discrete in t irne , Under spread-F conditions, the model presumably

could be modified by replacing the time-discrete 6(T-T ) in the channel

p

scatter f'uncti.on, (39)~ with a suitable nondiscrete time-scatter function,

possibly the exponential function

1

P exp[ -h-'-p)!ppJ

p

o

T 'T

P

(40)

where Pp is the time spread on the "path" (analagous to the frequency

spread, 2o-p)' Such a model has not been validated, however.

From the preceding descriptions of the propagation characteristics

of the HF channel and the HF channel modeI, it can be seen that the types

of distortion that an HF channel can impose on a signal can be classified

as follows:

44
Types of Channel Distortion

(1) Additive

(a) Noise

(i) Thermal (Gaussian)

(i.i) Impulsive (atmospheric" man-made)

(b) Interference (unwanted signals)

(2) Multiplicative

(a) Time scatter (frequency selective)

(I) Differential delay (multipath)

(i.i ) Dispersion (assumed negligible)

(b) Frequency scatter (time selective)

(L) Differential Doppler (multipath)

(Ii ) Fading

When a channel has a single propagation path with a delay" T

1 " and a

Doppler shift" v

1" th~ channel does not impose any delay distortion

because it is assumed the demodulator can compensate for the delay by

suitably synchronizing to the. single-path stgnal, However" with two

or more propagation paths with different delays" the multipath propagation introduces a differential-delay distortion (2ai above) even with

optimum receiver synchronization.

In an analagous way" when a channel has a single propagation path

with a delay" T

1 " and a Doppler shift" \)1" the channel does not impose

any Doppler distortion because it is assumed the demodulator can

compensate for the Doppler shift with a suitable Doppler-correction

circuit (as it is assumed to do for equipment frequency er-rors ). However" with two or more propagation paths with different Doppler shif'ts,

the multipath propagation introduces a differential-Doppler distortion

(2bi above) even with optimum Doppler cor-r-e ction ,

45
5. RECEIVER

5. 1 Receiving Antenna

It is common practice in HF communications to use either the same

antenna or antennas of similar design for both transmitting and receiving.

The classifications and descriptions of HF transmitting antennas that were

presented in Section 3. 4 therefore also apply to HF receiving antennas,

and do not need to be repeated. However, HF antennas sometimes are

designed and used for receiving only because of three advantages:

Advantages of Receiving Antennas

(1) Lower power

(2) Smaller size

(3 ) Adaptibility

The rf powers handled by receiving antennas are many orders of

magnitude lower than those handled by transmitting antennas. Consequently, the high-voltage insulation and corona problems that must be

considered in transmitting antenna designs are not present in receiving

antenna designs, which usually simplifies the physical design.

In general, an HF antenna with a given pattern can be made physically

smaller for receiving applications, because the decreased efficiency

(greater fractional power loss) that usually accompanies the smaller size

can be tolerated in HF receiving applications. A more lossy antenna can

be toler-ated because the ambient atmospheric noise level is "usually

substantially greater than the thermal noise level in a receiver with a

low noise figure (CCIR, 1964); i.e. , the power loss in the receiving

antenna reduce s both .the signal and atmospheric noise levels at the HF

receiver input, but does not significantly change the signal-to-atmospheric -and-receiver-noise ratio, provided the loss is not excessive. An

example of a smaller size, single-element receiving antenna is an untuned

loop that is a small fraction of a wavelength in diameter. Arrays of such

46
elements can be used to provide gain and directivity.

Antennaadaptibility can be defined as the ability to change electrically the pattern or steering of an antenna. While adaptive transmitting

antennas can be and are used" adaptibility is generally easier to obtain

in a receiver-only antenna: the outputs of the several antenna elements

can be electrically controlled over a large range of amplitude and 360 0

of phase shift 'by suitable low-lev~l active circuits to provide greater

versatility in both pattern shape and steering.

Receiving antennas" like transmitting antennas" introduce filtering

distortion imposed by their.generally frequency-selective responses.

Adaptive receiving antennaawith active circuits may also introduce

other types of equipment distortion (p. 8)" such as thermal noise and

interference" that depend on their design.

5.2 HF Receiver

A typical HF receiver is illustrated in Figure 15. It consists of a

tunable band-passHF amplifier followed 'by a first frequency converter"

a fixed-tuned band-pass first-IF amplifier" a second frequency converter"

and a fixed-tuned band-pass lower frequency second-IF amplifier that

delivers the receiver output aggregate (signal and distortion) to the

demodulator 0 Some receivers use three frequency converters" each

followed by a fixed-tuned band-pass IF amplifier. The first localosci.Ilator frequency is adjusted with theHF amplifier tuning to tune the

HF receiver to the desired HF signal frequency. The frequency translations in the HF receiver nominally restore the signal pulse trains to

the frequencies at which they were generated in the modulator" usually

in the ELF range.

The HF amplifier" which is tuned to the signal frequency" provides

image rejection for the first converter and suppresses out-of-signalband interference which otherwise" if sufficiently strong" might overload

the receiver. The HFamplifier is usual.lyde aigned to have a low noise

47
Input

from

Antenna

HF

Amplifier

1st

Frequency

Converter

1st Local

Oscillator

1st - IF

Amplifier

2nd

Frequency

Converter

2nd Local

Oscillator

2nd - IF

Amplifier

Output

to

Demodulator

Figure 15. Typical HF receiver.

figure and sufficient amplification to make the atmospheric noise delivered

by the antenna predominate over the thermal noise generated in the HF

amplifier and subsequent converters and IF amplifiers.

The two or more fixed-tuned band-pass IF amplifiers provide additional amplification and filtering 0 The filtering suppre s se s the unwanted

sideband generated by each frequency conver-ter, suppresses the localoscillator components if the balancing of the frequency converters is

inadequate I and also suppresses any undesired Qut-of-signal-band higher

order intermodulation products generated by converters that are not good

approximations of true multtplters , The IF filtering also provides

suppression of out-of-signal-band noise and inter-Ierence , particularly at

frequencies near the signal band that are not adequately filtered by the

usually wider band HF-amplifier filtering.

The aggregate delivered at the HF receiver output, and sometimes

the aggregate at an earlier point in the r e cetver-, are maintained at

nominally constant power levels by a suitable AGe circuit that controls

the gains of the ampl.ifie r s , The response time of the AGe is sometimes

selectable 0

It can be seen that the HF receiver performs three interleaved

primary functions:

48
HF Receiver Functions

(1) Frequency translation

(2) Filtering

(3) Amplification

In performing these functions, the HF receiver, like the HF transmitter, can introduce all of the types of equipment distortion listed on

p. 8 except quantizing noise (provided all-analog circuits are used),

synchronization distortion, and Doppler-correction distortion (because

it is assumed that any frequency error introduced by the local oscillators

in Figure 15 can be compensated or corrected by the Doppler-correction

circuit in the demodulator). While the distortions in the HF receiver

may be no greater than those in the HF transmitter" their effects on

system performance can be much greater under some channel conditions.

5.3 Demodulator

The aggregate delivered by the HF receiver to the demodulator

generally contains several trains of frequency-multiplexed or concentrically multiplexed signal pulse s with distortion components introduced by

the equipment and the HF channel , The demodulator separates the

several trains of pulses by suitable filtering and samples each filtered

train of pulses to obtain an estimate of the amplitude" the phase, or the

amplitude and phase of each pulse 0 Each pulse sample is delivered to a

decider" which for each data bit carried by the pulse" decides whether a

zero or one bit was transmitted.

Because the processing that a demodulator performs on each pulse

train is basically the same" demodulator operation can be described in

more detail by describing the processing for one tr-ain, the Ath. The

processing depends on whether a single-filter or a multiple-filter keying

method (p 0 15) is used in the modulator 0 Figure 16(a) illustrates the

processing for the Xth pulse train in a single-filter demodulator, while

49
X+1

z(t)

Doppler

Correction Synchronization

Decider

X ------....... A. b3X(k) I

(a) Single - Filter Demodulator

Doppler Synchronizotion Correction

X+1

Filter °X1(t) Sampler

dA1(..I)

Xl X1

IdA~(..l)1 Id ( j )I

0Xm( t ) °Xm(.i') z (t) Filter Sampler Decider

Xm Xm X Demult.

Filter °AM(t) Sampler dAMLl)

XM AM

( b) Multiple - Filter, Demodu lator

Figure 16. Portions of demodulators for pulse train A.

50
Figure 16(b) illustrates the processing for the Ath pulse train in a

multiple-filter demodulator. Both show what actual demodulators do in

effe ct, regardless of the specific instrumentation techniques that are

used. A description of the operation of the single-filter demodulator

will be presented first, and then a description of the multiple-filter

demodulator.

In the single-filter demodulator of Figure 16(a)J the HF-receiver

output aggregate J z(t) in complex-envelope notation, is delivered to a

single Ath filter whose purpose ideally is to maximize the signal- todistortion power ratio in its output, 0A(t). The types of demodulator

filters that can be used in both single-filter and multiple-filter demodulators are:

Types of Demodulator Filters

(1) Nonadaptive (tlme-dnvar-iant response)

(a) Matched

(b) Nonmatched

(2) Adaptive

(a) Quasi-static

(b) Dynamic

Nearly all digital radio systems at pr-e sent use nonadaptive demodulator fi.lter-s , filters whose responses do not change with time. N9nadaptive demodulator filters may be matchedor-rionmatched to the

signal pulses generated in the modulator. To define a matched filter,

let the fundamental pulse wavefor-m, p(t) in (12), p, 15, after multiplexing for the Xth pulse train, wA

(t) in (21), p, 19, be

(41 )

Then in the single -filter demodulator of Figure 16(a), a matched filter

is one whose generally complex impulse response is

hA,(t) gt.Y~(\ -t)

51

(42)
where g'A is an arbitrary complex gain, and T

A is a semi-arbitrary fixed

time delay required for physical filter realizability. The frequency

response of the matched demodulator filter the Fourier transform of

hA(t)1 therefore is

/

(43 )
t

T

t

T

•

6

•

3

Pulse 2

I I J

1 2 3 4 5 6

I

Pul -

b3A(k) ~l .t---_I I__I k

1 2 4 5

-1

o 3

2 4 5

-1

•

1

•

3

Figure 17 0 Characteristics of matched-filter system

with binary PSK under ideal conditions.

53
signal response, 0>"8(t), at the output of the single Ath matched demodulator filter in Figure 16(a). The response is illustrated by the solid

line segments in the third waveform in Figure 17" where it is assumed

the receiver gairr is set to give peak responses of ±1 • The illustration

ignores the :signaldelay introduced by the-equipment and channel between

the modulator output" wft ), and the demodulator input" z(t)" but includes

the delay in the demodulator filter. In the example of o>..s(t), the positive

and ne gative-dashed-Line equilateral triangles" each ofdur-ation BT', are

the demodulator filter responses to the individual rectangular pulses of

duration T in wA,(t). The sum of the dashed-line triangular responses

form the total response, o>..s(t), shown by the solid line segments. For

the illustrated response , the ar'bitr-ar-y. matched-filter gain coefficient"

gA in (42) and (43), is such that o>..s(t) is real. If the phase of g>.. were

changed by&-;:)gX' ,then the reaV0A,s(t) in Figure 17 would be multiplied/by

a constant phase factor ,exp(jtl~gAl, to become complex, but Figure 17

would still illustrate the amplitude component of the complex o.. (t). I AS

Under nonideal conditions" when channel and equipment distortions

are present" the-demodulator' filter output becomes

(44)

where 0>..it) isthe total distortion~omponent.,.When only white noise

distortion is present" a matched demodulator" filter maximizes the signalto-noise ratioin 0A(t) at integer values of relative times t ItT; i , e OJ no

other filter can provide a larger signal-to-noise ratio in its output.

However" when other types of distortion are pre sent , a matched demodulator filter generally does not maximize the signal-to-distortion ratio at

its output.

For all distortions other than white noise" there is generally for each

distortion condLi::i.on a nonmatched filter that maximizes the signal-todistortion ra:ti6inthe filter output, 0A(t). However, such a filter would

not maximize the signal--to-distortion ratio under other distortion

54
conditions. Therefore" nearly all HF digital receivers with single-filter

demodulators use nonadaptive filters that are nominally matched" so as

to obtain maximum signal-to-noise ratio in 0A(t).

Because channel distortions other than white noise predominate a

large part of the time" overall receiver performance can be improved

with an adaptive demodulator filter" one whose response is automatically

adjusted to maximize the signal-to-distortion ratio in its output, 0A(t)~

according to the distortion conditions. If hAC,. t) is the generally

complex time-varying impulse response of an adaptive demodulator

filter" then

00

0A(t) = z(t-,.) hA(,.~t) d'r

o

(45)

where z{t) is the input to the filter. The adaptive filter has a timevarying frequency response, HA(f~ t),that is the Fourier transform of

h\(T"t) on T.

An adaptive demodulator filter must incorporate a circuit which

measures or analyzes the aggregate on .a continuing basis. The data

obtained from the analysis" possibly coupled with a-priori knowledge of

the multiplexed fundamental pulse wavefor-m, PACt) in (41)~ is then used

in a suitable algorithm to adjust or control the parameters of the

adaptive filter to maximize the signal-to-distortion ratio in its output"

0A(t). A quasi-static adaptive filter is one whose parameters and

response change slowly with time to maximize the long-term signal-todistortion ratio in 0A(t). A dynamic filter is one whose parameters and

response change rapidly with time" up to rates comparable to the signal

bandwidth" to maximize the short-term signal-to-distortion ratio in

0A(t) [Watter-son, c. c. (1979)~ An adaptive receiver filt~r for interference suppression in digital spread-spectrum radio systems (U)" NTIA

Tech. Memo. 79-9C, pp. 1-122" Feb. (Secret) {U. S. Dept. of Commerce"

Boulder" CO 80303)J Quasi-static adaptive filters" like nonadaptive

filters" are normally linear" unless a nonlinear transfer characteristic

55
such as clipping is incorporated. Dynamic adaptive filters are inherently

nonlinear however because the control function that rapidly adapts the

filter response is dependent on the filter input aggregate; consequently

the superposition theore m does not apply and the filter is nonlinear. At

the present time adaptive receiver filters have received only a very

limited theoretical and experimental consideration (Di Toro et ale 1964;

Brown, 1977; Milstein et ale 1978).

In the single-filter demodulator of Figure 16(a)~ the demodulator filter

output , o,,(tL is delivered to a sampler. The sampler samples 0A(t) at

the pulse rate of the tr-ain; lIT to obtain an estimate of the complex

value of each pulse in the train. The pulse-sampling times are determined

by a clock whose timing (phase) is controlled by a synchronization circuit

that is not shown in Figure 16(a). Because o,,(t) is a complex envelope

fun ction, the successive samples of 0A(t) for a complex demodulator pulsesample sequence

(46)

where dAs(t) and d"d(t) are the signal and distortion components respectively G Under ideal conditions (no equipment or channel distortions),

d"d(t)= O~ and d,,(t)= d"s(t) may have anyone of M discrete complex

values corresponding to the M different waveforms that may be transmitted; +1 or -1 for the ideal binary PSK system in Figure 17 0 For the

single-filter (ASK~ PSK" and APSK) modulator keying values illustrated

in Figure 3~ p. 17 the M discrete values of d,,(.t)= d"s(.t) under ideal

conditions would be identical to the keying values except for an arbitrary

constant complex scaling.

Under nonideal conditions, distortion components are present in o,,(tL

and the demodulator pulse-sample sequence , d,,(.t)~ is consequently nondis crete; i 0 e G~· it has a continuous distribution in the complex d-plane

even when the signal cornpone nt , d"s(.t), is r e al, When equipment or

channel distortions are present in o,,(t)~ optimum synchronization exists

when the pulse samples are taken at times when the expected signal-to56
distortion ratio in o).,(t) is a maximum. With white noise distortion

present in the matched-filter binary-PSK example of Figure 17, the

illustrated sampling times constitute optimum synchronization because

the expected signal-to-noise ratio is greatest at these times. With a

nonmatched filter, optimum synchronization would be different. In

general, optimum synchronization depends not only on the filter r-esponse ,

but on the types and characteristics of the distortions that are present.

Regardless of the types of distortion pre sent, the loss or degradation in

receiver performance introduced by nonoptimum synchronization can be

viewed as being produced by synchronization distortion (equipment distortion 2ai in the list on p. 8).

In the single-filter demodulator of Figure 16(a)J each pulse sample in

dA(t) is delivered in turn to a decider which, for each of the N data bits

carried by that pul.s e , decides whether a zero or one bit was transmitted.

The bit--decision methods that n1.ay be used in both single-filter and

multiple-filter demodulators are:

Bit-Decision Methods

(1) Coherent

(2) Partially coherent

(3) Differentially coherent

(4) Noncoherent

Table 2 relates the four bit-decision methods to the single-filter and

multiple -filter keying methods described earlier. Each combination is

rated t he oretIc al only (T)~ practical (P)~ or impossible (1)8 The most

widely used practical combinations are circled. The reasons for the

ratings will be given in the descriptions of the bit-decision methods. At

this poirrt , we will consider the four bit-decision methods in turn as they

apply to the single -filter (ASKJ PSK~ and APSK) demodulator in Figure

16(a).

Coher-ent; partially coher-ent, and differentially coherent bit decisions

57
Table 2. Keying methods for var-i.oua-bit vde cision methods

---

Keying Method

Bit-Decision Single Filter Multiple Filter Method

ASK PSK APSK FSK CPK

Coherent T T T T T

Par-tial.lycoher-ent P P P P P

Differentially coherent I ® P I I

Noncoherent ,p I I ® P

T= theoretical only, P= practical, and 1= impossible.

Circled practical combinations are the most widely used •

are basically the same but differ <in that coherent bit decisions are only

theoretically possible, while' partfal'ly coherent and differentially coherent

bit decisions are practical approximations of coherent bit decisions.

When coherent, partially coherent" or differentially coherent bit decisions

are made in a single-filter demodulator, Figure 16(a), the decider in

effect divides the complex value of each pul.sejsample , d).,(t), by the

corresponding value ina complex reference sequence. r ).,(t), to obtain an

approximate keying .value,

(47 )

I'.J

K).,(t) is a nondiscrete (continuously distributed)approxima:tion of the

discrete (M-ary) true keyingvalue, K).,(t).'In general, K).,(t) differs from

K).,(t) for two reasons: becausedxCt) contains distortion components, and

r ).,(t) is not optimum.

The decider then in effect compares each approximate keying value,

K\(t), with stored values of the M possible true keying values, {Km},

such as those illustrated in Figure 3', p'. 17 • The purpose of the compar- f'.J

ison is to determine which of the Mtrue keying values is closest toK\(t),

58
and to decide the closest true keying value was the particular one of M

possible values that was transmitted. Specifically, the decider in effect

computes

Then if

ill: 0, 1, 2, ••• , M-1 (48)

the decision is made that the ~th pulse waveform was transmitted, where

ois a discrete (M-ary) estimate of fJ., the number of the pulse waveform

that actually was tr-ansmitted: i.eq~. may be Iner-r-or because KX(t) in

(47) is an approximation of the true keying value, KX(t).

In partially coherent, differentially coherent, andnoncoherent singlefilter systems, each selected pulae -wavefor-mnumber, ~, in effect is

used ina stored table of pulse waveform number, m, versus keying value s.,

K

m,

to determine KX(t), a discrete estimate ofthe true keying value,

KA(t). KA(t) is then used to generate the reference sequence , r A(t), in

a-manner' to be described.

In all sfngle efflter' demodulators, eachselected pulse-waveform ,.. numbe r , Jj."ineffect is used ina stored -tableofasstgned bit permutations,"

such as Table 1, p. 11, to determine and deliver the corresponding bit

permutation. For successive values of t, the corresponding successive "-

bit permutations form b 3A(k), a discr-ete es~ima.te of the binary data

sequence, b 3A(k), that is delivered to the Xth pulse-train generator in the ,.. modulator. The set of sequences, {b3A(k», delivered by the 11. deciders

(one sequence for each pulse train) ·arecombined in the demultiplexer in ,.. Figure 16(a) to form b 2

(j ), a discrete estimate of the binary data sequence,

b 2(j ), that is delivered to the modulator. The estimated binary data

sequence, b2(j ), is an output of the demodulator, as shown in Figure 1,

p. 4 0

In some single-filter systems w ith error coding, the magnitude ,of the

demodulator pulse -sample sequence in the Xthtrain, Id{t) I. is also

59
delivered to the demultiplexer, as illustrated in Figure 16(a). The set of

sequences, [ldA(.f.,)I}, delivered by the I\. deciders are paired with the

proper data bits in b2(j ) (each value of IdA(.f.,)! is used N times) to form

I d(j) f, a continuously distributed sequence which, for each value of j"

specifies the magnitude of the demodulator pulse sample from which the

data bit, b2(j ), was obtained. The sequence Id(j) I is delivered as a

demodulator output to the error decoder, as shown in Figure 1.

Now consider coherent" partially coherent, and differentially coherent

bit decisions in turn" for which (47)-(49) apply. For any combination of

basic pulse waveform" keying method, and multiplexing method, coherent

bit decisions by definition provide the theoretically best bit-error-probability performance that is possible under some specified channel conditions. Coherent bit decisions are usually defined under very restricted

channel conditions by four specifications:

Restricted Definition of Coherent Bit Decisions

(1) The channel contains only a single nonfading or arbitrarily slow

Rayleigh-fading path with white thermal noise the only channel

distortion.

(2) There are no equipment distortions.

(3) The demodulator uses a matched nonadaptive filter.

(4) The reference sequence, rA(.f.,), is identical to d

Ac(.f.,;l), the

demodulator pulse-sample sequence for KA(.f.,)= 1 when thermal

noise is absent.

Specification (3) maximizes the signal-to-noise ratio in dA(.f.,) and

causes the noise component in dA(.f.,) to have an autocorrelation sequence

that is zero for all integer displacements, ~t" except 6t= 0; i c e ,.; it

insures that the noise component in dA(.f.,) has no predictable component.

Consequently, the receiver bit-error-probabilityperformance is the

best that is theoretically possible.

It is desirable to extend the restricted definition of coherent bit

60
decisions to a general definition of coherent bit decisions that provides

the theoretically best possible performance with any type of additive and

multiplicative channel distortions:

General Definition of Coherent Bit Decisions

(1) Any type of channel distortion may be pr'e sent ,

(2) There are no equipment distortions.

(3) The demodulator in general uses a dynamic adaptive filter.

(4) The demodulator processes the pulse samples, [dA(t»), for all A

and all past values of t to generate a reference sequence, r A(t),

for each pulse train.

(5) For any specified channel conditions, the adaptive filtering and

the processing used to generate the reference sequences are

chosen to maximize the signal-to-distortion ratio in the f""V

approximate ke vina values. K .. (t). v '-J "A .

Unfortunately, such a general definition has limited practical value

because the optimum combination of filtering and reference generation

are difficult or impractical to specify except under some restricted

channel conditions. However, to the extent that it is practical, coherent

bit decisions will be considered with partially coherent, differentially

coherent, and noncoherent bit decisions throughout the report.

With partially coherent bit decisions, the reference sequence, r (t),

A

is generated by processing a finite number of preceding pulse samples in

the Xth pulse train. In PSK and APSK systems, where the keying value

KmJ: 0 for all m, rA(t) might be determined from

(50)

Equation (50) means that for each value of t, some operation or

processing, a , such as linear predictive filtering, is performed on the

"-

set of:S values of dA(~)/KA(~) for t-:ssgs t-l. For each g. dA(S) is

61
divided by KA(~) to remove the keying from dAs(g)~ the signal component

'" in dA(~'). WhenK).,(i;) is in er-ror, the keying on dAs(g) is not correctly

removed, of course . The operation in (50) t her-ef'or-e is performed on a

set of estimates of the values the pulse-sample sequence , dA(S)~ would

have if the keying values on al.Iof the pulses in the set were K = 1. The

m

method of obtaining rA(t) specified by (50) for PSK and APSK systems

might be modified for ASK systems (whereK '= 0 is one of the M keying m

values) by using values of d).,(g)/KA(~) only when KA(S)-:!:= O.

When differentially coherent bit decisions are made in PSK and APSK

syste.ms, the usual dfr'e ct-skeyfng sequence in the modulator, K,,(t), is

replaced by a phase-differential keying sequence , K Ab (t)~ as specified by

(19) for time -diffe r-entia.Ikeyi.ng and by (20) for frequency-differential

and concentric-differential keying. When time-differehtialkeying is used

in PSK systems, the differentia.lly coherent reference sequence in (47)

becomes

(51 )

i.e 0' the preceding pulse sample is used as a reference. When frequencydifferential or concentric-differential keying is used in PSK systems, the

differentially coherent r-efer-enceeequence in (47) becomes

(52 )

i. eo, the concurrent pulse sample in the adjacent (A -l)th train of pulses

is used as a reference.

When time-differential keying is used in APSK systems, the differentiallycoherent reference sequence becomes

dA(t-l)

ri\(.t) = IKi\(t-l >1 (53)

In APSK systems, unlike PSK systems, the keying values, {K }, have

m

more than one magnitude, as illustrated by Figure 3(c), p, 17.

62
Consequently, d

A(t-l) in (53 ) must be scaled by 1 II KA(t-1ll to change

its magnitude to-the nominal value it would. have if the pulse had been

keyed by one of the lowest-magnitude keying v-alues, 1, j1, -1 ,or -j1

in Figure 3(c)o The use of (53) in (47) then yields the desired approxi- f"V

mate APSK keying value, KA(t). Similarly, when frequency-different ial or concentric-differential keying Is used in APSK .systems, the

differentially coherent reference sequence in (47 ) becomes

d(A-1)(t)

IK(A~l)(~) I

(54)

Now consider the ratings, in Table 2,p.58, for single-filter systems

with coherent, partially coherent, and differentfal.Iy coherent bit decisions•

Coherent, partially coherent, and differentially coherent bit decisions

make lIse of both the amplitude and phase information in the demodulator

pulse samples, dAft), as specified by (47)-(49). With PSK and APSK,

the keying values, [K }, carry phase information, as shown by Figures m

3(b) and 3(c), p. 17.Cons~quently, aaahownbyTableB, with PSK and

-.APSK,poh~rentbit decistons are theorettcatlypoastble and most useful,

and partially coherent andditfer-enttallycoherent bit decisions are

practical and most useful, With ASK, coherent bit decisions are theoretically possible and partially cohe rentbtt decisions are practically

pos sible , However, if coherent or partially coherent bit decisions are

made, better performance can be obtained" with PSK or APSK; consequently, coherent or partially coherent bit decisions with ASK while

theoretically possible and practical, are not the most useful. With ASK,

differentially coherent bit decisions ar-eImpossible because the ASK

pulse train does not contain phase keying.

When noncoherent bit decisions are made in the single-filter demodulator of Figure 16(a), the phase information in the demodulator pulsesample s equence, dAft), is dis car-ded; i , e., IdAft) I is used to make the

noncoherent bit de cistorrs, Because Pq~ and APSK systems depend on

63
phase information in d\(.(..)1 noncoherent bit decisions are impossible in

PSK and APSK systems, as shown by Table 2, p. 58. Noncoherent bit

decisions in ASK systems are made in the manner specified by (47)-(49)

for coherent, partially coherent, and differentially coherent bit decisions

except for minor modifications: the positive real IdA.(.(..)I replaces d",(.t);

the reference s equence , r A(tL is positive real; a zero or positive real f'V

approximate keying value , klt>1 is obtained in place of the generally f"'...J /*V ,-....,.;

complex KA(t); and 6km('(") replaces 6K

m ( t ). With noncoherent bit

decisions in ASK systems, the reference sequence might be obtained

from a modification of (50) by using values of IdA(i;)l/kA(g) only when

kA(S)=!: O.

Now consider the operation of the multiple-filter demodulator illustrated in Figure 16(b) for the Ath pulse train. Unlike the single-filter

demodulator in Figure 16(a), which uses a single filter for each AS'K,

PSK, or APSK pulse train, the multiple-filter demodulator in Figure 16(b)

use M filters for each of the FSK or CPK pulse trains. As explained in

the descriptions of the multiple-filter keying methods, PPo 23-28, each

train of FSK or CPK pulses can be viewed as M dependent trains of binary

ASK pulses in which, for each pulse number, t, only one of the M binary

ASK pulses is on. The M filters in Figure 16(b) correspond to and separate the M trains of binary ASK pulses 0 The M filters may be nonadaptive

or adaptive, as specified on p. 51 0

The outputs of the M filters for the Xth pulse train, [0" (t)}, are

Am

delivered to M corresponding samplers 0 The M samplers simultaneously

sample the filter outputs at the pulse rate of the FSK or CPK pulse train,

lIT, and deliver M corresponding generally complex continuously distributed demodulator pulse-sample sequences, [d, (t)}. The sampling Am

times are determined by a clock whose timing (phase) is controlled by a

synchronization circuit that is not shown in Figure 16(b). For each pulse

in the Xth train, only one of the M samples will contain a signal component,

while all M samples will contain distortion components. If the ~th b inary

ASK pulse in the Xth FSK or CPK pulse train is on for the tth pulse, so

64
that only the sample of the ~th filter output contains a signal component,

then

(55 )

where a, (t) and d'\ d(t) are the signal and distortion components ,I\.ms Am

respectively.

The M pulse-sample sequences for the Xth FSK or CPK pulse train"

[dAm(t)L are delivered by the M samplers to a single decider for the

Xth pulse train" as shown in Figure 16(b).. With coherent or partially

coherent bit decisions" an approximate keying value"

m e 0" 1, 2" .•. " M-1 (56)

is obtained for each of the M binary ASK pulse trains that compose the

Xth FSK or CPK pulse train, as specified by (47).. However" the decision

process specified by (48) and (49) is not used" as it is in single-filter

systems. Rather, for each pulse" t" the decider determines which of

the M approximate keying values. [KAm(t»). has the greatest real

component to decide which of the M binary ASK pulses was on" thereby

deciding which of the M possible waveforms was transmitted. Specifically" if

m=O" 1" 2" .0." M-1 , (57)

A

then the decision is made that the uth pulse waveform was transmitted"

where 0 is a discrete (M-ary) estimate of Jj." the number of the pulse

waveform that actually was transmitted; i , eo" 0 may be in error because

all M of the demodulator pulse-sample sequences. [dAm(t)}. generally

contain a distortion component ..

While coherent and partially coherent bit decisions are theoretically

and practically possible with FSK and CPK" as shown in Table 2" p. 58"

65
they are not the most useful decision methods for the same reason they

are not the most useful decision methods with ASK: if coherent and

partially coherent bit decisions are made, better performance can be

obtained with PSK or APSK.

As shown in Table 2, differentially coherent bit decisions are impossible with FSKor CPK because the M binary-ASK pulse trains that

compose the Ath FSK or CPK pulse train .donot contain phase keying.

With noncoherent bit decisions in FSK .and CPK systems, for each

pulse, t, the decider determines which of the M pulse samples, fdA. m (t»),

has the greatest magnitude to decide which of the M possible waveforms

was transmitted; i.e., if

m e 0, 1, 2, ••• , M-l, (58)

the decision is made that the0th pulse waveform was transmitted, where

is a discrete (M-ary) estimate of u, the number of the pulse waveform

that actually was transmitted. As shown by Table 2, noncoherent bit

decisions are most useful with FSK and CPK, as they are with ASK, and

for the same reasons.

In multiple-filter (FSK and CPK) demodulators, as in single-filter

(ASK, PSK, and APSK) demodulators, each selected pulse-waveform

number, ~, in effect is used ina table of assigned bit.permutations to

determine and deliver the corresponding bit permutation. For successive

values of t, the corresponding successive bit permutations form b3A.{k ),

a discrete estimate of the binary data sequence, b 3A.(k ), that is delivered

to the Ath pulse-train generator in the modulator. The set of sequences,

[b3A.(k )} , delivered by the A deciders are combined in the demultiplexer

in Figure 16(b) to form b2{j), a discrete estimate of the binary data

sequence, b 2(j ) , that is delivered to the modulator 0 The estimated binary

data sequence, b2(j ), is an output of the demodulator, as shown in Figure

3, po 17.

In some multiple-filter systems with err-or coding, successive values

of the magnitudeofthe 0th pulse estimate in the Ath train, IdA,0(t) I in (58).

66
are also delivered to the demultiplexer, as illustrated in Figure 16(b).

The set of s equence s , [IdA..... (t)IL from the !I. deciders are paired with A

the proper data bits in b 2(j ) (each value of IdA0(t) I is used N times) to

form Id(j) r I a continuously-distributed sequence which, for each value

A '

of i- specifies the magnitude of the ~th demodulator puls e sample from

which the data bit, b2(j ), was obtained. The sequence Id(j)1 is delivered

as a demodulator output to the error decoderI as shown in Figure 1 1 p. 4.

In both single-filter and multiple-filter demodulators (Figure 16)1

a synchronization circuit is required to control the timing (phase) of the

sampler clock, Ide al.ly, eachpul.se sample should be 'taken at that time

during the pulse period when the expected signal-to-distortion ratio in

the demodulator filter output is a maximum. The synchronization circuit

operates from the one or more pulse trains that carry the digital data

ina manner that depends on the fundamental pulse waveform and the

keying method that is used. In frequency-multiplexed quaternary PSK

systems using adjoining rectangular pul.se s, slot synchronization is

commonly used. With slot synchronization and ~'pulse tr-ains, one of

1\+ 1 frequency-multiplexed subchannels carries no pulse train' (is vacant).

In the demodulatorI the filter 'tuned to the vacant subchannel responds to

all of the frequency-offset pulse trains at' nonoptimum-sarnplfng times.

The output of the vacant filter is-sampled twice for each pulse numberI

t l at times earlier and later than the single sampling time for the f\ pulse

trains. The early and late samples are combined and filtered to control

the phase of the sampler clock. In binary FSK systems using adjoining

rectangular pulses with noncoherent bit de cistons, the magnitude of one

or more of the demodulator filter outputs can be processed to control the

phase of the sampler clock ..

Most single-filter and multiple-frlter demodulators also incorporate

a Doppler-correction circuit whose- function in the frequency domain is

analagous to that of the synchronization (delay-correction) circuit in the'

time domain, A single Doppler-e cor-re ctton circuit is, used to shift the

frequencies of all 1\ pulse trains by a common amounttocompensate for

67
the mean Doppler shift imposed by the channel and e quiprnent , Ide ally,

the Doppler correction should be that frequency shift required to maximize the expected signal-to-distortion ratio in the demodulator filter

outputs. The Doppler-correction circuit may operate from one or more

of the pulse trains that carry the digital d ata, or it may operate from a

CW Doppler-correction signal just outside the signal band. A CW

Doppler-correction signal is commonly used in frequency-multiplexed

quaternary PSK systems using adjoining rectangular puls e s, The techniques used by Doppler-correction circuits in the frequency domain are

analagous to those used by synchronization circuits in the time domain.

For most appl.Ications, where a transmission continues for a relatively

long t i me , the r-esponsetime s of the synchronization and Doppler -correction circuits can be and usually are relatively long (tens or hundreds of

pulse periods)" In burst communication s ystems, where a transmission

may be short (tens or hundreds of pulse periods), short response times

are required.

The demodulator in general introduces all of the types of equipment

distortions listed on po 8"

5 0 4 Error Decoder

As illustrated in Figure 1, p. 4, the error decoder processes b2<J).

a discrete estimate of the binary data sequence , b2(j)~ that is generated

by the error coder in the transmitter. Some error decoders also process

f d(j) f the continuously distributed magnitude of the pulse -sample sequence

which, for each value of j~ specifies the magnitude of the demodulator

pulse sample from which the corresponding data bit, b2{j ), was obtained.

The purpose of an error decoder is to dete ct, and in gener al., to correct

as many errors in b2{j ) as practi.cal., In general, fewer errors can be

corrected than detected, and not all errors can be dete cted ,

For both block and convolutional codes (p. 9)" there are two major

68
types of decoding:

Type s of De coding

(1) Hard

(2) Soft

" With hard decoding" only b 2(j)" the estimate of the binary data,

sequence" is processed. The decoding is called hard because it makes

use of the discrete (hard) decisions made by the decider in the demodulator that constitute b2

{j ). Using a decoding algorithm suited to the

specific code that is used" the decoder in effect uses the redundancy

provided by the check bits to detect and correct errors.

With soft decoding, both b2(j ), the estimate of the binary data

sequence" and f d(j) r" the magnitude of the pulse-sample sequence" are

processed. The decoding is called soft because it makes use of the

continuously distributed (soft) nlagllitude of the pulse-sample sequence"

as well as the discrete estimate of the binary data sequence. In effect"

the soft decoding algorithm first uses b2(j ) to detect and correct those

errors which the hard decoding permits" and then uses f d(j) r to correct

additional errors. Substantial additional error correction is possible

when the errors are highly correlated with rd(j) r. This is the case in

any channel with substantial fading, such as HF channels. With such

channeIs, the short-term bit error probability on each pulse train is

inversely related to the magnitude of t he, pulse; t , e e" errors occur

when fading reduces the magnitude of the pulse" without affecting the

distortion level~ to decrease temporarily the signal (pulse)-to-distortion

ratio in the demodulator filter output to a level low enough to produce

errors in the bit-decision process.

Soft decoding is illustrated in Figure 18 for a (25" 16) block code with

n. =16 information bits and n =9 check bits (Chase" 1973). In the error

1 c

coder in the transmitter successive sets of 16 information bits in the

input information bit sequence" b1 (i)" are each combined with 9 check

bits to form a 5X5 matr-ix, This is illustrated in Figure 18(a)" where

69
-,

III 1

1 2 11 3 1

1'4 P15 D1 1 D1 2 D13 D1 4 D1 5

1

21 1

22 1

23 1

24 P

25 D 21 D22 D 23 D24 D25

1

31 1

32 1

33 1

34 P

35 D31 D32 D33 D34 D35

1

41

.1

42 1

43 1

44 P

45 D41 D42 D43 D44 D45

P

51 P52 P

53 P54 l?55 D51 D52 D53 D54 D55

L.

(a) Data-bit matrix (b) Pulse-sample matrix

Figure 18. Matrices for soft decoding of a (25., 16) block code.

the I elements are information bits and the P elements are parity check

bits 0 Given the 16 information brts, the parity check bits are chosen to

make the modulo-two sum in each of the five rows and five columns equal

to zero. The 25 bits in each block are distributed among the pulse t r airis,

A.., and in time , t., to reduce the probability of large bursts of errors in

any code block.

In the receiver de coder , the corresponding bit matr-ix, formed from A

b 2

(j ), is identical to Figure 18(a)exGeptfor those information and parity

check bits that are in error 0 The decoding algorithm initially checks the

parity of each row and column. If a single error occurs , its position is

unambiguously determined by the one row and one column that violate the

parity che cks, and a hard correction of the error can be effected. For

exarnple , if 1

23 only is in er'ror-, the .se cond row and third column violate

the parity check" .. thus permitting the hard correction of 1

23• If two or

more errors occur, the parity che cka cannotunambtguously determine

the locations of the bit e rr-ors, and soft error correction is utilized. For

exarnple , if 123:a~dP35 are in er-ror, the-parity checks in rows two and

three and column? thr-ee and five are .vtol.ated, indicating 1

23 and P

35 may

be in error or, ,¥;ithc~e.qual probabi.Iity, that 1

33 and P25 may be in error.

70
To resolve the ambiguity, the error decoder examines a corresponding

5X5 matrix of values of Id(j) l, as illustrated in Figure rsu». Each

subscripted D element in Figure 18(b) is the magnitude of the pulse

sample from which the bit value in the same row and column in Figure

18(a} was obtained. To determine which pair of bits is in er-ror-, 1

23 and

P35 or I

3 3 and P25' each pair of corresponding generally weighted D

values is summed , The pair with the smallest sum (the weakest pulses)

then specifies with a low probability of error which pair of bits is in

error, thus permitting their soft correction.

The soft decoding algorithm can easily be made to handle two errors

in the same row or column, and can quite practically be made to handle

as many as five or six errors in the illustrated example. The example

shows that soft decoding can provide substantially better error correction than hard decoding because it makes use of additional valuable

information: that the magnitude of the pulse samples and the bit errors

are highly correlated in HF digital radio systems because of the fading

characteristic of HF channels.

There are three ways in which error coding can be utilized in HF

digital radio systems:

Error Coding Methods

(1) Error detection and correction (one way)

(2) Error detection and repeat transmission (two ways)

(3) Error detection, correction, and repeat transmission (two ways)

In the first method" which is used in simplex (one-way) HF digital

communication systems, the error decoding is used to detect and correct

as many of the digital errors as practical. The second and third methods

can be used only in duplex (simultaneous two-way) systems. In the

second method, the error decoder oat each end of the two-way link only

detects errors and" when an error is detected in some pre-arranged

block of data, requests via the return link that the transmitter repeat

71
that block of data. In the third method" each error detector detects

errors and corrects them if they are few enough in number to be reliably

corrected; otherwise" it requests a repeat transmission. The second

and third methods can provide a reduction in error probability comparable

to the first method with simpler error coding" because error detection is

simpler than error correction. However" it requires a duplex system

and suitable buffering at each end to handle the random changes in overall

data rate that results from the repeat transmissions•

Following the detection and correction of errors in the estimate of the

" binary data sequence" b 2(j )" the error decoder separates the information

bits to form the receiver output. bi (0. an estimate of the binary information sequence. b i

(0. that was delivered to the transmitter.

Because error decoders typically are digital e quipments, they introduce

no distortion components.

5.5 Diversity Operation

With diversity operation" the digital data are received two or more

times" the number of times being the order of the diversity" D. The

redundant data from the D diversity channels are combined in a diversity

demodulator to improve the performance of the system. Substantial performance improvement is obtained when the correlation of the fading in

the D diversity channels is reasonably small or negative. Diversity

operation can be classified as follow s :

Types of Diversity

(1) Single transmission (space" antenna)

(a) Polarization

(b) Separation

(2) Multiple transmission

(a) Frequency

(b) Time

72
With single -transmission diversityI also called space diversity and

antenna dive r-stty, each keyed pulse is transmitted only once , but is

received over D antennas that feed D HF receivers whose outputs are

delivered to a single demodulator that is designed for diversity reception.

With polarization diversityI two concentric perpendicularly polarized

antennas provide dual (D= 2) diversity. With separation diver-arty, two

or more antennas with a common polarization are separated by from one

to several wavelengths. Separated antennas with different polarizations

provide polarization and separation diversity.

With multiple-transmission dive r stty, each keyed pulse is transmitted D times to a single receiving antenna. With frequency diversityI

the redundant pulses are transmitted simultaneously in D frequencymultiplexed pulse trains. With time diversity" the redundant pulses are

transmitted at different times in the same pulse train. With fr'equency

and time divers ity, the redundant pulses are distributed in both frequency

and time. Concentric multiplexing of the redundant pulses is not effective 0

Single-transmission separation diversity (Lb ) and multiple-transmission frequency diversity (2a) are commonly used in HF digital radio

systems.

With all types of diversity operation, the diversity demodulator in

effect combirie s the redundant data in the deciders (Figure 16)0 In systems

using coher-ent, partially coher-ent, or differentially coherent bit decisions, "J

each generally complex approximate keying value , K)..,( ..t> in (47)# p. 58# "-J

in single-filter systems or KAm(,f) in (56), p. 65, in multiple-filter

systems, is weighted and summed with the other D-1 redundant approximate keying values to form a single combined approximate keying value.

With noncoherent bit decisions, each real approximate keying value, 1""..) f1'V

k,(t) in single-filter systems or k (t) in multiple-filter systems, is

1\ Am

weighted and summed with the other D-1 redundant real approximate

keying values to forma single combined real approximate keying value.

In both cases, the combined approximate keying value is then processed

as described earlier for a system without diversity.

73
The weighting imposed on the D redundant approximate keying values

is usually one of three types. With selection combining, the magnitude

of the reference value, IrA(t)1 in single-filter systems and IrAm(t)! in

multiple-filter systems, is examined for each diversity channel. The

approximate keying value in the diversity channel with the largest

reference magnitude receives a weighting of one (is selected), while the

other D-l keying values all receive-weights of zero (are discarded).

With equal-gain combining, the D approximate keying values receive equal

weights of lID. With maximal-ratio combining, each approximate keying

value is weighted in proportion to the magnitude of the corresponding

reference value, Ir A(t) I Instngle-ftlter- systems and Ir Am(tH in multiplefilter systems, and in inverse proportion to the noise power in that

diversity channel (which are usually the same ),

5. 6 Performance Monitoring and Prediction

The performance of anyHFdigital radio system changes both with HF

operating frequency and time, because boththe additive and multiplicative

channel distortions (p , 45) change with frequency and time. For this'

reason, most systems haveanumber of available operating frequencies

or channels so that ideally at anytime the channel that provides the best

system performance can be chosen and used. However "this requires a

knowledge of the system performance for the channel that is being used

and a prediction of the system performance. on the other available channels.

Monitoring of the system performance is possible in a number of

ways. Visual monitoring of the received information printout is commonly

used to obtain a rough estimate of the error probability•.In the demodu- F'V fAV

Iator, the total distortion; ~KA~(t)in(49), p. 59;KAm(t) for m*~ in

(57), p. 65; or dAm(t) form:J=~in (58), p. 66; can have its magnitudes

squar-ed and averaged for afl. A pulse trains to determine the signal-tototal-distortion ratio,whie,hindirectlyspecifies the system performance 0

In systems with error coding, theer-ror-decoder' can monitor detected

74
and corrected bit errors to provide an automatic and accurate method of

monitoring system performance.

The prediction of system performance on available channels that are

not being used can be done in the following ways:

Performance Prediction Methods

(1) Simplex (one -way) systems

(a) Experience

(b) Propagationpredictions

(2) Duplex (two-way) systems

(a) Pa:ssivemonitoring

(b) Oblique pulae sounding

(c) Systemsounding

In simplex systems, performance prediction is limited to experience

and propagation predictions. The experience gained in operating an HF

digital radio system between two geogr-aphical locations provides useful

knowledge about the system performancethatcan .be expected on the

available channels at various, times. Propagation predictions can augment

this knowledge by providing useful information about expectedrnultipath

differential-delay and attenuation conditions as functions of frequency

and time. Both prediction methods have limited accuracy and cannot

predict unusual propagation, inter'fer-ence, or noise conditions. In

broadcast transmissions, where the same messages are directed to a

number of receivers at different Iocattonsveither- a commonly acceptable

channel is used or the messages aretransmittedsimultaneollsly on

several channels.

In duplex systems, three additional preduction methods are- avatlable,

With paasiveznonitor-Ing, real-time information on noise and interference

conditions on the available channels is obtained with an auxiliary receiver

that measures the noise and interference levels on the available channels.

With oblique 'pulse sounding, an auxiliarysoun.ding transmitter repeatedly

75
sends spaced pulses with successively different frequencies that scan the

HF spectrum. An auxi.liary sounding receiver at the other end of the

link operates in synchronism to present visually an oblique ionogram,

as illustrated in Figure 9" p , 36. Such ionograms are useful in predicting the differential-delay distortions in the available channels 0 With

system sounding" the HFdigital radio system itself is used to predict

system performance on each of the available channels 0 Periodically"

when the traffic permits or the receiving site so requests" the transmitter and receiver are sequentially switched to the other available

channels for brief periods (f"V 1 minute each)oForeach available channel,

the signal-to-distortion ratio is determined by the demodulator as described above to determine indirectly the bit error pr-obabi.Lity , (A

direct counting of bit errors to obtain an error-probability estimate

takes too long at lower error probabilities.) Automatic transmitter"

antennas" and receiver tuning is necessary. A pre -arranged message

is used to coordinate the transmitter and receiver channel scanning.

With all three duplex methods of performance prediction" the

receiving site requests the transmitting site to change the channel when

this is advantageous 0

6 0 SYSTEM PERFORMANCES

Two criteria will be used to specify system performance:

System Performance Criteria

(1) Information bit error probability

(2) Spectral efficiency (information rate Isignal bandwidth)

The bit-error-probability performance of a system with respect to

the various types of channel and equipment distortions is determined by

nine system design features that were described earlier:

76
*(1 )

*(2)

~:«3 )

>:«4)

(5 )

(6 )

(7 )

*(8)

*(9)

System Design Features

Fundamental pulse waveform (p. 12)

Keying method (p. 15)

Multiplexing method (p , 19)

De modulator filter type (p. 51)

Bit-decision method (po 57)

Transmitter power (po 29) ,

Antennas (ppo 31" 46)

Diversity (p, 72)

Error coding (pp 0 9" 68)

The spectral efficiency of a system" which is independent of channel

and equipment distortions" is determined primarily by the six system

design features above that are preceded by asterisks 0 Multiple-transmission diversity ~ffects spectral efficiency" but single-transmission

diversity does not 0 Spectral efficiency is also affected by an auxiliary

tone or signal that is transmitted for synchronization or Dopplercorrection purposes.

The effects of the system design features on bit-error-probability

performances will be evaluated in the following three sections" first with

respect to additive channel and equipment distortions" second with

respect to multiplicative channel and equipment distortions" and third

with respect to nonlinear equipment distor-tions, Spectral efficiencies

wiJl be evaluated in conjunction with the evaluation of bit-error-probability

. performances 0 To help in the evaluation of bit-error-probability performances" the channel and equipment distortions that were listed earlier

separately (PPo 8" 45) are presented together in Table 3 ..

6 01 Additive Distortions

Unless otherwise stated" it will be assumed throughout this section

that the fundamental pulse waveform and multiplexing method are abritr-ar-y,

77
Table 3. Channel and equipment distortions

Specific Distortions

Types of Distortion

Channel Equipment

Noise Thermal Thermal

Additive Impulsive Quantizing

Interference Unwanted signals Internal

Time scatter

Differential delay Synchronization

Multi- Dispersion Filtering

plicative Frequency scatter

Differential Doppler Doppler correction

Fading AGC

Nonlinear --- Nonlinear

the demodulator filters are matched, the antennas are arbitrary but nonadaptive, there is single -diversity operation, there is no error coding,

there are no transmitter distortions, and the channel and receiver may

introduce only additive distortions. When a channel introduces only

additive distortions, it must contain only a single propagation path, P= 1,

with no Doppler shift, \)1=0, and arbitrarily slow Rayleigh fading, 201 0,

the last to eliminate significant.. fading distortion. Such a channel has a

time-varying frequency response, H(f,t) in (34), p , 41, whose magni- ;

tude is constant (flat) in frequency and has arbitrarily slow Rayleigh

fading in time. When the r-ecetver Tntr-oduces only additive distortions,

the synchronization is perfect, there is no filtering distortion, there is

no Doppler-correction error, and the receiver gain is constant (no AGC

fluctuations.

First consider the case .where there are no receiver distortions and

white thermal noise is the only channel distortion. Let the signal-tonoise power ratio at the receiver input be specified by

S S/f1 Eb

P = - = = -- (59 ) N1 Nl/fl Nd

78
where S is the average total signal power; N1 is the' white noise power

in a bandwidth equal to the information bit rate, f

1 (p. 3); E b

=S/f1 is

the energy per information bit; and Nd=N1/f1 is the white noise power

spectral density; all at the z-e ce iver- input3• Then with a slow frequencyflat Rayleigh-fading channeI, the theoretical bit error probability as a

function of the signal-to-noise ratio at the receiver. input is specified by

the following five equations for various combinations of keying and bitdecision methods:

Pe(p) = ( 1 - -V1 ~p) Rj 4~ , P -7 co coherent PSK, M= 2,4. (60)

Pe(p) = ( 1 - '2~P) Rj 2~ , P -7 co coherent FSK, CPK, M=2. (61)

P~V-J collel~ent ASKI IVl= 2. (62)

P (p) = 1 e ' 2

P (p)

e

(1 ~p)

= (2~P)

diff-coherent PSKI M= 2. (6;3)

noncoherent FSKI CPKI (64)

M= 2.

The five functions are illustrated in Figure 19. Also included is an

approximate performance cur-ve for noricoher-ent ASK (Schwartz et ale I

1966). The differentially coherent PSK equation, (63)1 .and its plot in

Figure 19:1 apply to all three types of phase-differential keying: timediffer-ential., fr equency-differ-errttal, and concentric-differential keying.

3 When any type of white noise is the only distortion and bit-errorprobability is determined as a function of Eb INd for two or more

systems with generally different information rates and system design

fe ature s , such bit-error-probability performances can be fairly compared because they include the transmitter power used for check bits

with error coding', Doppler-correction tone s, and other auxiliary

components.

79
10 20 30

IINoncoherent ASK; M=2

! I COhere~t ASK; =2

__ Noncoherent FSK, CPK; M=2 __

Coherent FSK, CPK; M =2

I

Dif.- Coho PSK; M = 2

Coherent PSK; M = 2,4

o

Q) 10- 1

a..

... >.

.....

..c

c

.o

0

'-a..

'-

0

'-

'-

w

..... 10-2 CD

Signal-fa-Noise Ratio, Eb/Nd, dB

Figure 19 0 Bit-error-probability performances of matched-filter ASK1

PSK1 FSK1 and CPK systems over a slow I Irequency-fl.at,

Rayleigh-fading channel with white thermal noise,

Channel: P= 1, v1 = 0, 201 -7 0, sIr -700.

Equipment: No distortions 0

80
In the event the receiver introduces significant thermal noise" the

curves of Figure 19 apply if the receiver thermal noise is referred to

the receiver input and included with the channel noise in Nd in (59).

The same can be done for any receiver quantizing noise provided the

demodulator filtering converts it to near-thermal (near-Gaussian) noise 0

An examination of Figure 19 shows that with coherent bit decisions"

PSK provides the best bit-error-probability performance" FSK and CPK

provide the second-best performance" and ASK provides the poorest

performance 0 As shown by (60)-(62)" as p -? co" coherent PSK is 3. 0 dB

better than coherent FSK and coherent CPK" which in turn are 3. OdB

better than coherent ASKo Practical systems with partially coherent bit

decisions can closely approach the performances shown for coherent

systems 0 Differentially coherent PSK and noncoherent FSK and CPK

are 3. 0 dB poorer than the corresponding coher-ent systems" while

noncoherent ASK is 2.2 dB poorer than coherent ASK~

It is important to note that all of the performance curves in Figure 19

apply only to binary (M= 2) systems except for the coherent PSK curve"

which also applies to quaternary (M= 4) systems. The differentially

coherent PSK curve for M= 2 also is accurate for M= 4 at the lower biterror probabilities. Because the bandwidth of a PSK signal does not

change when M is changed from 2 to 4 (when the number of bitsfpulse"

N" changes from 1 to 2)" the spectral efficiency of PSK can be doubled

by increasing M from 2 to 4 without changing the bit-error-probability

performance of the system. Therefore" quaternary PSK not only has a

better thermal-noise bit-error-probability performance than binary FSK

(by 3 00 dB) and binary ASK (by 6 00 d'B), but also has greater spectral

efficiency: about four times greater than binary FSK and two times

greater than binary ASK when the same fundamental pulse waveform"

scaled for the same data rate" is used by all three systems.

As M is increased above 4 in PSK systems and above 2 in ASK

aystems, the signal bandwidths remain the same" but the performances

with respect to thermal noise become poorer 0 The poorer performances

81
can be viewed as the prices paid for the increased spectral efficiency that

results. FSK andCPK systems are different" however; as M is increased

above 2" the performance with respect to thermal noise i.mprove s, but

the spectral efficiency decreases. The' poorer spectral efficiency can be

viewed as the price paid for the improved thermal-noise performance.

APSK is normally used rather than PSK for M 8" because its performance is better. When the same fundamental pulse waveforms are

used" the bandwidth of an APSK signal is identical to that of aPSK signal.

ForM 8" the thermal-noise performance of APSK i spoor-er than that of

PSK for M= 2 or4 that is illustrated in Figure 19. However" the spectral

efficiency is higher. The poorer thermal-noise performance can be

viewed as the price that 'is paid for the higher spectral efficiency•

The performance of any system with respect to white thermal noise

is best with matched demodulator filters because such filters maximize

the signal-to-noise ratios at their outputs at the optimum pulse-sampling

times. However" the bit-error-probabilitycurves of Figure 19 also apply

to nonmatched demodulator filters if the curves are translated to the

right by the ratio in decibels of the nonmatched-to-matched filter-output

signal-to-noise ratios, provided the nonmatched filters" like the matched

filters" introduce no filtering distortion.

When white atmospheric or man-made impulsive noise replaces white

thermal noise" the relative performances of ASK" PSK" APSK" FSK" and

CPK systems remain approximately the. same" but their absolutep'erformancesmay be better or poorer than with white thermal noise of the same

spectral power density" Nd" at the receiver input. In a linear receiver

(no pulse clipping)" the performances are poorer at suitably low error

probabilities (less than about 10-1), because the impulses generally project well above the rmsnoise level to cause errors when thermal noise

would not [because the probability density fun-ction for the magnitude of

the complex impulsive noise envelope has a much longer high-magnitude

tail than the Rayle',Igh probability density function for the magnitude of the

complex envelope of thermal (Gaussian) noise]. When clipping is

82
incorporated in a receiver prior to the demodulator input in Figure 16,

po 50J the clipping of the larger noise pulses reduces the rms power of

the impulsive notse , improving the system performance relative to that

of a linear r ece iver-. If the clipping occurs ina relatively wide-bandwidth portion of the receiver (the wider, the better), the subsequent

narrow-bandwidth demodulator filters convert the clipped impulsive

noise to near thermal (near':~Gaussian)'noise. If the clipping level is

near optimum and the ratio of the wide to narrow bandwidths is large

enough, the performances of the systems with white impulsive noise can

be better than with white thermal noise of'the same spectral power density

at the receiver input. Again, matched demodulator filters provide the

best performance.

When channel or receiver interference r-e place s white thermal noise,

the relative performances of ASKJPSK,APSK, FS'K,'andCPK systems

remain approximately the same. Howeve r , their absolute' performances

will depend greatly on the character of the interference and the types of

demodulator filters o When the interference is'noise-like-in character,

has> a bandwidth that is equal to or larger thanthesignalbandw'idth, and

has.a spectral power density over the signal band that is compared to

white thermal noise of the same spe ctral-power density, the performances of the systems with respect to interference' will be compar-able to

their thermal-noise performances.

When the bandwidth of the interference is smaller than the bandwidth

of any pulse tr-ain, the bit-error-probability pe rformance for that pulse

train will be compar-able to the performance with white thermal noise' of

the same power in the output of the matched or nonmat ched nonadaptive'

demodulator fi lter , However, with an adaptive filter, the'performance

with narrow -band interference can be substantially better • This can be

illustrated with CW interference and a quasi-static adaptive demodulator

filter with an adjustable narrow suppression band incorporated in its

otherwise matched or approximately matched fr-equency-r.esporrse, When

the narrow suppression band Iaautomattcal.lycenter'ed €1Rthe CW

83
interference, it can effectively remove the interference while introducing

only a very small amount of multiplicative filtering distortion. With CW

interference, a quasi-static adaptive filter can provide a very substantial

improvement in performance (tens of decibels) relative to matched-filter

performance. If the bandwidth of the interference is increased, the adaptive filter automatically increases the suppression bandwidth. However,

the multiplicative filtering distortion increases, and the performance

improvement is therefore less than with CW interference. With a quasistatic adaptive filter, the performance improvement disappears when the

interference bandwidth becomes a substantial fraction of the bandwidth of

the pulse train. However, with a dynamic filter, substantial performance

improvement can still be obtained if the bandwidth of the modulation on the

interference (rather than the bandwidth of the interference itself) is suitably

smaller than the bandwidth of the pulse train, because the suppression

characteristics of the adaptive filter are dynamically adjusted according to

the modulation on the interference 0 Ideally, the quasi-static or dynamic

adaptive filter adjusts its response to maximize the signal-to-total-distortion ratio at its output at an optimum sampling time, where in the present

case the total distortion is additive interference and multiplicative filtering distortions combined.

The preceding descriptions of system bit-error-probability performances with additive channel and equipment distortions are generally affected

by a change in transmitter power 0 If X is the average transmitter power,

an increase of tJ.X in transmitter power will improve the system performance by 10 log(l +DX/X) dB with respect to channel and equipment thermal

noise (assuming the change in signal Ieve l does not change the noise figure

of the HF receiver via its AGC), but by a generally smaller amount

[<lOlog(l + ~X/X) dB] with respect to channel and receiver impulsive

noise and interference.

If the gain of the transmitting antenna is increased, an equivalent

change in transmitter power, ~X, results, and the effects on system performances are those described for a change in transmitter power 0 If the

84
gain of the nonadaptive receiving antenna is increased, the performances

will generally improve with respect to additive receiver distortions by

an amount up to the increased gain. The narrower beamwidth of the

higher gain receiving antenna can provide improved performances with

respect to additive channel distortions that are suitably dir-e ctional,

Noise typically is only mildly directional, so little if any improvement

would result, but interference is highly directional, and the narrower

beamwidth can provide substantial performance improvements if the

direction of the interference is suitably different from that of the signal.

If the nonadaptive receiving antenna is replaced by an adaptive

receiving antenna of the same gain, then the system performances with

respect to additive receiver distortions are unchanged. However, the

nulls of the adaptive antenna pattern can automatically be adjusted

(within limits) to provide greater suppression of the directional additive

channel distortions" particularly interference" t he r eby irrlproving the

performances over those with a nonadaptive receiving antenna.

The performances of the single-diversity systems described above

are substantially improved by using second-order or higher order diversity. With single -transmission (polarization and separation) diversity,

the spectral efficiency does not change as the order of the diversity" D,

increases 0 With multiple -transmission (frequency and time ) diversity,

the spectral efficiency decreases inversely with D" and an increase in

transmitter power of 1 alog(D) dB is required to retain the same signalto-noise ratio in each diversity channel. At the same time, the performance improvements that single-transmission and multtp'le-rtr-ansrrrission

diversity can provide are identical" provided the degree of independence

of the fading on the diversity channels is the same for both types of

diversity. Therefore, multiple-transmission diversity requires D times

more transmitter power and D times more bandwidth for the same data

rate than single-transmission diversity to achieve the same performance

improvement.

Of three types of diversity combining, selection combining, equal-gain

85
combining, and maximal-ratio combining, the last provides the theoretically greatest performance improvement. With maximal-ratio diversity

combining, the theoretical bit error probability for matched-filter

coherentPSK systems with M=2 or 4 is

Pe (p ;D) = 11 - , 1 P .~~ (~k) [4(1 P>]k I

coherent PSKJ M= 2J 4 J

(65 )

when the arbitrarily slow fading of the signal in the diversity channels is

independent" when thermal channelor c-eceiver noise is the only distortion in each diversity channel" and when these norse s in the diversity

channels are independent (ProakisJ

i 1968).

Equation (65) is illustrated in Figure 20. It can. be seen that the

performance improvements provided by incr-easing the order of d ive r aity,

D J are subatantial, but the improvement increases less rapidly as D

becomes larger 0 The dive r srtyper'for-mance.s for coherent FSK with M= 2

and coherent ASK w ithMe 2 are 3.0 dB and ,6• 0 dB poorer respectively

than the diversity penforrnance s shown in Figure 20 for coherentPSK

with M= 2 or 4 0 The performances with selection combining and equalgain combining are poorer than those illustrated for maximal-ratio combiriing, but not by very much, The performance improvements are less

when the fading on the diversity channeIs is positively cor-r-elated, but the

Impr-ovement sar-egr-eater' wrthnegatively correlated fading, which can

occur with polarization diversity and frequency diversity. The matchedfilter curves of Figure 20 also apply for nonmatched filters when the

curves are translated to the right by the ratio in decibels of the nonmatched-to-matched filter-output signal-to-noise r atios, provided the

nonmatched filters", .Iike the matched filters" introduce no filtering distortton,

The perf'or-mances of the aystems de scribed above can also be substantially improved when error coding is incorporated. Aspreviously

86
Q) 10-2

a..

>-

...

.o

0

.c 10- 3 0

\-

a..

\-

0

'-

'-

w

.....

CD 10-4

M= 2 4,

o 20 40

Signal-to-Noise Ratio, Eb/Ndt dB

60

Figure 20 0 Bit-error-probability performances of matched-filter

coherent binary and quaternary PSK systems over

slow, frequency-flat, independently Rayleigh-fading

diversity channels with independent white thermal

noise and maximal-ratio combining,

Channel: p= 1~ v1 =O~ 201 0, 8/1 ~co.

Equipment: No distortions.

87
described" soft decoding can provide substantially better error correction than hard decoding because it makes use of additional valuable information: that the magnitude of'.the demodulator pulse samples and the bit

errors are highly correlated in HF digital radio systems because of the

Rayleigh-fading characteristic of HF channels 0 The improvement in

system performance provided by soft decoding can be illustrated by comparing the performances of two systems using time-differentially coherent

quaternary (M= 4) PSK with similar but slightly different nonmatched

demodulator filters" one system without error coding and the other with

the (25" 16) block code with soft decoding that is shown in Figure 18" p, 70"

and described on pp. 69 -71. When the bits in each code block in the

system with error coding are assigned to different pulses separated in

time sufficiently to suffer independent fading (so the bit errors in each

block are independent)" then the bit-error-probability performances of

the two systems" obtained by computer simulation (Chase" 1973) are as

illustrated in Figure 21.

It can be seen that the coding provides a substantial improvement in

bit-error-probability performance" particularly at low error probabilities where the curve for the system with coding is much steeper. The

system with the (25" 16) soft error-correcting coding has a spectral

efficiency that is 16/25=0.64 times that of the system without coding

(neglecting Doppler-correction tones). The moderately poorer spectral

efficiency can be viewed as a modest price to pay for the substantial

improvement in bit-error-probability performance. In their linear

portions" the no-coding curve in Figure 21 is 2. OdB poorer than the

differentially-coherent PSK curve in Figure 19 (which applies for M= 4

in its linear portion) because a Doppler-correction tone is incorporated

(1 00 dB loss) and a nonmatched filter rather than a matched filter is used

(1 00 dB loss).

Now consider the effects of additive transmitter distortions 0 In all of

the preceding discussions of the effects of additive channel and receiver

distortions on system performance" it was assumed the additive

88
M=4

o 20 40

10-.1 t-----t---~+___-_+_--~-___+_----=-_+__-

10- 2

....

..c

c

..c

0 10-3 Ia..

I0 (25,16) "-

"-

w Soft .i.:»:

.... Decoding

CD 10-4

Signal - to - Noise Ratio, Ebl Nd, dB

Figure 21. Bit-error-probability performances of nonmatched-filter,

frequency-multiplexed" time -differentially coherent"

quaternary PSK systems with and without (25, 16) soft

error-correcting coding over a slow, frequency-flat,

Rayleigh-fading channel with white thermal noise.

Channel: P= 1, "i = 0, 20'1 0, sIr co.

Equipment: No distortions.

89
distortions were independent ofthe stgnal, which is generally true. However this is not true for transmitter additiye distortions which, when

passing through a fading channel , suffer the same fading as the signal.

Consequerrtly, the signal never fades into the transmitter additive distortions,as it does with the channel and receiver additive distortions, to

produce bit errors. If the tr-ansrntttervaddittve distortions are generated

atasuitablylo'W level relative to,thesignal(say<,-30 dB}, which is

usually .thacase, they affe ctthe-aystem p~,rformange~erylittleandcan

be ignored.

6".2 Multiplicative Distor-t.ions

Unless otherwise stated, it Will be assumed throughout this section

that the fundament alpulse wavefor-m, the keying method, and the multiplexing methodare arbitrary; the demodulator uses matched or nonmatched nonadaptive filters; the bit-decision method is arbitrary; the

antennas are arbitrary but nonadaptive; there is single-diversity

operation; there is no error coding; and the channel and equipment

(transmitter and receiver) may introduce only multiplicative distortions.

When a channel introduces only multiplicative distortions, it will generally

contain several propagation paths, P 1, with arbitrary delays, {T }, ,...... . ."". .p

arbitrary Doppler' shifts, [v}, and arbitrary frequency spreads, [20 }. " p " P

Such a channel has a time-varying frequency response, Hlf', t ), whose

magnitude fluctuates in frequency and time at rates proportional to the

amounts of time scatter and frequency scatter respectively. When

equipment Introduce s only multiplicative drstor-ttons , it of course introduces no noise or internal interference.

All of the multiplicative channel and equipment distortions affect the

bit-error-probability performances of digital systems by appearing in

the demodulator in two forms:

90
Forms of Multiplicative Distortions

(1), Crosstalk distortions

(2) Coherence distortions

When multiplicative channel or equipment distortions are present,

they introduce interpulse interference that constitutes crosstalk drstor'>

tions• Crosstalk distortions' affe ct .the bit-error-probability performances of systems with all combinations of bit-decision and keying

methods (Table 2, p, 58). When .multfpficatfve channel or equipment

distortions are present, the resulting fluctuations in the time-varying

frequency response of the system (channel and equipment) introduce a

degree of incoherence in the amplitude and phase of the signal that

constitutes coherence distortions. Coherence distortions affect 'the biterror-probability performances of systems with all combinations of hi'l:-

decision and keying methods except noncoherent FSK and CPK. Croastalk and coherence multiplicative distortions will be considered in 'turn,

The appearance of multiplicative "channel andequipment distortions

in the form of crosstalk dtstortions can be illustrated with a specific

system; Consider a frequency-multiplexed single-filter '(A'SK, PSK, or

APSK) system that uses adjoining rectangular pulses of duration T'.

Assume the demodulator filters are nonmatched and have rectangular

impulse responses of durationT < T that provide a guard time,T =

r .'. . . . g

T-T , whose purpose is to suppress channel and equipment time-scatter

r . .....

distortions. First consider the reception of a single pulse, the tthin

the Xth pulse train, over a single specular (nonfading) path. Assume

the pulse sampling time (synclu'onization) is fixed, there is no filtering

distortion, no Doppler correction, and no AGC distortion (constant

equipment gain). Let dAh', v;t) be the Xth detector (sampler) response

in the tth pulse sample to the -tth pulse in the Xth train as a function of

the single path delay, r (measured relative to the demodulator t ime),

and the path Doppler shift, v. Under, the specified channel and equipment

conditions, dA(T, v;t), is the same for all pulse numbers, t. In

91
fr-e quency-fnultipl.exed systems, it is also the same for all pulse trains,

A, but differs from one pulse train to another in concentrically multiplexed pulse trains because the basic pulse waveforms differ from train

to train. Figure 22 illustrates Id)..,(T, v;t) I for the single -filter system

using adjoining rectangular pulses with a guard time. The response is

shown as a function of the normalized path delay, if = T ITr , and the

normalized path Doppler shift, \J = Trv (Watterson and Minister, 1975).

In the illustration, T IT = 9/13.

r

The detector response, d)..,(T, v;t), also specifies the response of the

Xth detector at the tth sampling time to all of the pulses that are transmitted in the frequency-multiplexed pulse trains. Assume for the moment

that the single specular path has an arbitrary delay and an arbitrary

Doppler shift (no channel distortions). Then in the absence of equipment

distortions, the demodulator synchronization and Doppler-correction

circuits exactly compensate the arbitrary delay and Doppler shift on the

single specular path, The Dirac delta functions (vertical arrows) in

Figure 22 then illustrate the time and frequency locations of three timeadjacent pulses, the (t-1)th, the tth, and the (t+1 )th, in seven adjacent

frequency-multiplexed pulse trains, the (A. -3)th through (A +3 )th, in the

Xth detector response in the tth sample. The product of each delta function

with Id)..,h, v;t) I when integrated on T and v specifies the magnitude of the

response of the Ath detector at the tth sampling time to that undistorted

pulse. For this ideal case (no channel or equipment distortions), it can

be seen that at the tth sampling time, the Xth detector responds only to

the desired tth pulse in the Ath train at (".., v;t)= (0, O;t)" because all of

the other pulses are located at zeros of the detector response. Consequently, there are no channel or equipment crosstalk distortions.

The preceding description for an ideal channel can be extended to the

more realistic Gaussian-scatter HF channel described in Section 4. 2 by

viewing the Gaussian-scatter channel as the sum of P fading paths, each

of which is viewed as a continuum of infinitesimal specular paths with a

common delay, different Doppler shifts with equal infinitesimal adjacent

92
Figure 22. Perspective plot of the magnitude of the response of

a detector with guard time to a rectangular pulse.

The delta functions illustrate the responses to pulses

in frequency multiplexed pulse trains over an ideal

channel ,

frequency spacings" and random phases" where the magnitudes of the

infinitesimal specular components are proportional to Vs('I", v), the

square root of the channel scatter function in (39)" p , 42. The square

root of the channel scatter function" suitably displaced in T and v" then

replaces each of the delta functions in Figure 22 that represent a single

specular path. When this is done with the hypothetical channel scatter

function of Figure 14 1 p , 43 1 and there are no equipment distortions"

the result is illustrated in Figure 23. Each curve is a contour plot of

IdA<rr, v;t)I, and each pair of arrows represents a top view of the square

root of the two-path channel scatter function (displaced and normalized).

The figure illustrates the resp~nses in the tth sample in the Xth detector

93
'---~I--l

--T

'........~I---l

·~-------2

- 1311 .... 2 02 1t 13

9_9 .9

1

9 9_9

~gI-~-+-Tg-i-1r~Tg 2\ L .. 2

-1/

Figure 23 • Contour plot of the magnitude of the response of a

detector with guard time to a rectangular pulse.

The pairs of .arrows illustrate the responses to

pulses in frequency-multiplexed pulse trains over

a realistic two-path Rayleigh-fading channel.

94
to 21 pulses: the (.t-1 )th" tth" and (t+ l)th pulses in the seven (A -3)th

through (A + 3)th pulse trains.

In Figure 23" the differential path delay" T

2-T1 " is less than the guard

time" T. Consequently" t he Xth .dete ctorvhas zero responses to the

g

(t-l )th and (.t+ l)th pulses in all of' the pul.se rtr-ains, and there is no

channel differential-delay distortion" despite the presence of two paths

with a nonzero differenttal delay; i.e. ",the"' channel.dfffer-enttaf-de.lay

distortion is suppressed by thaguar-dtimefv However-, because of the

nonzero differential Doppler shift, \.1 2-v1, and the nonzero frequency

spreads, 20'1 and 20-2, the dE~tectordoeshaveundesiredresponses to the

tth pulses in the non-Athpulse trains"g.swell' as the desired response

to the tth pulse in the Xth train.The~~desired crosstalk constitutes

channel differential-Doppler.. and fading ,distortions• If the differential

path delay, T

2-T1 , is increased in Figure 231:0 exceed the guard time, Ts'

the detector sample contains unde str-ed-responses to the (t-1)th pulses

and the (t+l)th pul.ses- in all tr-ains, andthe undesired responses to the

tth pulses in the non-Xth pulse tr'ainatncr-ease , The increase in the

total crosstalk constitutes, differential-delay distortion. If channel

disper-ai.on (not included in the model of Section 4. 2) is introduced" it

spreads the signal in time, the total crosstalk increases, and the

additional crosstalk constitutes channeLdisper sfon distortion.

Multiplicative>'equipment-distortiohs ar-ersrmi'lar, If the synchronization is advanced or r-etar-ded from its optimum (minimum-crosstalk)

value, the crosstalk increases, and the additional crosstalk constitutes

equipment synchronization distortion. If equipment filtering distortion

is introduced" it spreads the signal in time" the total crosstalk increases,

and the additional crosstalk constitutes equipment filtering distortion.

Similarly" if the Doppler correction is offset from its optimum (minimum-crosstalk) v-alue, the croastalk increases" and the additional

crosstalk constitutes equipment Doppler-vcor-r-e ctton distortion. If

fluctuations are intr-oduced in any equipment AGC circuit, the resulting

modulation of the signal spreads its spectrum to introduc~ additional

95

/
crosstalk that constitutes equipment AGe distortion.

In the example of Figures 22 and 23 J it can be seen that the guard

time provides protection against channel and equipment time-scatter

distortions. The price paid for this protection is a reduction in the

spectral efficiency of the system by a factor T ITJand a reduction in

r

the lJit-error-probability performance with respect to white noise additive distortions by the same factor [10 log(T IT) dB]. In the absence of

r

a guard time (when T =T) and with no equipment distor-ttons, the rms

r

channel differential-delay distortion increases approximately linearly

from zero as the channel differential delay, T

2-T1 J increases from z er-o,

rather than increasing approximately linearly from zero as the channel

differential delay incr-ea'se s above the guard time, T =T-T. The rms

g r

synchronization distortion similarly increases approximately linearly

with synchronization error. With or without the guard time, the rms

channel differential-Doppler and frequency-spread distortions increase

approximately linearly from zero as the differential Doppler shift, 'V2-'ViI

and the frequency spreads, 201 and 202J together increase linearly from

zero.

It is possible by using sin( 1Tt IT )I( 1Tt IT ) as a fundamental pulse waver r

form and nonmatched filters with impulse responses sin(1Tt/T)/(1Tt/T) to

rotate the detector response in Figures 22 and 23 by 90° J thereby

obtaining a guard time in frequency, \), rather than in time, r . It is not

possible to obtain guard times simultaneously in frequency and time J

however.

Detector responses can be obtained for any fundamental pulse waveform that may be used in single-filter or multiple-filter systems. Such

detector responses are generally easy to obtain and are not only useful in

visualizing crosstalk multiplicative di.stor-tions, but are required for any

calculations of such distortions needed to determine theoretical bit-errorprobability performance with respect to these distortions.

Rectangular fundamental pulse waveforms do not provide the best biterror-probability performances with respect to crosstalk distortions. It

96
is possible to design fundamental pulse waveforms which, with matched

or nonmatched demodulator fi.lte r s , have a detector response of the form

illustrated in Figure 24. This hypothetical response is similar to the

response of Figure 22 in having zeros at the locations of all of the

undesired pulses (no filtering distortion). Howeve r-, it is better than the

detector response of Figure 22 in also having a zero total der-ivative ,

rather than a nonzero total de r-ivative , at these points. Consequently,

the rms crosstalk distortion is approximately a parabolic functi.on ,

rather than a linear function, of the channel and equipment time-scatterdistortion and frequency-seatter-distortion parameters. Systems with

such parabolic detector responses consequently have substantially better

bit-error-probability performances with respect to multiplicative channel

and equipment crosstalk distortions.

Crosstalk multiplicative distortions appear in the demodulator pulse

samples, dA.{.f.,} or dAm{.f.,}, and affect the system bit-error-probability

performance in the same way that channel and equipment additive distortions do. Therefore., the relative performances of ASK., PSK., APSK.,

FSK., and CPK systems described in the preceding section for additive

distortions also hold for crosstalk multiplicative distortions.

The appearance of multiplicative channel and equipment distortions

in the form of coherence distortions can also be illustrated with a

frequency-multiplexed single-filter (ASK., PSK., or APSK) system.

Assume initially the channel has a single specular path (no channel

di.stor-tions ), and there are no equipment distortions. Then if dA(t;l) is

the value of the tth sample in the Xth detector when .the keying is

excluded from the pulse sample [L, e . ., the value of the pulse sample

when KA.{.f.,}= 1J, then dA.{.f.,;l} has the same value for all pulses, .f." in all

pulse trains, A., and contains no distortions.

Now assume the ideal channel is replaced by a Gaussian-scatter

channel with both time-scatter and frequency-scatter distortions.

Further assume the detector response, dA{T, v;.f.,}, is ideal in that it

suppresses all crosstalk distortions introduced by the channel and

97
/

Figure 24. Perspective plot of the magnitude of a hypothetical

detector response with zero total derivatives as well

as zeros at the locations of undesired pulses in a

system with frequency-multiplexed pulse trains.

equipment multiplicative distortions. (This is not possible of course

but can be assumed possible for present purposes. ),Th;en~becausethe

channel time-varying frequencyresponse,H(f, t), fluctuates in both

frequency and time, the values of the pulse samples with keying excluded"

d

A

(t ;l ), fluctuate in amplitude and phase from pulse to pulse in both

"frequency", AI and "time ff, t. If multiplicative equipment distortions

are .al.so intr-oducedyfhey impose additional fluctuations on the ··pulse

samples. Suchamplitude and phase fluctuations in the pulse sample S

imposed by channel' and equipment multiplicative distortions constitute

coherence multiplicative distortions.

Coherence multiplicative distortions are illustrated in Figure 25 by

a hypothetical example fora stngle-Hlter system. The circles on the

solid curve illiim¥l:Ne'dA<t;1), the complex values of succeeding pulse

98
1m [dX(1 ; 0]

1m [rx(..l)]

d ~('.l;1 )

Re[d XL.i;1 )]

----------..--- Re[r X( 1)]

Figure 25. Example of coherence multiplicative distor-tions in the

succeeding demodulator pulse samples in a single-filter

ASK,PSK, or APSK:systemwith KA(t)='lin the absence

of additive and.cr-oastalk multiplicative distortions.

samples excluding keying in the Ath detector for O$t:57. Successive

pulse samples in this example .differ because of the fluctuations in time

in the response of the systems (channel and equipment) that are imposed

by channel and equipment frequency-scatter distortions. If A and tare

interchanged in Figure 25, the example can illustrate the values of the

tth pulse samples excluding keying in pulse trains 0 $; A~7, in which

case the values diffe:r because of the fluctuations Infrequency in the

system response that-are' imposed by channel and eq%Pffi~,nt time -scatter

-99
distortions 0

In all types of systems except noncoherent multiple -filter (FSK and

CPK) systems (Table 2" p, 58)" a complex approximate keying value" I"..J I"..J

K (t) in (47)" p , 58" or K, (.t) in (56)" p. 65" is obtained in effect by A Am

dividing the pulse s ample , dA(·t) or dAm(,f,). by a reference va.lue , r A(,f,) or

rAm(-f,) respectively. For all bit-decision methods (including coherent). f"V f'.,J

the approximate keying value s , KA(-f,) or KAm(,f,)# contain coherence

multiplicative distortions (are approximate) because the reference

sequence # r A(,f,) or rAm(,f,)# does not exactly follow the fluctuations in

d

A(,f,;l) or dAm(-f,;l) imposed by coherence multiplicative distortions.

In coherent (ASK# PSK# APSK# FSK# and CPK) systems. r {O or

rAm(,f,)# is obtained for each pulse in the theoretically best manner

possible. Even so, each reference value , r{t) or rAm(,f,). differs from

dA(,f,;l) or dAm(,f,;U. its corresponding pulse sample excluding keying , by f"'V f""",...I

a small arnount , and the approximate keying value , KA(,f,) or KAm(,f,).

contains a small amount of coherence multiplicative distortion. The

imperfect reference values are illustrated for the single -filter system in

Figure 25 by the triangles that fallon the dashed curve.

In partially coherent (ASK" PSK" APSK" FSK" and CPK) systems"

rA(,f,) or rAm(,f,) is obtained for each pulse in the manner specified for

single-filter systems by (50)" p. 61; i , e. "in each pulse train in singlefilter systems" and in each of the M binary ASK tra,ins in each pulse train

in multiple-filter systems" 2 of the preceding pulse samples are processed

to obtain r A(,f,) or r Am(-f,). Such reference values differ from the corresponding pulse samples excluding keying by a generally somewhat larger

amount than with the theoretically best coherent bit decisions. The

resulting coherence multiplicative distortions in the approximate keying f"V I".J

value s , KA(,f,) or KAm(,f,)# are produced by the channel and equipment

frequency-scatter distortions. The bit-error-probability performances

of practical par-tial.ly coherent systems with respect to coherence multiplicative distortions can presumably approach the corresponding

performances of ideal coherent systems.

100
In time-differentially coherent (PSK and APSK) systems, where the

preceding pulse sarnple , dA,(t-l)# is used as a reference for pulse sample

dA(t)# the full amount of the frequency-scatter coherence distortions

between time-adjacent pulse samples appears in the approximate keying rv

value # KA(t). In frequency-differentially coherent aystems, where the

concurrent pulse sample in the adjacent frequency-multiplexed pulse

t r-ain, d(A_l)(t)# is used as a reference for pulse sample dA,(t)# the full

amount of the time-scatter coherence distortions between frequency- rv

adjacent pulse samples appears in the approximate keying value" KA(t).

Consequently" in both time -differentially coherent and frequencydifferentially coherent systems" the bit-error-probabil~typerformances

with respect to coherence multiplicative distortions are typically much

poorer than those of corresponding partially coherent and coherent PSK

and APSK systems.

Figure 26 illustrates the bit-error-probability performance of timedifferentially coherent binary and quaternary PSK systems with respect

to channel fading distortion. The channel has a single Rayleigh-fading

path with zero Doppler shift and no additive distortions. The PSK

systems use adjoining rectangular pulses of duration T= 13.33 ms and

demodulator filters with rectangular impulse responses of duration T =

r

9.09 ms that provide a guard time T

g = 4.24 ms, The detector r e sponse ,

dAh #v;t)# has a magnitude approximately as illustrated in Figure 22#

p. 93. It is assumed there are no equipment distortions. The three

curves in Figure 26 show the bit error probabilities for the crosstalk

fading distortion" the coherence fading distortion" and the total (crosstalk and coherence) fading distortion as functions of the single -path

frequency spread" 20"1 e It can be seen that the coherence distortion is

considerably greater than the crosstalk distortion" and predominates in

determining the performance of the systems with respect to frequencyscatter distortions 0 The coherence distortion predominates over the

crosstalk distortion despite the fact the detector r e sponae , dAh#v;t),

has a nonzero derivative with respect to \) at its zeros on the v axis"

101
M=4

/

'" 10~ 1

.Q

C

..c

o

a.

0,

...

w

....

CD

Total Fading

Distortion

-------.+---

Coherence

Distortion

10-4 to--- - --4-##---- ----I~.... --:-----+-.~~--,-.;...--------+-.-------I

10-5 .......---..+- -I-------+--.----I-----+-- ----+-------f

100

FrequencySpreod t 201 t Hz

Figure 26. Bit-error-prol;lability perfo:r;-mancesof'nonmatchedfilter, frequency-multiplexed',ltime-differentially

,coherent, quaternary PSKsystemsover a frequencyA~~."Rayleigh-fadingchannel.

C.;~!Ulnel: P= 1, "i=9, Eb!Nd-+OO, 8/1 -+ 00.

Equipment: Adjoining rectangular pulses, T= 13.33 ms;

, , ' demodulator guard tfme , T =4.24 ms;

no equipment distorttons, g

102
and consequently is more susceptible to frequency-scatter crosstalk

distortion than a detector response of the type illustrated in Figure 24.,

p. 98;. If the time -differentially coherent bit de cisions were replaced by

partially coherent bit de cisrons, the perfor-mance with respect to coherence distortions would improve substantially., possibly enough to let the

crosstalk distortion be predominant in determining the bit-error-probability performance of the systems with respect to frequency-scatter

distortions.

In concentric-differentially coherent (PSK and APSK) systems, the

concurrent pulse sample in the adjacent-number-ed pulse train, d(A.";1)<'t),

is used as a reference fdI,"the pulse sample d)..,(t). The (A. -1) refere~ce

pulse is concentric in trmeund fr-equency with the A data pulse, unlike

the reference pulses in time-differentially coherent and frequencydifferentially coher-ent systems that are displaced in time and frequency

respectively. Consequently, because of the concentr-Icity, the fluctuations imposed on the two pulses by coherence multiplicative distortions

differ by an amount that is determined by 'the differ-ence of the two

detector responses, tlA.(T',V;.f.,) and d(A. -1 r- v;.t), inthenetghbor-hoods of

their orIgtns, (rr., 'J;t)= (0, O;t). If suitable care -Is given t6: thede stgns

of the pulse waveforms and demodulator filters., the rms difference of

the data and reference pulse samples can be made t oIncr-e ase from zero.

approximately in pr-opor-tion to the square of the channelvand equipment

time -acatte'r and-frequency-scatter par-ameter-s.In time-C;iifferentially

coherent and frequency-differentially coherent systems, the rms difference of the data and reference pulse samples unavoidably increases from

from zero approximately linearly with increases in the frequency-scatter

and time-scatter parameters r-espectively, Thebit-error-probability

performances of concentric-differentially coherent systems with respect

to coherence multiplicative distortions are then sUbst~tiallybetter than

those of time-differentially 'coherent and fr-equency-cdiffer-entiaIly coherent

systems and comparable with the performances ofpar'tial.ly coherent

systems. In Figure 25, the- triangles, r It}, can represent the reference

103
pulse samples, d(A_l)(t), in concentric-differentially coherent systems.

Noncoherent multiple-filter (FSK and CPK) systems are immune to

coherence multiplicative distortions because these systems do not use

reference sequences, rAm(t). For each pulse number, t, in each pulse

train" A" noncoherent FSK and CPK systems' decide which one of M

binary ASK pulses was on by comparing the magnitudes of M pulse

samples, [ldAm(t)1 L as specified by (58), p. 66. Consequently, while

channel multiplicative distortions cause the pulse samples to fluctuate in

time and frequency" the fluctuations (coherence multiplicative distortions)

do not affect the relative mag.nitudes of the M pulse samples in [I d, (t) r }; . Am

the single on pulse generally has a magnitude greater than zero while

the M-1 off pulses have zero magnitudes regardless of the fluctuations.

Consequently" noncoherent FSK and CPK systems are immune to coherence multiplicative distortions.

In any system" if the fundamental pulse waveform is scaled up in time"

and the spacing of adjacent pulses in each train" T" is scaled up by the

same amount, the detector response, dAh, v;t), is expanded in time, 'l",

and compressed in frequency" v (Figures 22-24). The system then is

less susceptible to time -scatter (crosstalk and coherence) multiplicative

distortions" but is more susceptible to frequency-seatter (crosstalk and

coherence) multiplicative distortions. If T is scaled down" the opposite

is true. Therefore" in practical systems" T is usually chosen to minimize the combined (total) multiplicative distortions for typical amounts

of frequency-scatter and time-scatter distortions. Typical values of T

range from about 20 down to 6. 7 ms, corresponding to single-train pulse

rates of 50 to 150 pulsesIsecond. This explains why higher data-rate

systems use a number of multiplexed trains to carry the data" rather

than a single high-pulse -rate train.

While matched nonadaptive demodulator filters provide the best biterror-probability performances with respect to white additive channel

and equipment noise" non matched nonadaptive filters can provide better

performances with respect to channel and equipment time-scatter or

104
frequency-scatter multiplicative distor-tions , This is illustrated by the

detector response in Figure 22~ po 93~ for a single-filter system using

adjoining rectangular pulses with a mismatched nonadaptive filter that

provides a guard time that improves the system bit-error-probability

performance with respect to time-scatter distortions. However" dynamic

adaptive demodulator filters can provide even better performance with

respect to all types of multiplicative channel and equipment distortions.

In the absence of additive and nonlinear distort ions, this is ac cornpl.ished

by continuously adjusting the response of each demodulator filter to

maximize the signal-to-multiplicative-distortions ratio at its output at

the optimum sampling times. In the general (and usual) case when

additive and nonlinear distortions as well as multiplicative distortions

are pre sent, the response of each dynamic adaptive demodulator filter is

adjusted continuously to maximize the signal-to-total-distortion ratio at

its output at the optimum sampling times. In gene r al, dyanamic adaptive

demodulator filters can provide better (and sometimes substantially

better) bit-error-probability performances than nonadaptive filters with

respect to all types of distortion except white noise 0 When white noise

distor-tion predominate s , dynamic adaptive filters can ideally become

matched" of course" to equal the performances of nonadaptive matched

filters.

The bit-error-probability performance of any system with respect to

both crosstalk and coherence forms of multiplicative channel and equipment distortions is determined by the character of the distortions and all

of the system design features (p. 77) except transmitter power 0 This

means that.in the absence of all additive channel and equipment distortions" increasing the transmitter power will not change the bit error

probability because the levels of the signal and multiplicative distortions

in the demodulator increase by the same fractional amount s, It also

means that in the absence of all channel and equipment additive distor-tions,

the transmitter power can be decreased to an arbitrarily small amount

without affecting the system performance 0 In practice this is not possible"

105
of course I because additive channel and equipment distortions are always

pre sent, the performance of the system with respect to the additive

distortions is dependent on transmitter power I and sufficient transmitter

power must be used to obtain an acceptable signal-to-additive -distortions

ratio in the receiver.

If the gain of the transmitting antenna is incr-eased, the equivalent

change in transmitter power has no effect on system performance with

respect to channel and equipment multiplicative distortions 0 However I

the resulting narrower antenna be amwidth can discriminate against some

ionospheric propagation modes that were significant with the wider beamwidth antenna, This reduces th~ amount of channel differential-delay

distortion and improves the system bit-error-probability performance if

such distortion is significant 0 The same argument applies with respect

to the receiving antenna. High-gain transmitting and receiving antennas

are therefore desirable to minimize channel differential-delay distortion o '

Both diversity and error coding can substantially improve the biterror-probability performance of any HF digital radio system with respect

to additive channel and equipment distortions as described in the preceding se ction , The reason for this is because all types of channel and equipment distortions ultimately appear in the demodulator as distortion com- f"V f"V

ponents in the approximate keying values. KA(,f,) or K:>...m(,f,) in most

systems [or in d:>...m(,f,) in noncoherent FSK and CPK systems] to produce

errors in the following bit-decision pr-oce as , Errors occur when the sig- f"V f"V

nal component in K:>...(,f,) or K:>...m(,f,) fades to a level comparable to the rms

level of the total distortion to increase greatly the short-term probability

of an error in the bit-decision process. This is illustrated in Figure 25

for coherence multiplicative distortions in single -filter systems 0 For

,f,= O. the rms value of the distortion component. d

A(O;l) -r:>...(0). is small

compared with the magnitude of the reference component. r :>...(0). The t"'V

rms amplitude and phase error in K:>...(O)= d:>...(O)!r:>...(O) then is small and

very unlikely to produce an error in the bit-decision process. For t= 51

the rms value of the distortion component, d:>...(5;1)-r:>...(5). remains

106
unchanged. However, the reference value, r

A(5). has a much smaller

magnitude because it has followed the fading signal to a lower Ievel , As t"V

a result, the rms amplitude and phase error in K A(5) is much larger and

quite likely to cause an error in the bit-decision process.

The same effect results from additive distortions and crosstalk multiplicative distortions" all of which add to the signal values" illustrated by

the circles in Figure 25, to form a different dA(t) that has a larger rms

separation from the reference values. However" while the additional

additive and crosstalk multiplicative distortions increase the average

bit-error probability" the bit errors still occur when the signal fades to

a level comparable to the rms total distortion Ieve I,

It can be seen then that the bit errors in any HF digital radio system

are highly correlated with the strength of the fading signal for all types

of channel and equipment additive and multiplicative dist or-t iona , Therefore" diversity can provide substantial i rrrprove ment ill tile bit-errorprobability performance of any system with respect to all types of channel and equipment additive and multiplicative distortions when the fading

in the diversity channels has a reasonable degree of independence or is

negatively cor-r-elated , Similarly" block error coding with soft decoding

can provide substantial improvement in the bit-error-probability performance of any system with respect to all types of channel and equipmerit additive and multiplicative distortions when the fading on the pulses

carrying the bits in each code block has a reasonable degree of independence 0 To obtain independence" the bits in each block are normally

assigned to pulses that are separated as much as is practical in time"

and in frequency-multiplexed systems, to pulses that are also separated

in frequency 0 The bit errors in each block are essentially independent"

and the maximum performance improvement results" when the channel

and equipment frequency scatter are comparable to or greater than the

reciprocal of the adjacent time spacing of the pulses carrying the bits in

each b lock , Less but still substantial performance improvement results

when the frequency scatter is as small as one-tenth of the reciprocal of

107
the spacings of the code-block pulses 0 In the latter case , the loss in

performance improvement can be recovered under some but not all

multipath channel conditions by the additional distribution of the codeblock pulses in frequency in frequency-multiplexed s ystems,

6. 3 Nonlinear Distortions

Nonlinear distortions in the transmitter produce intermodulation

components , some of which may fall in the frequency band of the aignal ,

Such nonlinear distortion components are similar to additive transmitter

distortions in that when passing through a Rayleigh-fading channel, they

suffer the same fading as the s.igrial , Consequently, the signal never

fades into the transmitter nonline ar' distortions, as it does with additive

channel and r-e cetver distortions and multiplicative channel and equipment (transmitter and receiver) distortions 4 o If the transmitter nonlinear distortions, like the transmitter additiverlistor-tions, are generated at a suitably low level relative to the signal (say < -30 dB), which is

usually the cas e , they affect the system performance very little and can

be Ignored ,

The bit-error-probability performance of a system with respect to

receiver nonlinear distortions depends not only on the amount of the nonlinearity in the receiver but, in multiple-pulse-train systems, on the

type of multiplexing that is used: frequency-multiplexed systems are far

more susceptible to receiver nonlinear distortions than single-pulsetrain systems or concentrically multiplexed multiple -pulse -train systems 0

This can be explained with the help of Figure 27 which presents the

results of channel-simulator performance measurements on three HF

4 Under frequency-selective fading conditions the signal in one of

several frequency-multiplexed pulse trains can fade into transmitter

multiplicative distortions (filtering and AGe distortions) that appear in

the demodulator in the form of crosstalk distortions from other pulse

train s , Such transmitter multiplicative distortions are usually weak

and not stgniftcant, however 0

108
10

MX-190

ACQ-6

USC-tO

0.1 1

Differential Delay, T2-TI , ms

(LW

-0

C

o

(LQ)

.. 10-2

(f)

Q)

o

W

.x:

g 10-4 r----~----___,o('_-_u

rn

""0

C

o

Figure 27. Bit and block error-probability performances of the

USC-1 O~ ACQ-6~ and MX-190 fr-equency-imul t ipl.exed ,

time-differentially coherent , quaternary PSK modems

over a two-path" frequency-selective" Rayleigh-fading

channel 0

Channel: P=2~ A 2=A1=3.0dB1 \)2='J1=0~ 20"2=201=

0.2 Hz~ ~Eb/Nd~OO" sir ~COO

Equipment: Additive I multiplicative I and nonlinear

distortions present.

109
digital modems (modulator-vdemodul.ators ), the USC-10~ ACQ-6~ and

MX-190 (Watterson and Minister 1975). All three are frequencymult.iplexed, time -differentially coher ent, quaternary-PSK systems with

information rates of f

1 = 2400 bits/second. The USC-10 and ACQ-6 use

13.33 -ms adjoining rectangular pulses with a 4 0 24-ms demodulator

guard time (Figure 22~ po 93) in 16 pulse trains with 110-Hz adjacent

frequency spacings without er-r-or' codirig , The experimental MX-190 uses

13 0 33 -ms adjoining rectangular pulses with a 2. 67 -rns demodulator guard

time in 25 pulse trains with 93 0 75 -Hz adjacent frequency spacings with

error coding, the (25~ 16) block code with soft decoding described earlier

(pp~ 69-71)0 The 25 bits in each code block are assigned to 25 concurrent pulses in the 25 pulse trains. In Figure 27 bit-error probabi.Ii.ty,

Pe' and block-error probability. P

E (the probability of one or more bits

in a 672-bit block being in error)" are presented as functions of the

differential delay" T2 -T1 in a two-path Gaussian-scatter channel specified by the model in Section 4 02 0 The signals on the two independently

Rayleigh-fading paths had equal relative attenuations (equal rms values)"

A2=A1 = 3 00 dB; no Doppler shifts , 'J 2 = \)1 = 0; equal frequency spre ads,

201 = 202= 0.2 Hz; no noise. E b/Nd-7 oo; and no interference. S/I-7oo.

In Figure 27, the USC-10 and ACQ-6 bit-error-probability curves

are characterized by five intervals: low" middle and high plateaus (the

last not shown) with two intermediate positive -slope intervals 0 In the

low-plateau interval (T2 - '-1 < 0.2 ms ), the errors are caused primarily

by additive distortions generated in the demodulators: internal interference in the USC-10 and quantizing noise (8 bits Isample) in the ACQ- 6 0

In the absence of these demodulator additive distor-tions, the channel

fading distortion would produce a bit error probability of P = 4X 1 0-5 in

e

both systems (see Figure 26 for 201=0.2 Hz). In the lower-positiveslope and middle-plateau intervals (0. 2<T2 - rr1 < 2 ms), additional errors

are introduced by nonlinear distortions generated in the demodulators

ahead of the filters In the Iow -p.late au, lower-positive-slope" and middleplateau interva.Is, channel differential-delay and receiver-synchronization

110
distortions are excluded by the 4.24-ms guard time (Figure 22" p, 93)0

In the upper-positive-slope and high-plateau interval (T2-T1 >2 ms), the

errors are caused primarily by channel differential-delay and demodulator synchronization distortions that are not excluded by the guard time 0

In the absence of synchronization distortion" the curves would break

and rise from the middle plateau when the channel differential delay

exceeded 4 0 24 ms 0

The reason the demodulators' nonlinear distortions are not significant

in the low-plateau interval but are significant in the lower-positive-slope

and middle-plateau intervals is as follows: When the differential delay

is less than about 00 2 ms, the Rayleigh fading is relatively flat in the

1 0 8 -kHz band occupied by the 16 frequency-multiplexed pulse trains 0

All pulse trains then fade approximately together" and the nonlinear

distortion (inter-pulse-train intermodulation products) fades with the m,

The demodulator nonlinear distortion then has 110 sigl1ificarlt effect on

system performance 0 When the channel differential delay increases

above about 0 02 m s , the fading across the 1 0 8-kHz signal band becomes

incr.easingly frequency selective" and some pulse trains are weak while

others are strong 0 Bit errors are then produced by the weak pulse trains

fading into the relatively strong intermodulation products produced by

the strong pulse trains 0 From this de scription" it can be seen that

frequency-multiplexed systems are particularly susceptible to nonlinear

receiver distortions when there is enough channel time -scatter distortion 0

It can also be seen that single pulse trains and concentrically multiplexed

pulse trains are presumably less susceptible to receiver nonlinear distor-tioris , If the bit error probability with respect to receiver nonlinear

distortions is to be held below 10-6 I the nonlinear distortion level in a

frequency-multiplexed system would need to be approximately < -60 dB

relative to the rms level of the Rayleigh-fading stgnal, The same biterror-probability performance with respect to receiver nonlinear distortions in single -pulse -train and concentrically multiplexed multiple -pulsetrain systems presumably could be achieved with a receiver nonlinear111
distortion level < -30 dB relative to the rms aigna'l Ievel ,

Receiver nonlinear distortions appear in the demodulator pulse

sarnpl.e s , dA(t> or dAm(t)1 and affect the system bit-error-probability

performance in the same way that channel and equipment additive distortions do , Therefore" the relative performances of ASK" PSK" APSK"

FSK" and CPK systems described in Section 6 0 1 for additive distortions

also hold for receiver nonlinear distor-tions,

Because the bit errors produced by receiver nonlinear distortions are

highly correlated with the strength of the fading signal" diversity can

v

provide substantial improvement in the bit-error-probability performance

of any system with respect to receiver nonlinear distortions" as it can for

channel and equipment additive and multiplicative distortions" provided

the fading in the diversity channels has a reasonable degree of independence or is negatively cor-re lated , Similarly" block error coding with

soft decoding can provide substantial improvement in the bit-error-probability performance of any system with respect to receiver nonlinear

distortions" as well as channel and equipment additive and multiplicative

distortions, provided the fading on the pulses carrying the bits in each

code block has a reasonable degree of independence. The importance of

the independence and the effectiveness of soft error-correcting decoding

are illustrated by the MX-190 bit-error-probability curve in Figure 27 0

The MX-190 curve differs in form from the USC-10 and ACQ-6 curves

primarily because of the (25" 16) coding the MX-190 Incor-porate s , Recall

that the 25 bits in each code block are assigned to 25 concurrent pulses

in the 25 pulse trains 0 In Figure 27" as the channel differential delay"

'T2 - rr1 " approaches zero and the channel fading becomes flat in frequency"

bit errors are very likely to occur in all 25 of the concurrent data bits in

a code block when all 25 pulse trains simultaneously fade into the de moulator quantizing noise (8 bitsI sampl.e ), The data bit errors in a code

block are then highly correlated" the error-correcting decoding is

ineffective" and the information-bit error probability asymptotically

-4 approaches 6X10 (shown by the dashed line). As the channel differential

112
delay increases" the channel fading becomes increasingly frequency

selective" and the data bit errors caused by the demodulator quantizing

noise and nonlinear distortion become more randomly distributed in

frequency and time. While there may be more errors" because of the

nonlinear distortion" they occur with a higher degree of independence"

no code block is overwhelmed by too many errors" and the soft errorcorrecting decoding becomes effective 0 The curve illustrates the

importance of assigning the bits in each code block to pulses that are

separated in time. Had this been done in the MX-190" its bit-errorprobability performance curve in Figure 27 would remain well below

P

e

=10-6 for channel differential path delays T

2-T1 <0.7 ms, It is

important to retain good bit-error-probability performance under frequency-flat (small time -scatter) channel conditions because such channel

conditions occur a substantial fraction of the time.

7. PERFORMANCE IMPROVEMENTS

The purpose of this section is to use the results of the preceding

sections to select the best methods that may be used to improve the performance and reliability of U. S. military HF digital radio communications. There are two general methods that can be used to improve

system performance: by using better system designs and by using

better operating techniques. These methods will be considered in turn

in the following two sections.

7.1 System Design

The HF digital radio systems presently used by the various U. S.

military services are primarily of the following three types:

113
Common Types of Miliary HF Digital Radio Systems

(1) Single -pul.se-train, noncoher ent, binary FSK systems without

error coding that operate at information rates from 50 to 150

bits/second with or without single-transmission space diversity

(eog o, the TH-22).

(2) Multiple -pulse -tr ain, frequency-multiplexed, noncoherent, binary

FSK systems without error coding that operate at 600 bits Isecond

with dual multiple-transmission in-band frequency diversity or at

1200 bits/second without diversity (e.g., the UCC-1)o

(3 ) Multiple -pulse -train, frequency-multiplexed time -differentially

coherent" quaternary PSK systems without error coding that

operate at 1200 bits/second with dual multiple-transmission

in-band frequency diversity or at 2400 bits /second without diversity (e.g., the USC-10).

All of the systems use adjoining rectangular pulses and nonadaptive

demodulator filters with various transmitter powers and a large variety

of antennas. The frequency-multiplexed systems typically use one

standard voice band (3 kHz).

In general, it is not economically or technically practical to modify

existing equipments to improve their per-f'ormance s , Therefore, there

are only two generally feasible methods that can be used to improve the

performance characteristics of military HF digital radio systems: by

incorporating additional equipment without replacing or modifying existing equipments and by replacing existing e quipmerrts with equipments of

better de sign.

There appears to be only one type of additional equipment that might

be incorporated into existing systems to improve their bit-error-probability performances: error-coding equipment. The incorporation of

suitable error coders at the inputs of present modulators (Figure 1, p. 4)

and compatible hard decoders at the outputs of present demodulators

would significantly improve the bit-error-probability performances of

114
existing systems with respect to all types of channel and equipment distortions (Table 3 1 p, 78). HoweverI the price of the improved bit-errorprobability performances would necessarily be reductions in the systems'

information rates by factors equal to the coding ratios [(1)1 p. 9J and

corresponding decreases in the spectral efficiencies of the systems.

While decreases in the spectral efficiencies may be acceptable , the

reductions in information rates may not be for practical reasons.

Although the incorporation of error-coding equipment into existing

military HF digital radio systems can improve their bit-error-probability

per-formance s , considerably greater improvements in bit-error-probability performances can be obtained with simultaneous improvements in

spectral efficiences by replacing some of the existing equipment with

new equipment that has more efficient designs. Improvement in spectral

efficiency as well as bit-error-probability performance is very desirable

to minimize any unnecessary waste of the HF spectrum and to minimize

the interference with other systems. It is also necessary if the reliable

transmission of good quality digital voice signals in a 3-kHz band is to

be made practical. To determine the characteristics that new equipment

should have to optimize simultaneously brt-er'r-or-vpi-obabifity performances and spectral eff'i.ciencie s , the system design features listed on

p. 77 will be considered in turn to determine the best combinations based

on the system performance evaluation of Section 6.

All fundamental pulse waveforms provide the same best bit-errorprobability performance with respect to channel and equipment white

noise when matched demodulator filters are used. The choice of fundamental pulse waveform also has no effect on bit-error-probability performance with respect to coherence multiplicative distortions when the

pulse spacings are unchanged. How ever , this is not true with respect to

crosstalk multiplicative distor-tfona, whose levels in the detector response

are strongly affected by the choice of fundamental pulse waveform and

demodulator filter in combination. As explained earlier (p , 96)1 the

almost universally used adjoining rectangular pulses with matched or

115
nonmatched filters do not provide the best performance .with respect to

crosstalk multiplicative distortions. Better fundamental pulse waveform

designs are possible and should be developed and used.

'I'hekeying and bit-decision methods can best be considered In-combination (Table 2, p. 58). Of the available practical combinations,

partially coherent PSK and partially coherent APSK are undoubtedly the

best for the following reasons : Partially coherent PSK provides the best

bit~error-probabilityperformances with respect to all types of channel

and equipment distortions, additive, multiplicative, and nonlinear5•

Also,PSK and APSK provide substantially better spectral efficiencies

(M times better) than··FSKand.,CPK.•

Frequency multiplexing and concentric multiplexing both provide

comparable spectral efficiencies when used with suitably designed fundamental pulse waveforms• However,concentrically multiplexed systems

presumably are far less susceptible to receiver nonlinear distortion, and

are preferable for this reason.

The best type of demodulator filter is one which maximizes the signalto-total-distortionratio at its output at the optimum sampling times. No

nonadaptive filter can do this except for a single distortion condition,

such as matched filters do when white noise, distortion predominates.

However,dynamic adaptive filters ideally, can maximize the signal-tototal-distortion ratios at their outputs under all distortion conditions.

Dynamic adaptive demodulator filters are therefore the best because they

can provide significant and sometime ssubstantially better bit-errorprobability performances with, respect to nonwhite additive distortions

and multiplicative distortions than nonadaptive and even quasi-static

adaptive filters • However,little use has been made of them primarily

because little is known about their theoretical performance and practical

5 Partially coherent PSK should not be confused with the commonly used

time-differentially coherent PSK whose per-for-mance with respect to all

types of distortion is significantly or substantially poorer.

J16
design. Therefore I the theoretical and experimental development of

adaptive demodulator filters should be pursued.

Transmitter power affects thebit-error-probability performance of:

a system only with respect to additive channel and equipment distortions.

In properly designed receivers, additive equipment distortions are not

significant (considered below). Of the two types of additive channel

distortions (noise and interference), noise is probably predominant in

determining the bit-error-probability performances of systems only a

small fraction of the time. Therefore" except for systems that may use

relatively low transmitter power-s, increasing transmitter power will

have relatively little effect in improving system performances with

respect to noise. Increasing transmitter powers to improve system

performances with respect to interference is undesirable because it is

self-defeating; if all transmitter powers are raised proportionally" no

improvement with respect to interfer-ence is achieved. 'I'her-efor-ej-except

for systems that may be using relatively low powers" increasing tr-ans-.

mitterpowers is not desirable.

It Isnot possible to specify one best type of antenna for transmitting

or receiving. In general" both transmitting and receiving antennas

should have gains as high as are practically consistent with acceptable

size" portability" and steerability. Electronically adaptable receiving

antennas are highly desirable' because of their ability to reject interference. However" little use has been made of them because of their-Irmited

availability. Therefore" the .theor-etrcal and experimental development

of adaptive receiving antennas should be pursued. - -- -.-

Diversity reception in general can substantially improve the biterror-probability performances of any system with respect to all types:

of channel and equipment distortions. However" the performance improvement provided by single-transmission diversity (p.72) without'

increasing transmitter power or signal bandwidth can be equaled by

mulfiplevtr-ansmfasfon dive.rsity only with an increase in transmitter

power by a factor of D, the order of diversity" and by an increase in

117
signal bandwidth by a factor of D. At the same t irne , single-transmission

diversity requires D receiving antennas and D HF receivers, while

multiple-transmission diversity requires only a single receiving antenna

and a single HF receiver. However, with dual diversity (D= 2), a single

antenna with dual polarization can provide single-transmission polarization diversity. Therefore, the best dual diversity method is probably

polarization diversity because it can be obtained with a single receiving

antenna without increasing transmitter power, signal bandwidth, or interference to other systems. Higher order single-transmission separation

diversity with D receiving antennas or D /2 dual-polarized antennas should

be used when practical.

Error coding, like diversity, can significantly or substantially improve

the bit-error-probability performance of any system with respect to all

types of channel and equipment distortions. In gener-al, the performance

improvement increases as the complexity of the coding increases; i ;e , I

as the block size in block codes or constraint length in convolutional codes

(p. 9) increases. The bit-error-probability performance improvement

also generally increases as the coding r-atio, and consequently the

spectral efficiericy, decrease. It is not possible to specify one best code;

in general, the performance improvement must be balanced against the

complexity (practicality) of the code and the reduction in spectral efficiency to obtain an optimum compromise. However, soft decoding in

convolutional or block codes can provide substantially better error

cor-r-ection, and therefore substantially better performance improvement,

than hard de coding, because it makes use of additional valuable information: that the magnitude of the demodulator pulse samples and the bit

errors are highly correlated in HF digital radio systems because of the

Rayleigh-fading characteristics of HF channels. Therefore, soft errorcorrecting coding should be used with a code that achieves an optimum

balance between bit-error-probability performance improvement, coding

complexity, and reduction in spe ctral efficiency.

The preceding evaluation considered the best combinations of system

118
design features (Pe 77) for simultaneously maximizing the bit-errorprobability performance and spectral efficiency of an HF digital radio

system. While spectral efficiency is independent of the type and amount

of channel and equipment distortions" bit-error-probability performance

is not. Therefore" it is also possible to improve the bit-error-probability performance of a system by r-educing or effectively eliminating

equipment distortions.

Because transmitter distortions are generated prior to the HF chan--

nel" they suffer the same fading as the signal. The signal therefore does

not fade into the transmitter distortions as it does the receiver distortions

to produce bit errors. Consequently" greater transmitter distortions

can be tolerated than receiver distortions without significantly affecting

the bit-error-probability performance of a system. If the rms level of

the transmitter distortions is approximately < -30 dB r e lative to the rms

level of the signal" the distortions have no significant effect on the biterror-probability performance of a system. Most present-day systems

meet this criterion" so significant system performance improvements

are not possible with further reductions in transmitter distortions.

Because HF channels exhibit multipath propagation that produces

frequency-selective fading" the relative level of i-e ceiver- distortions

must be substantially lower than transmitter distortions" approximately

< -60 dB, to have little or no significant effect on bit-error-probability

performance in frequency-multiplexed systems. Many if not most

present-day systems do not meet this criterion" and their bit-errorprobability performances are substantially degraded as a result. It is

quite pr-actical to eliminate effectively all receiver distortions except

synchronization and Doppler-correction distortions. Internal interfer- '

ence can be effectively eliminated by suitable decoupling (filtering and

shielding). Demodulator analog-to-digital converters typically use 8

bitsIsample which introduces excessive quantizing noise; this can easily

be substantially reduced and effectively eliminated by using converters

with 12 or more bitsIsample. The HF receiver filtering distortion

119
introduced by analog lumped-element IF filters can be effectively eliminated by using digital filters" which can completely eliminate delay

distortion and greatly reduce amplitude distortion. A greater selection

of filter responses is also .much easier to obtain.

Substantial improvements in demodulator synchronization and Dopplercorrection circuits are also possible. For example" the USC-10 and

ACQ-6 frequency-multiplexed" time-differentially coher-entj cquater-nary

PSK systems that were described earlier (p. 108) incorporate 4.24-ms

guard times. 'With optimum synchrontzatfon, both systems would reject

channel differential-delay distortion for any number of paths whose maximum differential delay does not exceed the-guard time. Howeverj ias

'shown by the USC-IO and ACQ-6 bit-error-probability curves in Figure

27" p. 109" the slot synchronization circuits in these modems permit

differential-delaydistortion'·to enter rapidly when" the two-path differential delay exceeds about 1. 9 ms for the USC-10 and 2.1 ms for the

ACQ-6" values that are somewhat less than one-half the 4.24-ms guard

time. Better synchronization and Doppler-correction circuits are

desirable and practical" and should be developed.

MostHFreceivers incorporate a fast AGC circuit for use with digital

systems. It can be argued that a fast AGCcircuit can partly compensate

amplitude changes ina signal imposed bya fading channel" but not the

phase "changes" thereby par-tly reducing the amplitude portions of the

crosstalk and coherence frequency-scatter distortions. Fast HF receiver

AGC circuits are therefore presumably desirable. It is known (Watterson

and Minister" 1975 ) that under frequency-flat channel fading conditions

fa single fading path with 'no Doppler shift)" a fastAGC will keep a frequency-multiplexed" time -differentially coherent" quaternary PSK signal

from fading into excessive demodulator additive distortions to improve

system performance with respect to these distortions" while producing

no change in system performance with respect to the channel fading

di.stor-tions, presumably because the phase portion of the coherence

fading distortion is not affe cted , However" it is also known that' under
multipath channel conditions a fast AGC can degrade the bit-errorprobability performance of a system. Unequal AGC attack and release

times may be a factor. Additional work needs to be done on the effects

of various receiver AGC characteristics on the performances of various

types of digital systems.

7 • 2 System Operation

The performance of any HF digital radio system changes both with

HF operating frequency and time" because both the additive and multiplicative channel distortions change with frequency and time • For this,

r-eason , most systems have a number of avaflable operating frequencies

or channels so that ideally at any time the channel that provides the best

system performance can be chosen and used. However" this requires a

knowledge of the system performance for the channel that is being used

(performance monitoring) and an estimate of the system performance on

the other available channels "(performance prediction).

Of th.e three performance-monitoring methods that are described on

p, 74"wonitoring of the signal-to-total-distortion ratio in the demodulator should be used because it is simple" ,effective" and can be used in

systems with or without error coding. In systems with error coding"

monitoring of the detected and corrected bit errors should also be used

because it is most accurate and specifies the system bit-error-probability performance directly.

Five performance-prediction methods are listed onp, 75. In simplex

systems" the two methods .of predicting system performance on available

channels" experience and pr-opagatfonpr-edfctdons , should both be used

because" while they have limited accur-acy, they are the only methods

available It In duplex systems" system sounding is the best of the three

performance -prediction methods for several reasons: System sounding

provides the most accurate .predictions because it utilizes the actual

communication system, including antennas; i , e." rather than measuring

121
channel characteristics to predict indirectly how the HF digital radio

system will perform" it directly measures the performance of the

system , System sounding also requires no auxiliary equipment" and

does not introduce additional interference into other systems as oblique

sounders...do ,

8. SUMMAR Y AND CONCLUSIONS

This report has presented a comprehensive survey of HF digital radio

communication techniques to determine the best methods of improving the

performance and therefore the reliability of HF digital radio communicattoris , HF digital radio 'systems consist of three major parts: the transmitter" the HF ionospheric channel" and the receiver 0 The performances

of such systems can be specified in terms of bit error probability and

spectr-al efficiency (information rate Isignal bandwidth). The bit-errorprobability performance of a system is determined by the signal processing techniques that are used in the transmitter and receiver" and by the

types and magnitudes of the distortions that are imposed on the signal by

the equipment and theHF channel. The spectral efficiency of a system

is deter-mined by the srgnal processing techniques and is independent of

channel and equipment distortions 0

The transmitter in general contains an error coder" a modulatorI an

HF transmitter" and an antennae The characteristics of the tr-ansmitte r

that affect system performance were considered in detail by classifying

and describing the types of error codes: block and convolutional; the

digital keying methods: ASK" PSK1 APSK1 FSK" and CPK; the multiplexing techniques: frequency multiplexing and concentric multiplexing;

the HF transmitter operation: frequency translation" filtering" and

amplification; the size" gain" bandwidth" and steering characteristics

of a large variety of transmitting antennas; and the additive" multiplicative" and nonlinear equipment distortions introduced by the various

parts of the transmitter.

122
The HF channel in general consists of a number of propagation

modes or paths over which the signal travels from the transmitter to

the receiver. Because the paths introduce different propagation delays,

the channel introduces time -scatter multiplicative distortion, and

because each path introduces Doppler shift and Rayleigh fading on the

signal, the channel introduces frequency-scatter multiplicative distortions. A description was presented of a validated HF channel model

that was used to characterize the channel.

The receiver in general contains an antenna, an HF receiver, a

demodulator, and an error decoder. The characteristics of the receiver

that affect system performance were considered in detail by classifying

and describing the types of antennas, including adaptive receiver antennas

for suppressing interference; the HF receiver operation: frequency

translation, filtering, and amplification; the types of demodulator filters:

matched and nonmatched nonadaptive filters and quasi-static and dynamic

.adaptive filters; the bit-decision (detection) methods: coherent, partially

.coherent, differentially coherent, and noncoherent; the types of error

decoding: hard and soft; and the additive, multiplicative, and nonlinear

equipment distortions introduced by the various parts of the receiver.

Also classified and described were the types of diversity operation:

single -transmission polarization and separation diversity and multipletransmission frequency and time diversity; and performance monitoring

and prediction methods.

The bit-error-probability performance ofa system with respect to

the various types of channel and equipment distortions is affected by

nine system design features: the fundamental pulse waveform, the

keying method, the multiplexing method, the type of demodulator filter,

the bit-decision (detection) method, the transmitter power, the antennas,

diversity, and error coding. The spectral efficiency of a system is

determined by the first four and last two of the same design features.

The effects of the system design features on bit ver-r-or-vpr-ohabffity performance were evaluated with respect to additive channe] and equipment

123
distortions, multiplicative channel and equipment distortions, and nonlinear equipment distortions in turn. The effects of the system design

features on spectral efficiency were evaluated in conjunction with the

evaluation ofthebit-error-probabilityperformance. The results of the

evaluation were then used to determine the best methods of improving

the performance and r-eliabi.lityof militaryHF digital radio communications• These methods are summarized in the following conclusions:

(1) In general, it is not economically or technically practical to

modify existing .equipment to improve its performance. 'I'herefor-e ,

there are only two generally feasiblemethod.sthat can be used to improve

the performance characteristics of military HF digital radio systems:

fa) by incorporating additional equipment without replacing or modifying

existing equipment, and (b) by replacing existing equipment with equipment of better.. deaign,

(2) There appears to be only one type of additional equipment that

might be incorporated with existing systems to improve their bit-errorprobability performances: error-coding equipment with hard decoding,

because most present-day military HF digital radio systems do not use

error coding 0 However, the necessary reduction in information rate

(equal to the coding ratio) may not be acc.eptableforpracticalreasons 0

(3) While the incorporation of er-ror vcoding equipment into existing

military HFdigital radio systems can significantly improve their biterror-probability performances, substantially greater improvements in

bit-error-probability performances can be obtained with simultaneous

improvements in spectral efficiencies by replacing some the the existing

equipment with new equipment that utilize an optimum combination of

design features. The best equipment designs are considered in the

conclusions that follow.

(4) The universally used adjoining rectangular fundamental pulse

waveform should be replaced by better waveforms that can and should

be developed.

(5) The be stcombinatton of keying method andbit .... decision (detection)

124
method is partially coherentPSK with M= 4 or 8, or par-tial.ly coherent

APSK with M 16, depending on the spectral efficiency desired, because

they simultaneously provide the best spectral efficiency and the best

bit-error-probability performances with respect to- all types of channel

and equipment distortions.

(6) Concentric multiplexing is' better than frequency multiplexing

because it provides comparable spectral efficiency with presumably' much

better immunity to receiver nonlinear distortions.

(7) Dynamic adaptive dem-odulator filters can provide the best biterror-probability performances with respect to all types of channel and

equipment distortions because they ideallymaximfzethe signal-to-totaldistortion ratios at their outputs at the optimum 'sampling (detection)

times. Their performances can be· substantially better than those of

nonadaptive filters, particularly with respect to channel interference

and multiplicative distortions. Their theoretical and experimental

development should be pursued.

(8) Except for aystems that maybe using relatively low powers,

increasing transmitter powers is not de str-able ,

(9) Transmitting and receiving antennas should have gains as high

as are practically consrstent with acceptable size, por'tabflity, and

steerability. Electronically adaptive receiving antennas, because of

their ability to reject interference, ar-e-highly desirable, .and their theoretical and experimental development should be pursued •

(10) Diversity can provide .substantial improvements in. system biterror-probability performance and should be utilized. Single-transmission polarization and separation diversity are much better than

multiple -transmission frequency and time diversity because the latter

requires D times more transmitter power and D times-more bandwidth,

where D is the order of diver-sity, to provide the s ameImpr-ovement in

bit-error-probability performance.

(11) Error coding can provide substantial improvements in system

bit-error-probability performance and should be util'~~·dl:· It is not

125
possible to spe cify one best code; in general" the performance improvement must be balanced against the complexity (practicality) of the code

and the reduction in spectral efficiency to obtain an optimum compromise.

However" soft decoding in convolutional or block codes can provide

substantially better error correction" and therefore substantially better

performance improvement" than hard decoding" because of the Rayleighfading characteristic of the HF channel.

(12) Transmitter distortions" because they fade with the signal" have

less effect on system bit-error-probability performance than receiver

distortions" into which the signal can fade. The rms level of transmitter

distortions should be < -30 dB relative to the r ms level of the signal.

Most present-day transmitters meet this criterion. Receiver distortions

should be < -60 dB relative to the rms level of the signal with or without

AGe. Most present-day receivers do not meet this criterion" and their

bit-error-probability performances are substantially degraded as a result.

It is quite practical to reduce substantially or to eliminate effectively all

receiver distortions except synchronization and Doppler-correction

distortionsII Synchronization and Doppler -correction distortions can be

substantially reduced with the development of improved synchronization

and Doppler -correction circuits 0

(13) The relationship betweenHF receiver AGe characteristics and

system bit-error-probability performance needs further investigation.

(14) In all systems" the signal-to-total-distortion ratio in the demodulator can easily and should be continuously determined to monitor system

performance 0 In systems with error coding" the detected and corrected

'bit errors should also be monitored.

(15) In simplex systems" the two methods of predicting system

performance on unused available channels" experience and propagation

predictions" should be used because" while they have limited accuracy"

they are the only methods available 0

(16) In duplex systems" system sounding (p. 76) is the best method

of predicting system performance on unused available channelsII

126
9. RE COMMENDATIONS

Based on the preceding results, the following recommendations are

made:

(1) The U. S. Department of-Defense should consider the practicality

of incorporating error coding equipment with hard decoding in present

military HF digital radio systems that have no coding to improve system

performance for an interim period.

(2) The U. S. Department of Defense should strongly support the

theoretical and experimental investigation of improved fundamental pulse

waveforms" concentric multiplexing" adaptive demodulator filters"

partially coherent detection" electronically adaptive receiving antennas,

and soft error-correcting coding in the development of new equipment

for longer term improvement of military HF digital radio communications.

10. ACKNOWLEDGEMENTS

The author gratefully acknowledges the helpful suggestions provided

by H. Akirna, E. M.Gray" and J. R. Juroshek in their reviews of the

report.

11. REFERENCES

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operating frequencies for high frequency communication circuits,

IRE Trans. Ant. Propo AP-7" pp. 397-404" June".

Brown" G.J. (1977)" High-frequency interference suppression, Tech.

Re pt , noscrrt: 155" PPo 1-104" August (Naval Ocean Systems

Center" San Diego" CA 92152)0 \

ccrn (1964)" Worldwide distribution and characteristics of atmospheric

radio noise" Rept o 322, Doc. Xth Plenary Assembly" pp. 1-78

(Acce ss, No. PB-255060" National Technical Information Service"

Springfield" VA 22161).

127
Chase" D. (1973)" A combined coding and modulation approach for

communication over dispersive channels" IEEE Trans. Commun ,

COM-21" pp. 1.59-174" March.

Davies" K. (1965)" Ionospheric Radio Propagation" National Bureau of

Standards .MonographB0 (U .S~" Gov'fPr-inting ,Office" Washington"

DC 20402).

DiToro" M.J. "J;~ Hanulec" P. Ahrens" and M.Glass (1964)1 HF antimultipath dev!ce(AdapticoIll)" Final Rept." Contract No. DA-36-

AMC-02339(E)., pp. 1.1-7.6, June (Ft. Monmouth" NJ07703).

Granger" J. F. N. (1950)" Wing-cap and tail-cap aircraft antennas" SRI

Rept. No. 6c~Pr:oj. 188" pp. 1-49,,, March (Stanford Research

Institute, ,Menlo P,.ark",CA 94025)~

Jahnke, E., F.Emde l andF. Losch (1960)" Tables of Higher Functions"

pp. 100-109 (McGraw-Hill Book Co." NewYork, NY).

Jastk, H.(Editor)-(19,61)1 Antenna Engineering. Handbook (McGraw-Hill

Book Co. I New York" NY).

Milstein" L.B., P.K. Das, andD.R. Arsenault (1978)1 Narrowband

jammer suppression in spread spectrum systems using SAW devices"

'NTC 78 Confv-Recor-d, pp. 43. 2.1-·43,.-2. 5, Dec,., (IEEE Service

Center" 445 Hoes Lane" Piscataway" NJ 08854).

Proakis, J. G.(1968)1 Probabilities of error for adaptive reception of

Me-phase stgnals, IEEE T:rans.Co'mmun'. Tech. COM-16 1 pp , 71-81"

February.

Salaman, R •.K. (1962)"A new ionospheric multipath reduction factor I

IRE Trans.Commun. Systems CS-l O,pp. 221-222" June.

Schwart z , M." W·.R. Bennettj vandS; Stein (1966), Communication

Systems and" Techniques" p •. 401(McGraw-Hill Book Co. ,New York"

NY).

Tanner" R.L. (1958)" Shuntandnotch-fe,daircraft antennas" IRE Trans.

Ant. Prop. AP-6, pp. 35-43, January.

Watterson" C.C." J. R.Juroshek,arid·W. b.Bensema(197 0)1 Experimental confirmation of an HF channel model" IEEE Trans. Cornmun ,

Technol. COM-1S, pp. 792-803 1 December.

Watterson" C.C." and C. M. Mini.ster- (1975)1 HF channel-simulator

measurements and perfor-mance analyses on the USC-10, ACQ-6" and

MX-190 PS'Kmodems" OT Rept.75-56" pp. 1-265" July (Access. No.

COM75-11206, National Technical Information Service, Springfield,

VA 22161).

128
FORM OT-29

(3-73)

u.s. DEPARTMENT OF COMMERCE OFFICE OF TELECOMMUNICATIONS

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NO.2. Gov't Accession No.3. Recipient's Accession No.

NTIA Report 79-29

4. TITLE AND SUBTITLE

Methods of Improving the Performances of

HF Digital Radio Systems

7. AUTHOR(S)

Clark C. Watterson

8. PERFORMING ORGANIZATION NAME AND ADDRESS

Institute for Telecommunication Sciences, National

Telecommunications and Information Administration"

Boulder" Colorado 80303

11. Sponsoring Organization Name and Address

U. So Army Communications-Electronics

Engineering Installation Agency"

Fort Huachuca" Arizona 85613

14. SUPPLEMENTARY NOTES

5. Publication Date

October 1979

6. Performing Organization Code

NTIA/ITS

9. Project/Task/Work Unit No.

9103560

10. Contract/Grant No.

CCC-PO-14-78

12. Type of Report and Period Covered

Final Report

13.

15. ABSTRACT (A 200-word or l ess factuai summary of most significant information. If document includes a significant

bibliography ot literature survey, mention it h ere, )

The bit-·error-probability performances of HF digital radio systems with

respect to channel and equipment additive .. multiplicative, and nonlinear

distortions are evaluated with respect to the nine system design features that

affect the performances. The system design features are the fundamental

pulse wavefor-m, the keying method (ASK" PSK" APSK" FSK" and CPK)" the

multiplexingemethod (fr'equencyand concentric multiplexing)" the type of

demodulator filter (matched and nonmatched nonadaptive filters and quasistatic and dynamic adaptive filters).. the detection method (coherent" partially

coherent" differentially coherent" and noncoherent), the transmitter power"

the antennas" diversity" and error coding. Spectral efficiency (information

rate Isignal bandwidth) is also evaluated. The best combination of design

features is determined.

16. Key Words (Alphabetical order, separated by semicolons)

Adaptive filtering; additive distortion; APSK; ASK; bit error probability;

bit error rate; channel model; coding; coherent; CPK; detection: differentially

coherent; digital; distortion; diversity; error rate; fading; FSK;HF; ionosphere; keying; modem" multipath; multiplexing; multiplicative distortion;

noncoherent; nonlinear distortion; partially coherent; performance; PSK;

radio; spectral efficiency•

17. AVAILABILITY STATEMENT

rn UNLIMITED.

D FOR OFFICIAL DISTRIBUTION.

U. S. GOVERNMENT PRINTING OFFICE 19~9 - 682-174/164 Reg. 8

18. Securi ry Class (This report)

Unclassified

19. Security Class (This page)

Unclassified

20. Number of pages

138

21. Price:

L'SCOMM-DC 29716-P73