Phase and amplitude analysis of radio echoes from the ionosphere

Phase and amp~~de analysis of radio echoes from the iono~here J. D. WHITEHEAD and P. E. MONRO Department of Physios, University of Queensland, St. Lucia, Queensland, 4067, Australia (Received 25 h’overnber 1974; in revisedforma14 February

1975)

Abstract-Radio echoes from the ionosphere are Doppler shifted in frequency due to horizontal and vertical motions. Fourier analysis of the phase and amplitude of the received signal may be used to give angular and height resolution. It is shown that the angnlar resolution is the angular size of the first Fresnel zone and that for D-region echoes, taken as an example, the height resolution is si~ifieantly better than the usual method of pulse separat.ion.

1. INTRODUCTION In radio sounding coherency received resolve

of the echo.

it may

of the transmitted

phase and amplitude between

experiments sampling

and

rate

maximum

change

measurements

increase

enables

without

The Fourier

method

system

that

the

echoes lie within

the range of resolution

from

one Fourier

compo-

is not too severe). RE8OLUTION

To estimate the angle of arrival resolution, moves

the is

ambiguity.

V.

of the ionospheric

horizontally

The reflection

echo reflected vertical

has

only to deal with a single echo (provided

2. ANGLE OF ARRIVAL

a model

The

twice

guarantees

nent to another

us to

spectrum

simply

effectively

The Dop-

than

shift if the Doppler

of its angle of arrival

or height depends on the system used.

and that the ‘spill-over’

system&i-

frequency.

be greater

an echo,

the error in the measurement

of & series of

echoes.

with

and meas-

no other

and Dop-

the order of 0.1 Hz for HI?

should

Doppler

to be measured

of their differing

analysis

the various

pler shifts are typically

to

relrative to the phase

radio wave)

with time and Fourier

distinguish

be possible

Because of the coherency

pler shifts, the phases (defined tally

and phase

If two or more echoes are

them by taking advantage shifts.

it is often pos-

of the amplitude

at the same time,

Doppler

It must be emphasized

of the ionosphere,

sible to take advantage

that resolution

urement are not the same. Hevingresolved

reflector

without

it

change at the velocity

m&y be total

back

we use

in which

or partial.

to the transmitter

angle 8, the Doppler

For an

at an off-

shift f is given

by

PFISTER (1971) has used Fourier analysis to resolve echoes having various angles of arrival in a

c

of this note is to calculate, or estimate, the resolution in angle of arrival or height which is then pos-

provided

sible.

transmitted

To estimate the angle of arrival resolution,

fo_-y

-2pB

f=

similar manner to that described here. The purpose

0 < 1. c is the velocity frequency,

of light, f.

the

and I the radio wavelength

we use as a model a rigid but irregular surface,

in free space.

This equation

which may

takes

account

of the movement

of the reflection

waves, moving horizontally with constant velocity.

point

relative

to

(PFISTER, 1971;

Echoes from different directions then have different

BROWNLIE et r&E.,1973.)

totally

Doppler shifts.

retie&or

reflect the radio

For height resolution, it is assumed

that the reflectors the vertical

or partially

are moving

movement

partially

vertically,

reflects

(or scatters)

with time because 8 changes.

Each

However,

change of B depends on the curvature

the radio

tion point and we can only estimate

waves. In

reflector.

general

and

The Doppler shift itself does not stay con&ant

but that

changes with height.

the

is quite

the rate of at the reflec-

a value for it.

We have to a first approximation both

situations,

observation

the total

is limited

resolve

echoes with only slightly

shifts.

Using

resolution obtained.

typical

is much

available

time

and thus is the ability values,

better

different

it is shown

than

of to

dtl _wdt

Doppler that the

can be normally

V

(2)

H

where H is the height of the reflector.

From

(2)

the

3437

we

may

calculate

how

rapidly

(1) and Doppler

1428

J. D.

WHITEHEAD

shift changes with time, that is - 2vz

df --dt

CH

f

and P. E. MONRO Proceeding then with the calculation, the Doppler shift produced by a vertical movement U of the reileetor is

”

f=-fo

We now

say that the maximum useful time of observation T may be defined so that the frequency resolution f ( Ml/T) between the Fourier components is equal to the change in Doppler shift of any echo in the time T, that is

=’

z_+

2Tfo

T2

and for two echoes differs by

Af =

CH

We can distinguish between echoes differing in Doppler shift by Af so that the angular resolution is, using (1) and (5),

A&r*= 2Vfo

J

2 U2Tfo

We assume we have partial reflections from various heights vertically overhead, i.e. 0 = 0, but the vertical velocity of the reflector U changes with height R

U -.UT R

2H

8. HEIQHT RESOLUT’IOB

U

%UfoAH

and the new Doppler shift differs from the old by

m.?_.

This means in fact that echoes coming from reflection points only a Fresnel zone apart may be resolved using Fourier analysis.

dU -=&R

c

if the echoes differ in height by AH. We now add to our model by assuming that as a particular reflector moves in height, it changes velocity to take on the velocity associated with its new height. Thus the change in velocity after a time T is

Thus

Af=

-2U

-xi-’

As before Af is the resolution in Doppler shift and equals approximately l/T. We make the change in Doppler shift of one echo equal to this, that is 1 Af = T

2U2Tfo, Rc

(12)

Hence (13)

(‘1

where R is the vertical scale size of the wind structure. Note that dU/dB may be positive or negative. In a real ionospheric situation, Doppler shifts are produced by both horizontal and vertical motion. The vertical motion is not usually measured but what information we have, from E-region meawremerits, suggests that vertical velocities may be about 10 msec-l, horizontal velocities 100 msec-I, and off-vertical angles of arrival 0.1 rad, so that the Doppler shifts produced are about equal. The theory for height resolution presented here is based on the change in vertical velocity with height. However in practice all that is required is that the Doppler shift of the echoes varies with range. If echoes can be resolved because of their differing Doppler shifts, their ranges can be measured as if one had a single, clean echo. Angle of arrival is then required to l?nd the echo height (as distinct from range).

(11)

Using (9) and (13) to give the height resolution (14) 4. PRACTICAL APPLIOATIONII Angle of awival Equation (6) implies that the resolution in angle of arrival for 3 MHz radio sounding of the E-region is O-02-0.03 radians and is equal to that obtainable using an antenna array 4 or 5 km in size! Having resolved the echoes, it is still necessary to measure the angles of arrival: this could be done in principle by using a simple 3 element array if we can measure phase differences sufficiently accurately. The time of observation given by equation (5), taking V - 100 msec-l, is 20-25 sec. A typical off-vertical angle is 0.1 radian, so that a typical Doppler shift is O-2 Hz.

1429

Phase and amplitude analysis of radio echoes from the ionosphere The Fourier

the various Aj

analysis Further

= 0.05 Hz.

maximum Doppler

shifts

with

shift for recordings

for the N’th difference

a resolution

in phase of each

&6+/2N

(15)

Fourier harmonic,

where &h is the phase

of the radio

signals.

the Doppler

shift

exactly

one of the Fourier

This

will

error

harmonic

of arrival

(in the plane of the two antennas),

is also proportionel,

to the off-vertical

through

angle and N

Af, to the off-vertical

The result is thet the maximum

off-vertical

error in the

angle due to this dat8 reduction

method

(16)

J SH

Why then do we need to use large antenna arrays?

gravity

in the direction

w8ves present moving

in verious

directions,

only

and

direction,

corresponds

to a weighted

provides

with various

but

its

value

mean of the gravity

perpendicular

and thus our observed

In

the

D-region

(GARDNER many

discrete

heights.

It this

analysis;

analysis

method

suggested

with time.

of

the

is bi8sed.

these w8ves.

analysis d8t8,

waves A large

(BROWN-

if the equipment lems.

only an

8 useful

data

one.

to provide

8

is very much easier

itself has good angular resolution.

analysis of small date samples has its probJust 8s an antenna

side-lobes,so

theFourier

methods-Fourier

pattern

one.

followed

Each

by itself

subsmntially

the presence

of much stronger

our estimates

8re sometimes often exceed

partly

V/H (equation

echo is strongly

to resolve

of weak echoes in

ones.

focussed

density

analysis or

deconvolution

method.

and error

because d6/dt may

2) especially and partly

of

echo

of echo

used in the

Deconvolution

by

the

by AUSTIN et al. (1969) uses only phase information,

not its change

(14) gives the height

resolu-

(17)

For 3 MHz

sounding

when the

because

we

and taking

AH This is about resolution

R=6km,

= 550 m.

8 factor

(13)

of 10 better

obtainable

using

to an accuracy

than the basic

40,8sec

pulses.

is not

8lW8yS

velocity

available.

gradient

of the vertical

heights.

These will show 88 8 prolonged

echo from

for one particular

Fourier

ponent.

however,

from

Usually

echoes

differing

by more than AH (equation

different

and resolvable

the actual principle)

echo

to produce

each Doppler messured

shift

reasoneble

averages

comranges

15) will have

shifts.

it would

8 separate

To measure

be possible

(in

A-scan picture

for

end thus the range

8s sccurately

(obtained

Doppler

ranges,

The

will be zero at some

8 renge of heights

With

The

of 550 m once the echo

should present no particulrtr difficulties.

resolution

could

be

as if one had 8 single echo.

csre and a good sign81 : noise ratio

partly

because

the complex

the

method

suggested

sign81 for many seconds), the

error in determining

the range should be less th8n

500 m. Equation

of the resolution

optimistic

and

is defec-

reduce the

of error and make it possible

and measure the angle of arrival

The

by echo

complementary

independent.

tive, but the two together

Thirdly,

has troublesome

by a dominant analysis

deconvolution-are

statistically possibility

array

analysis shows contamina-

tion of other frequencies two

provides

albeit

of the

small number of echo directions Fourier

the

tion

This

deconvolution

but

Equation

is resolved

sorting

range

to deconvolute

loses the phase information

Fourier

method, come from

or a continuous

return either before the electron

W8Ve

LIE et al., 1973.)

Further

heights

reflection

1953) echoes

is possible

in all directions

initid

partial

and PAWSEY,

measurement

the Fourier

part of the HF

in height

array which can be used to reduce angles of arrival

Secondly,

a substantial

If

ambigu-

arrays in existence.

weak gravity

to the domin8nt

spectrum

can detect

coupling.

to eliminate

speeds

average

We may thus fail to observe

waves moving

phase

If we have sever81

V itself changes with time in

magnitude speeds.

method of F.

of antenna

are inserted

ities, you have already antenna

Typically

and thus a spacing of

Such 8 spacing is also required

effect

the instantaneous

which is less then the resolution. of all, the Fourier

the

antennas

strength

-Z-

First

eliminate

extra

errors.

is required to take full advantage

of the data analysis.

during

is

resolution

8 few wavelengths

Resolution

frequencies.

&j is proportional

equipment

m8y be expected

arises

not be in general

However

-10“

errors

to

taken at two antennas

because

angle.

of

it may be shown that the

error in the difference

is

have neglected

separation of

will provide

Doppler

observ8tion.

(13) gives the optimum Teking

U = 10 msec-l,

time for each T = 55 sec.

This is about the s8me value as found for the angular resolution shifts

situ8tion

and arises because the Doppler

due to vertical

movement

has been

taken

J. D. WHITEHEAD

1430 to

be

the

Provided

same

as

the Doppler

does not matter Typical

horizontal

potential

amplitude

analysis,

that

economical computer

would output Doppler

height

A greater

is every

7 psec.

the

initial

an amplitude:

Fourier

rate

To take advantage

resolution,

to feed the data for

the

It

1 km in height might

directly

Fourier

be most

into a mini-

analysis.

This

height curve for each

shift in the range say

50.1 Hz spaced at

In addition files

to achieving

data reduction

(because

considerable

to give electron

the zero pulse width

saving

density

theory

in

pro-

can be

analysis

provides

sorting process of ionospheric tially

complex

0.02 Hz. further

the echoes come from stratified

PFISTER W.

layers.

excellent

angular

a

powerful

initial

echoes to give poten-

and height

resolution.

AcknowEedgements-This work forms part of the programme for ionospheric research in the Department of Physics, University of Queensland is supported by the Radio Research Board and the Australian Research Grants Committee. Part of the work done by one of us (J. D. Whitehead) was performed whilst on leave at the Ionospheric Research Laboratory, Pennsylvania State Universit,y. The work wa,s completed with the partial support of the National Science Foundation under Grant Ko. GA33446 XI and the Office of Naval Research under Grant No. N00014-67-A-0385-0017. The authors wish to thank Dr. J. S. NISBET for stimulating discussions.

REFERENCES AUSTIN G. L., BENNETT R. G. ‘I?. and THORPE M. R. BROWNLIE G. D., DRYBURGH L. D. and WHITEHEAD J. D. GARDNER F. F. and PAWSEY J. L.

question

5. CONCLUSIONS

measurements

should be measured every

at least,

of whether

shifts are 0.06 Hz and to avoid

in the Fourier

increases the signa1:nois.e ratio. the

used) it would also settle the controversial

movement.

shift changes with range it

should be taken every few seconds. of

MONRO

how it is produced.

Doppler

ambiguity

for

and P. E.

1969

J. atmos. terr. Phys.

81,1099.

1973

J. atmos. terr. Phys. 35, 2147.

1963 1971

J. otwws. terr. Phys. 3, 321. J. atfnoa. terr. Phys. 33, 99.