<s>
Phase-comparison	B-Algorithm
monopulse	I-Algorithm
is	O
a	O
technique	O
used	O
in	O
radio	O
frequency	O
(	O
RF	O
)	O
applications	O
such	O
as	O
radar	B-Application
and	O
direction	B-Device
finding	I-Device
to	O
accurately	O
estimate	O
the	O
direction	O
of	O
arrival	O
of	O
a	O
signal	O
from	O
the	O
phase	O
difference	O
of	O
the	O
signal	O
measured	O
on	O
two	O
(	O
or	O
more	O
)	O
separated	O
antennas	O
or	O
more	O
typically	O
from	O
displaced	O
phase	O
centers	O
of	O
an	O
array	O
antenna	O
.	O
</s>
<s>
Phase-comparison	B-Algorithm
monopulse	I-Algorithm
differs	O
from	O
amplitude-comparison	B-Algorithm
monopulse	I-Algorithm
in	O
that	O
the	O
former	O
uses	O
displaced	O
phase	O
centers	O
with	O
a	O
common	O
beam	O
pointing	O
direction	O
,	O
while	O
the	O
latter	O
uses	O
a	O
common	O
phase	O
center	O
and	O
displaced	O
beam	O
pointing	O
directions	O
.	O
</s>
<s>
In	O
phase-comparison	B-Algorithm
monopulse	I-Algorithm
,	O
typically	O
an	O
array	O
is	O
subdivided	O
into	O
sub-arrays	O
,	O
and	O
then	O
a	O
"	O
sum	O
"	O
and	O
a	O
"	O
difference	O
"	O
or	O
"	O
del	O
"	O
channel	O
are	O
formed	O
.	O
</s>
<s>
The	O
monopulse	B-Algorithm
ratio	O
is	O
formed	O
by	O
dividing	O
the	O
imaginary	O
part	O
of	O
the	O
del	O
channel	O
by	O
the	O
real	O
part	O
of	O
the	O
sum	O
channel	O
.	O
</s>
<s>
Two	O
monopulse	B-Algorithm
ratios	O
are	O
formed	O
just	O
as	O
with	O
a	O
linear	O
array	O
,	O
each	O
one	O
indicating	O
the	O
deviation	O
angle	O
in	O
one	O
dimension	O
from	O
the	O
center	O
of	O
the	O
beam	O
.	O
</s>
<s>
There	O
are	O
some	O
common	O
misconceptions	O
about	O
phase	O
comparison	O
monopulse	B-Algorithm
.	O
</s>
<s>
Monopulse	B-Algorithm
processing	O
is	O
done	O
entirely	O
with	O
the	O
received	O
signal	O
in	O
the	O
array	O
manifold	O
and	O
beam	O
forming	O
network	O
.	O
</s>
<s>
Second	O
,	O
phase-comparison	B-Algorithm
monopulse	I-Algorithm
does	O
n't	O
technically	O
actually	O
do	O
a	O
phase	O
comparison	O
,	O
but	O
rather	O
simply	O
divides	O
the	O
del	O
channel	O
by	O
the	O
sum	O
channel	O
to	O
arrive	O
at	O
a	O
ratio	O
wherein	O
the	O
angle	O
information	O
is	O
encoded	O
.	O
</s>
<s>
We	O
can	O
define	O
the	O
beam	O
pattern	O
(	O
array	B-Algorithm
factor	I-Algorithm
)	O
of	O
a	O
uniform	O
linear	O
array	O
(	O
ULA	O
)	O
with	O
N	O
elements	O
,	O
as	O
:	O
</s>
<s>
This	O
pattern	O
is	O
also	O
known	O
,	O
for	O
monopulse	B-Algorithm
purposes	O
,	O
as	O
the	O
"	O
sum	O
"	O
pattern	O
,	O
as	O
it	O
was	O
obtained	O
by	O
summing	O
all	O
of	O
the	O
elements	O
together	O
.	O
</s>
<s>
Let	O
us	O
now	O
develop	O
the	O
monopulse	B-Algorithm
"	O
difference	O
"	O
or	O
"	O
del	O
"	O
pattern	O
by	O
dividing	O
the	O
array	O
into	O
two	O
equal	O
halves	O
called	O
subarrays	O
.	O
</s>
<s>
In	O
monopulse	B-Algorithm
practice	O
,	O
this	O
is	O
what	O
is	O
actually	O
done	O
.	O
</s>
<s>
The	O
monopulse	B-Algorithm
ratio	O
is	O
formed	O
as	O
:	O
</s>
<s>
One	O
can	O
see	O
that	O
,	O
within	O
the	O
3dB	O
beam	O
width	O
of	O
the	O
system	O
,	O
the	O
monopulse	B-Algorithm
ratio	O
is	O
almost	O
linear	O
.	O
</s>
<s>
One	O
can	O
also	O
note	O
that	O
the	O
monopulse	B-Algorithm
ratio	O
is	O
continuous	O
within	O
the	O
null-to-null	O
beam	O
width	O
,	O
but	O
has	O
asymptotes	O
that	O
occur	O
at	O
the	O
beam	O
nulls	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
monopulse	B-Algorithm
ratio	O
is	O
only	O
accurate	O
to	O
measure	O
the	O
deviation	O
angle	O
of	O
a	O
target	O
within	O
the	O
main	O
lobe	O
of	O
the	O
system	O
.	O
</s>
<s>
Before	O
performing	O
monopulse	B-Algorithm
processing	O
,	O
a	O
system	O
must	O
first	O
detect	O
a	O
target	O
,	O
which	O
it	O
does	O
as	O
normal	O
using	O
the	O
sum	O
channel	O
.	O
</s>
<s>
All	O
of	O
the	O
typical	O
measurements	O
that	O
a	O
non-monopulse	O
system	O
make	O
are	O
done	O
using	O
the	O
sum	O
channel	O
,	O
e.g.	O
,	O
range	O
,	O
Doppler	O
,	O
and	O
angle	O
.	O
</s>
<s>
Therefore	O
,	O
a	O
monopulse	B-Algorithm
processor	O
functions	O
by	O
first	O
detecting	O
and	O
measuring	O
the	O
target	O
signal	O
on	O
the	O
sum	O
channel	O
.	O
</s>
<s>
Of	O
course	O
,	O
if	O
the	O
array	O
is	O
2-dimensional	O
,	O
such	O
as	O
a	O
planar	O
array	O
,	O
there	O
are	O
two	O
del	O
channels	O
,	O
one	O
for	O
elevation	O
and	O
one	O
for	O
azimuth	O
,	O
and	O
therefore	O
two	O
monopulse	B-Algorithm
ratios	O
are	O
formed	O
.	O
</s>
