<s>
Beamforming	B-Algorithm
or	O
spatial	O
filtering	O
is	O
a	O
signal	O
processing	O
technique	O
used	O
in	O
sensor	B-Algorithm
arrays	I-Algorithm
for	O
directional	O
signal	O
transmission	O
or	O
reception	O
.	O
</s>
<s>
This	O
is	O
achieved	O
by	O
combining	O
elements	O
in	O
an	O
antenna	B-Algorithm
array	I-Algorithm
in	O
such	O
a	O
way	O
that	O
signals	O
at	O
particular	O
angles	O
experience	O
constructive	O
interference	O
while	O
others	O
experience	O
destructive	O
interference	O
.	O
</s>
<s>
Beamforming	B-Algorithm
can	O
be	O
used	O
at	O
both	O
the	O
transmitting	O
and	O
receiving	O
ends	O
in	O
order	O
to	O
achieve	O
spatial	O
selectivity	O
.	O
</s>
<s>
Beamforming	B-Algorithm
can	O
be	O
used	O
for	O
radio	O
or	O
sound	O
waves	O
.	O
</s>
<s>
It	O
has	O
found	O
numerous	O
applications	O
in	O
radar	B-Application
,	O
sonar	B-Application
,	O
seismology	O
,	O
wireless	O
communications	O
,	O
radio	O
astronomy	O
,	O
acoustics	O
and	O
biomedicine	O
.	O
</s>
<s>
Adaptive	O
beamforming	B-Algorithm
is	O
used	O
to	O
detect	O
and	O
estimate	O
the	O
signal	O
of	O
interest	O
at	O
the	O
output	O
of	O
a	O
sensor	B-Algorithm
array	I-Algorithm
by	O
means	O
of	O
optimal	O
(	O
e.g.	O
</s>
<s>
To	O
change	O
the	O
directionality	O
of	O
the	O
array	O
when	O
transmitting	O
,	O
a	O
beamformer	B-Algorithm
controls	O
the	O
phase	O
and	O
relative	O
amplitude	B-Application
of	O
the	O
signal	O
at	O
each	O
transmitter	O
,	O
in	O
order	O
to	O
create	O
a	O
pattern	O
of	O
constructive	O
and	O
destructive	O
interference	O
in	O
the	O
wavefront	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
sonar	B-Application
,	O
to	O
send	O
a	O
sharp	O
pulse	O
of	O
underwater	O
sound	O
towards	O
a	O
ship	O
in	O
the	O
distance	O
,	O
simply	O
simultaneously	O
transmitting	O
that	O
sharp	O
pulse	O
from	O
every	O
sonar	B-Application
projector	O
in	O
an	O
array	O
fails	O
because	O
the	O
ship	O
will	O
first	O
hear	O
the	O
pulse	O
from	O
the	O
speaker	O
that	O
happens	O
to	O
be	O
nearest	O
the	O
ship	O
,	O
then	O
later	O
pulses	O
from	O
speakers	O
that	O
happen	O
to	O
be	O
further	O
from	O
the	O
ship	O
.	O
</s>
<s>
The	O
beamforming	B-Algorithm
technique	O
involves	O
sending	O
the	O
pulse	O
from	O
each	O
projector	O
at	O
slightly	O
different	O
times	O
(	O
the	O
projector	O
closest	O
to	O
the	O
ship	O
last	O
)	O
,	O
so	O
that	O
every	O
pulse	O
hits	O
the	O
ship	O
at	O
exactly	O
the	O
same	O
time	O
,	O
producing	O
the	O
effect	O
of	O
a	O
single	O
strong	O
pulse	O
from	O
a	O
single	O
powerful	O
projector	O
.	O
</s>
<s>
The	O
same	O
technique	O
can	O
be	O
carried	O
out	O
in	O
air	O
using	O
loudspeakers	O
,	O
or	O
in	O
radar/radio	O
using	O
antennas	O
.	O
</s>
<s>
In	O
passive	O
sonar	B-Application
,	O
and	O
in	O
reception	O
in	O
active	O
sonar	B-Application
,	O
the	O
beamforming	B-Algorithm
technique	O
involves	O
combining	O
delayed	O
signals	O
from	O
each	O
hydrophone	O
at	O
slightly	O
different	O
times	O
(	O
the	O
hydrophone	O
closest	O
to	O
the	O
target	O
will	O
be	O
combined	O
after	O
the	O
longest	O
delay	O
)	O
,	O
so	O
that	O
every	O
signal	O
reaches	O
the	O
output	O
at	O
exactly	O
the	O
same	O
time	O
,	O
making	O
one	O
loud	O
signal	O
,	O
as	O
if	O
the	O
signal	O
came	O
from	O
a	O
single	O
,	O
very	O
sensitive	O
hydrophone	O
.	O
</s>
<s>
Receive	O
beamforming	B-Algorithm
can	O
also	O
be	O
used	O
with	O
microphones	O
or	O
radar	B-Application
antennas	O
.	O
</s>
<s>
A	O
narrow	O
band	O
system	O
,	O
typical	O
of	O
radars	B-Application
,	O
is	O
one	O
where	O
the	O
bandwidth	B-Algorithm
is	O
only	O
a	O
small	O
fraction	O
of	O
the	O
center	O
frequency	O
.	O
</s>
<s>
With	O
wideband	O
systems	O
this	O
approximation	O
no	O
longer	O
holds	O
,	O
which	O
is	O
typical	O
in	O
sonars	B-Application
.	O
</s>
<s>
In	O
the	O
receive	O
beamformer	B-Algorithm
the	O
signal	O
from	O
each	O
antenna	O
may	O
be	O
amplified	O
by	O
a	O
different	O
"	O
weight.	O
"	O
</s>
<s>
For	O
the	O
full	O
mathematics	O
on	O
directing	O
beams	O
using	O
amplitude	B-Application
and	O
phase	O
shifts	O
,	O
see	O
the	O
mathematical	O
section	O
in	O
phased	O
array	O
.	O
</s>
<s>
Beamforming	B-Algorithm
techniques	O
can	O
be	O
broadly	O
divided	O
into	O
two	O
categories	O
:	O
</s>
<s>
Conventional	O
beamformers	B-Algorithm
,	O
such	O
as	O
the	O
Butler	B-Algorithm
matrix	I-Algorithm
,	O
use	O
a	O
fixed	O
set	O
of	O
weightings	O
and	O
time-delays	O
(	O
or	O
phasings	O
)	O
to	O
combine	O
the	O
signals	O
from	O
the	O
sensors	O
in	O
the	O
array	O
,	O
primarily	O
using	O
only	O
information	O
about	O
the	O
location	O
of	O
the	O
sensors	O
in	O
space	O
and	O
the	O
wave	O
directions	O
of	O
interest	O
.	O
</s>
<s>
In	O
contrast	O
,	O
adaptive	O
beamforming	B-Algorithm
techniques	O
(	O
e.g.	O
,	O
MUSIC	O
,	O
SAMV	B-Algorithm
)	O
generally	O
combine	O
this	O
information	O
with	O
properties	O
of	O
the	O
signals	O
actually	O
received	O
by	O
the	O
array	O
,	O
typically	O
to	O
improve	O
rejection	O
of	O
unwanted	O
signals	O
from	O
other	O
directions	O
.	O
</s>
<s>
As	O
the	O
name	O
indicates	O
,	O
an	O
adaptive	B-Algorithm
beamformer	I-Algorithm
is	O
able	O
to	O
automatically	O
adapt	O
its	O
response	O
to	O
different	O
situations	O
.	O
</s>
<s>
Beamforming	B-Algorithm
can	O
be	O
computationally	O
intensive	O
.	O
</s>
<s>
Sonar	B-Application
phased	O
array	O
has	O
a	O
data	O
rate	O
low	O
enough	O
that	O
it	O
can	O
be	O
processed	O
in	O
real	O
time	O
in	O
software	B-Application
,	O
which	O
is	O
flexible	O
enough	O
to	O
transmit	O
or	O
receive	O
in	O
several	O
directions	O
at	O
once	O
.	O
</s>
<s>
In	O
contrast	O
,	O
radar	B-Application
phased	O
array	O
has	O
a	O
data	O
rate	O
so	O
high	O
that	O
it	O
usually	O
requires	O
dedicated	O
hardware	O
processing	O
,	O
which	O
is	O
hard-wired	O
to	O
transmit	O
or	O
receive	O
in	O
only	O
one	O
direction	O
at	O
a	O
time	O
.	O
</s>
<s>
However	O
,	O
newer	O
field	B-Architecture
programmable	I-Architecture
gate	I-Architecture
arrays	I-Architecture
are	O
fast	O
enough	O
to	O
handle	O
radar	B-Application
data	O
in	O
real	O
time	O
,	O
and	O
can	O
be	O
quickly	O
re-programmed	O
like	O
software	B-Application
,	O
blurring	O
the	O
hardware/software	O
distinction	O
.	O
</s>
<s>
Sonar	B-Application
beamforming	B-Algorithm
utilizes	O
a	O
similar	O
technique	O
to	O
electromagnetic	O
beamforming	B-Algorithm
,	O
but	O
varies	O
considerably	O
in	O
implementation	O
details	O
.	O
</s>
<s>
Sonar	B-Application
applications	O
vary	O
from	O
1Hz	O
to	O
as	O
high	O
as	O
2MHz	O
,	O
and	O
array	O
elements	O
may	O
be	O
few	O
and	O
large	O
,	O
or	O
number	O
in	O
the	O
hundreds	O
yet	O
very	O
small	O
.	O
</s>
<s>
This	O
will	O
shift	O
sonar	B-Application
beamforming	B-Algorithm
design	O
efforts	O
significantly	O
between	O
demands	O
of	O
such	O
system	O
components	O
as	O
the	O
"	O
front	O
end	O
"	O
(	O
transducers	O
,	O
pre-amplifiers	O
and	O
digitizers	O
)	O
and	O
the	O
actual	O
beamformer	B-Algorithm
computational	O
hardware	O
downstream	O
.	O
</s>
<s>
High	O
frequency	O
,	O
focused	O
beam	O
,	O
multi-element	O
imaging-search	O
sonars	B-Application
and	O
acoustic	O
cameras	O
often	O
implement	O
fifth-order	O
spatial	O
processing	O
that	O
places	O
strains	O
equivalent	O
to	O
Aegis	O
radar	B-Application
demands	O
on	O
the	O
processors	O
.	O
</s>
<s>
Many	O
sonar	B-Application
systems	O
,	O
such	O
as	O
on	O
torpedoes	O
,	O
are	O
made	O
up	O
of	O
arrays	O
of	O
up	O
to	O
100	O
elements	O
that	O
must	O
accomplish	O
beam	O
steering	O
over	O
a	O
100	O
degree	O
field	O
of	O
view	O
and	O
work	O
in	O
both	O
active	O
and	O
passive	O
modes	O
.	O
</s>
<s>
Sonar	B-Application
arrays	O
are	O
used	O
both	O
actively	O
and	O
passively	O
in	O
1-	O
,	O
2-	O
,	O
and	O
3-dimensional	O
arrays	O
.	O
</s>
<s>
1-dimensional	O
"	O
line	O
"	O
arrays	O
are	O
usually	O
in	O
multi-element	O
passive	O
systems	O
towed	O
behind	O
ships	O
and	O
in	O
single	O
-	O
or	O
multi-element	O
side-scan	O
sonar	B-Application
.	O
</s>
<s>
2-dimensional	O
"	O
planar	O
"	O
arrays	O
are	O
common	O
in	O
active/passive	O
ship	O
hull	O
mounted	O
sonars	B-Application
and	O
some	O
side-scan	O
sonar	B-Application
.	O
</s>
<s>
3-dimensional	O
spherical	O
and	O
cylindrical	O
arrays	O
are	O
used	O
in	O
'	O
sonar	B-Application
domes	O
 '	O
in	O
the	O
modern	O
submarine	O
and	O
ships	O
.	O
</s>
<s>
Sonar	B-Application
differs	O
from	O
radar	B-Application
in	O
that	O
in	O
some	O
applications	O
such	O
as	O
wide-area-search	O
all	O
directions	O
often	O
need	O
to	O
be	O
listened	O
to	O
,	O
and	O
in	O
some	O
applications	O
broadcast	O
to	O
,	O
simultaneously	O
.	O
</s>
<s>
In	O
a	O
narrowband	O
sonar	B-Application
receiver	O
the	O
phases	O
for	O
each	O
beam	O
can	O
be	O
manipulated	O
entirely	O
by	O
signal	O
processing	O
software	B-Application
,	O
as	O
compared	O
to	O
present	O
radar	B-Application
systems	I-Application
that	O
use	O
hardware	O
to	O
'	O
listen	O
 '	O
in	O
a	O
single	O
direction	O
at	O
a	O
time	O
.	O
</s>
<s>
Sonar	B-Application
also	O
uses	O
beamforming	B-Algorithm
to	O
compensate	O
for	O
the	O
significant	O
problem	O
of	O
the	O
slower	O
propagation	O
speed	O
of	O
sound	O
as	O
compared	O
to	O
that	O
of	O
electromagnetic	O
radiation	O
.	O
</s>
<s>
In	O
side-look-sonars	O
,	O
the	O
speed	O
of	O
the	O
towing	O
system	O
or	O
vehicle	O
carrying	O
the	O
sonar	B-Application
is	O
moving	O
at	O
sufficient	O
speed	O
to	O
move	O
the	O
sonar	B-Application
out	O
of	O
the	O
field	O
of	O
the	O
returning	O
sound	O
"	O
ping	O
"	O
.	O
</s>
<s>
In	O
addition	O
to	O
focusing	O
algorithms	O
intended	O
to	O
improve	O
reception	O
,	O
many	O
side	O
scan	O
sonars	B-Application
also	O
employ	O
beam	O
steering	O
to	O
look	O
forward	O
and	O
backward	O
to	O
"	O
catch	O
"	O
incoming	O
pulses	O
that	O
would	O
have	O
been	O
missed	O
by	O
a	O
single	O
sidelooking	O
beam	O
.	O
</s>
<s>
A	O
conventional	O
beamformer	B-Algorithm
can	O
be	O
a	O
simple	O
beamformer	B-Algorithm
also	O
known	O
as	O
delay-and-sum	O
beamformer	B-Algorithm
.	O
</s>
<s>
The	O
beamformer	B-Algorithm
is	O
steered	O
to	O
a	O
specified	O
direction	O
only	O
by	O
selecting	O
appropriate	O
phases	O
for	O
each	O
antenna	O
.	O
</s>
<s>
If	O
the	O
noise	O
is	O
uncorrelated	O
and	O
there	O
are	O
no	O
directional	O
interferences	O
,	O
the	O
signal-to-noise	O
ratio	O
of	O
a	O
beamformer	B-Algorithm
with	O
antennas	O
receiving	O
a	O
signal	O
of	O
power	O
,	O
(	O
where	O
is	O
Noise	O
variance	O
or	O
Noise	O
power	O
)	O
,	O
is	O
:	O
</s>
<s>
A	O
null-steering	B-Protocol
beamformer	I-Protocol
is	O
optimized	O
to	O
have	O
zero	O
response	O
in	O
the	O
direction	O
of	O
one	O
or	O
more	O
interferers	O
.	O
</s>
<s>
A	O
frequency-domain	O
beamformer	B-Algorithm
treats	O
each	O
frequency	O
bin	O
as	O
a	O
narrowband	O
signal	O
,	O
for	O
which	O
the	O
filters	O
are	O
complex	O
coefficients	O
(	O
that	O
is	O
,	O
gains	O
and	O
phase	O
shifts	O
)	O
,	O
separately	O
optimized	O
for	O
each	O
frequency	O
.	O
</s>
<s>
The	O
delay-and-sum	O
beamforming	B-Algorithm
technique	O
uses	O
multiple	O
microphones	O
to	O
localize	O
sound	O
sources	O
.	O
</s>
<s>
One	O
disadvantage	O
of	O
this	O
technique	O
is	O
that	O
adjustments	O
of	O
the	O
position	O
or	O
of	O
the	O
number	O
of	O
microphones	O
changes	O
the	O
performance	O
of	O
the	O
beamformer	B-Algorithm
nonlinearly	O
.	O
</s>
<s>
One	O
of	O
the	O
techniques	O
to	O
solve	O
this	O
problem	O
is	O
the	O
use	O
of	O
genetic	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Such	O
algorithm	O
searches	O
for	O
the	O
microphone	B-Algorithm
array	I-Algorithm
configuration	O
that	O
provides	O
the	O
highest	O
signal-to-noise	O
ratio	O
for	O
each	O
steered	O
orientation	O
.	O
</s>
<s>
Beamforming	B-Algorithm
techniques	O
used	O
in	O
cellular	O
phone	O
standards	O
have	O
advanced	O
through	O
the	O
generations	O
to	O
make	O
use	O
of	O
more	O
complex	O
systems	O
to	O
achieve	O
higher	O
density	O
cells	O
,	O
with	O
higher	O
throughput	O
.	O
</s>
<s>
An	O
increasing	O
number	O
of	O
consumer	O
802.11ac	O
Wi-Fi	O
devices	O
with	O
MIMO	O
capability	O
can	O
support	O
beamforming	B-Algorithm
to	O
boost	O
data	O
communication	O
rates	O
.	O
</s>
<s>
To	O
receive	O
(	O
but	O
not	O
transmit	O
)	O
,	O
there	O
is	O
a	O
distinction	O
between	O
analog	O
and	O
digital	B-Algorithm
beamforming	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
if	O
there	O
are	O
100	O
sensor	O
elements	O
,	O
the	O
"	O
digital	B-Algorithm
beamforming	I-Algorithm
"	O
approach	O
entails	O
that	O
each	O
of	O
the	O
100	O
signals	O
passes	O
through	O
an	O
analog-to-digital	O
converter	O
to	O
create	O
100	O
digital	O
data	O
streams	O
.	O
</s>
<s>
By	O
contrast	O
,	O
the	O
"	O
analog	O
beamforming	B-Algorithm
"	O
approach	O
entails	O
taking	O
the	O
100	O
analog	O
signals	O
,	O
scaling	O
or	O
phase-shifting	O
them	O
using	O
analog	O
methods	O
,	O
summing	O
them	O
,	O
and	O
then	O
usually	O
digitizing	O
the	O
single	O
output	O
data	O
stream	O
.	O
</s>
<s>
Digital	B-Algorithm
beamforming	I-Algorithm
has	O
the	O
advantage	O
that	O
the	O
digital	O
data	O
streams	O
(	O
100	O
in	O
this	O
example	O
)	O
can	O
be	O
manipulated	O
and	O
combined	O
in	O
many	O
possible	O
ways	O
in	O
parallel	O
,	O
to	O
get	O
many	O
different	O
output	O
signals	O
in	O
parallel	O
.	O
</s>
<s>
This	O
cannot	O
be	O
done	O
as	O
effectively	O
for	O
analog	O
beamforming	B-Algorithm
,	O
not	O
only	O
because	O
each	O
parallel	O
signal	O
combination	O
requires	O
its	O
own	O
circuitry	O
,	O
but	O
more	O
fundamentally	O
because	O
digital	O
data	O
can	O
be	O
copied	O
perfectly	O
but	O
analog	O
data	O
cannot	O
.	O
</s>
<s>
In	O
MIMO	O
communication	O
systems	O
with	O
large	O
number	O
of	O
antennas	O
,	O
so	O
called	O
massive	O
MIMO	O
systems	O
,	O
the	O
beamforming	B-Algorithm
algorithms	O
executed	O
at	O
the	O
digital	O
baseband	B-Algorithm
can	O
get	O
very	O
complex	O
.	O
</s>
<s>
In	O
addition	O
,	O
if	O
all	O
beamforming	B-Algorithm
is	O
done	O
at	O
baseband	B-Algorithm
,	O
each	O
antenna	O
needs	O
its	O
own	O
RF	O
feed	O
.	O
</s>
<s>
To	O
remedy	O
these	O
issues	O
,	O
hybrid	O
beamforming	B-Algorithm
has	O
been	O
suggested	O
where	O
some	O
of	O
the	O
beamforming	B-Algorithm
is	O
done	O
using	O
analog	O
components	O
and	O
not	O
digital	O
.	O
</s>
<s>
There	O
are	O
many	O
possible	O
different	O
functions	O
that	O
can	O
be	O
performed	O
using	O
analog	O
components	O
instead	O
of	O
at	O
the	O
digital	O
baseband	B-Algorithm
.	O
</s>
<s>
Beamforming	B-Algorithm
can	O
be	O
used	O
to	O
try	O
to	O
extract	O
sound	O
sources	O
in	O
a	O
room	O
,	O
such	O
as	O
multiple	O
speakers	O
in	O
the	O
cocktail	O
party	O
problem	O
.	O
</s>
<s>
It	O
is	O
advantageous	O
to	O
separate	O
frequency	O
bands	O
prior	O
to	O
beamforming	B-Algorithm
because	O
different	O
frequencies	O
have	O
different	O
optimal	O
beamform	O
filters	O
(	O
and	O
hence	O
can	O
be	O
treated	O
as	O
separate	O
problems	O
,	O
in	O
parallel	O
,	O
and	O
then	O
recombined	O
afterward	O
)	O
.	O
</s>
