Maximum Likelihood Receiver

1
Maximum Likelihood Receiver
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• The transmitter sends one of M signals si(t), for
  i1,2,,M
• The M signals forms a constellation in the
  signaling space

s1
s5
s2
s3
s6
s4
s7
3

• The received signal x(t) si(t) n(t) is
  decomposed to its components in the signal space.

xisi1n1

Decision Rule
X
?
y1(t)
x2si2n2

X
?
si(t)
y2(t)
xt)
xNsiNnN

X
?
yN(t)
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Since xi are independent Gaussian distributed
random variable their joint density function is
given by
An ML receiver selects sj that maximize fXsj.
Define
To be the likelihood function
Maximizing the likelihood function is equivalent
to minimizing the quantity
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The maximum Likelihood receiver picks the signal
that is closed to the received signal in the
signal space
s1
s5
s2
x
s3
dmin
s6
s4
s7