This receiver is optimal if the signal alternatives are equally likely.
The received signal is compared with all noise-free signal alternatives.
That is why the channel must be known to the receiver!
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“Correlation receiver”:
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ML receiver when M=2.
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How large is the bit error probability?
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FUNDAMENTAL RESULT!
Example:
zo(t)=0, z1(t) rectangular with amplitude A and T=Tb.
Rb=400 kbps, A^2/No is 70 dB
Pb=?
D^2=A^2/Rb
D^2/(2No)=(A^2/No)*(0.5/Rb)=12.5
Table 3.1 on Page 182: Pb=Q(3.536)=2.3*10^-4
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How much received energy per bit is required for a
given Pb?
d2 measures energy efficiency: the larger the better.
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Two very important special cases:
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A “typical” problem formulation.
Consequences:
Note! The received signal power Pz decreases with communication distance.
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M-ary signaling.
Symbol decisions in the receiver in Figure 4.8.
Ps = symbol error probability
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The union bound is an upper bound and it is especially
good at “high” signal-to-noise ratios.
In that case it is also easy to calculate!
Assume 4-PAM: Then 3 different distances exist.
So, the minimium Euclidean distance is important!
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This motivates why Gray-coding is used.
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Example: M equal energy orthogonal signals (FSK, or PPM).
D^2=2E for all pairs.
Union bound = (M-1)Q( )
++++++++++++++++++++++++++++
The coefficients in general:
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1948!
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