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Binary Signal Sets

Equally likely information bits are to be transmitted over an additive, white Gaussian noise channel with spectral height $\frac{N_0}{2}$ using the depicted signal set.


\begin{picture}
(100,50)

\setlength {\unitlength}{1mm}
 
\multiput(5,25)(50,0){...
 ...ine(1,1){20}}
\put(75,5){\line(1,1){20}}
\put(75,5){\line(0,1){40}}\end{picture}

1.
Draw the block diagram of the minimum probability of error receiver.
2.
Compute the probability of error attained by this receiver.
3.
Repeat parts (a) and (b) for the following signal set:
\begin{picture}
(100,50)

\setlength {\unitlength}{1mm}
 
\multiput(5,25)(50,0){...
 ...ne(1,-1){20}}
\put(75,5){\line(0,1){20}}
\put(75,5){\line(1,1){20}}\end{picture}

4.
Sketch and accurately label the two signal sets in appropriately chosen signal spaces.
5.
Compare the results for the two signal sets and explain.


Prof. Bernd-Peter Paris
3/3/1998