Next: Pulse Position Modulation Up: Collected Problems Previous: Vertices of a Hyper-cube

Binary Signal Sets

The following signal set is employed to transmit equally likely signals over an additive white Gaussian noise channel with spectral height $\frac{N_0}{2}$ .

$\begin{picture} (490,200)(55,580) \setlength {\unitlength}{0.01in} % \thick... ... \put(385,600){\line( 1, 2){ 80}} \put(465,760){\line( 1,-2){ 40}}\end{picture}$

1.: Sketch and accurately label the block diagram of the receiver which minimizes the probability of error.
2.: Compute the probability of error of your receiver from part (a).
3.: Consider now the following receiver:

$\begin{picture} (100,30) \setlength {\unitlength}{1mm} \put(0,10){\vector(1... ...ebox(30,7){if $R \gt 0$, say $s_0$}} \put(90,10){\vector(1,0){10}}\end{picture}$
Compute the probability of error of this receiver if g(t) is given by
$\begin{displaymath} g(t) = \left\{ \begin{array} {cl} 1 & \mbox{for $0 \leq t < 1$}\\ -1 & \mbox{for $1 \leq t < 2$} \end{array} \right. \end{displaymath}$
4.: Determine the best signal set, s₀(t) and s₁(t), such that the receiver in part (c) is optimum and the average signal energy is equal to E=2.
5.: Compute the probability of error achieved by the receiver in part (c) and your signal set from part (d).

Prof. Bernd-Peter Paris
3/3/1998