22.5.1 Modulation

In the simplest case of binary CSK, a single chaotic basis function g ₁( t) is used, i.e.,

At least two types of CSK based on a single basis function can be imagined: Chaotic On-Off Keying (COOK) and antipodal CSK.

In COOK, symbol "1" is represented by s ₁( t) = ?2 E _bg ₁( t) and symbol "0" is given by S ₂( t) = 0. Equivalently,

where E _b denotes the average energy per bit and we have assumed that the probabilities of symbols "1" and "0" are equal.

The upper limit on the noise performance of a modulation scheme is determined by the separation of the message points in the signal space; the greater the separation, the better the noise performance. Figure 22.8 shows the signal-space diagram for COOK, where the distance between the message points is ?2 E _b.

Figure 22.8: Signal-space diagram for binary COOK.

In antipodal CSK, symbol "1" is represented by and symbol "0" is given by , i.e.,

Figure 22.9 shows the signal-space diagram for antipodal CSK.

Figure 22.9: Signal-space diagram for binary antipodal CSK.

The distance between the message points is in this case. Consequently, the noise performance of antipodal CSK is potentially superior to that of COOK.

While the modulator determines the distance between the message points, the noise performance of the system depends on the efficiency...