## Example 5.3

#### Sketch the constellation diagram for 8-ary ASK with a bipolar modulating signal and with a carrier frequency of cos(wct + 45o). What would be the output from a non-coherent detector for this type of ASK waveform?

### Solution

#### A constellation diagram is usually drawn with symbols having a phase cos(wct + 0o) on the horizontal axis, and those with phase cos(wct + 90o) on the vertical axis. For the carrier in this example, the symbols must lie on a line at 45o to the horizontal axis as shown below.

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#### The bipolar nature of the input modulating signal means that the amplitudes of the ASK symbols will have both positive and negative values. A negative value amplitude for an ASK symbol simply means that the carrier phase is inverted for these symbols (that is, they appear in the opposite quadrant of the constellation diagram).

#### A bipolar ASK signal cannot be detected properly with an envelope detector because it will not pick up the carrier inversion. All negative amplitude symbols will thus be decoded incorrectly as the equivalent positive amplitude symbols.