## Example 5.8

#### A radio receiver is limited in its performance by thermal noise generated in the receiver front-end. The receiver is capable of decoding both coherent binary ASK and binary PSK signals. If the average power rating of the transmitter is constant when it is sending both ASK and PSK data, which modulation format will be able to send data at the fastest rate for a given bit error probability in the receiver, and how much faster can it be?

### Solution

#### The BER equations for coherent ASK and coherent PSK are as follows:
Pe ASK = 0.5erfc[Eb/2N0]1/2
Pe PSK = 0.5erfc[Eb/N0]1/2

#### It can be seen that the PSK system can tolerate a noise power density that is twice that for ASK or an Eb value that is half that for ASK.
In this example, the noise power density at the input to the receiver is fixed for both ASK and PSK, and therefore it is possible to halve the Eb value for PSK and still match the ASK performance, allowing the PSK system to send data at twice the rate for the same average transmitter power.