## Answer 5.4

#### The voltage output of the coherent detector will be degraded from optimum by a factor cos(45o) or to 70.7% of its maximum value as a result of the carrier phase error.
This in turn equates to a reduction in symbol energy at the input to the receiver by a factor of cos2(45o) = 0.5 or 3 dB. (Symbol energy is proportional to power x symbol length or voltage2 x symbol length).
Now non-coherent ASK has a 3 dB performance penalty over perfect coherent ASK and hence with a 3 dB degradation due to the carrier phase error for this case, each type of modem would perform identically.