#### Example 5.2 | #### Question 5.2

## Coherent detection

| A coherent detector operates by mixing the incoming data signal with a locally generated carrier reference and selecting the difference component from the mixer output. Representing the modulated data signal as a(t) cos wct and the reference carrier as cos(wct + q) , the mixer output becomes: a(t) cos wct cos(wct + q) = 0.5 a(t)cos(q) + 0.5 a(t)cos(2wct + q) If the carrier is phase coherent with the incoming modulated carrier signal (that is, there is no frequency or phase difference between them, q = 0o), then the output is proportional to a(t) and perfect detection is achieved.

If q = 90o, however, then cos(90o) = 0 and no output is obtained! It is thus essential to ensure that the carrier oscillator in the receive modem unit is in some way phase-locked to the carrier oscillator in the transmitter modem. Although coherent detection appears much more complicated than non-coherent detection, it is able to recover the data signal more accurately in the presence of noise.

####