## Coherent detection vs non-coherent detection (cont.)

Let us now consider the case of detecting the ASK signal in the presence of noise. For simplicity we will assume that the carrier is in the 'off' state and that we have a specific noise component of length N and phase 60o. The non-coherent detector, which is performing amplitude detection, is simply measuring the length of the composite (ASK + Noise) vector regardless of the vector phase. It would thus produce an output voltage proportional to N, the noise vector length. |

The coherent detector, on the other hand, acts by mixing the incoming signal with the reference carrier cos wct. The result is that the voltage at the detector output due to the noise is reduced by a factor cos(60o) = 0.5 and is thus proportional to N/2. If the noise vector happens to be in phase with the carrier reference, there is no reduction in noise, while if the noise vector is 90o out of phase, the noise is reduced to zero. On average, the coherent detection method reduces the noise voltage out of the detector by a factor of root 2 and the noise power by 2. In other words, coherent detection of ASK can tolerate 3 dB more noise than non-coherent ASK for the same likelihood of detection error.