## Coherent detection vs non-coherent detection

In order to understand why coherent detection gives a better noise performance than non-coherent detection, it is helpful to view the phasor or vector diagram representation of ASK. A vector diagram maps the amplitude of a signal by the length of the line on the vector diagram, and maps the instantaneous phase by the angle of the line with respect to a horizontal reference frequency and phase (for data modulation, this reference is usually the carrier signal cos wct.) Thus for ASK, we can map the two symbol states (carrier on or off) as two vectors on this diagram, one with length zero corresponding to the carrier-off state, and one with length A in line with the carrier reference, corresponding to the carrier-on state.

We can also map noise by recognizing that a noise signal can be written as a vector n(t) cos[wct + q(t)] where n(t) is a time varying amplitude and q(t) is a time varying phase. If we were to plot snapshots of the noise on the vector diagram, we would find that they were randomly distributed throughout all four quadrants of the vector space as shown.

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