Analysis of the Sine Wave Coherent Detection in the Presence of Noise†

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Abstract
This paper analyses the additive coherent detection of a sine wave in the presence of the narrow-band Gaussian noise. Particular emphasis is laid on the determination of the coherent detection optimum conditions which are important in the instrumentation of experimental physics. An expression is derived which gives the dependence of the output signal-to-noise ratio upon the input signal-to-noise ratio, the coherent wave-to-noise ratio and the phase angle between the input sine and coherent wave. The results of the analysis are given in normalized form and can be directly applied to additive coherent detection systems in which combinations of diode rectifier elements are used.

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