Effect of Multiplicative Noises on the Precision of Measuring the Frequency of a Coherent Signal against the Background of White Noise

The effect of multiplicative noises acting simultaneously with white noise on the precision of measuring the frequency of a coherent signal specified as a sequence of coherent pulses is considered and analyzed. The condition for the absence of systematic errors at the output of a tracking meter is determined. The slope of its discrimination characteristic, the spectral density of fluctuations at the output from the discriminator, and the coefficients, which characterize the normalizing effect of automatic gain control (AGC), are found. The mentioned parameters specify the value of worsening in the meter precision characteristics under the influence of multiplicative noises. It is shown that the effect of multiplicative noises grows with a decrease in the undistorted signal part level and an increase in the ratio between the energy of a signal, which is coherently accumulated in linear discriminator circuits, to the spectral additive noise power density. It is demonstrated that the effect of multiplicative noises is most pronounced in the cases when the noise modulation function spectrum has a width comparable with the bandwidth of linear discriminator circuits.