Measuring a Signal Information Parameter at a High Level of Additive and Multiplicative Noises

The effect of simultaneous additive and fluctuation multiplicative noises with a high level on the precision of measuring a signal information parameter is considered and analyzed. The expressions determining the conditional probabilities of the correct measurement of an information parameter and a false count are derived. The probability densities are determined for the channels of an $$N$$ -channel receiver, and the particular case of a two-channel device is considered. The probability of a correct parameter measurement at a high level of multiplicative noises is approximately equal to the probability of detecting a signal in the channel where the undistorted signal component exists. For an $$N$$ -channel receiver, the threshold voltage providing the specified measurement characteristics is determined. The dependences characterizing the probability of a correct measurement on the level of the undistorted signal component are derived for the case of a bell-like power distribution of undistorted signal fluctuations over the channels of a receiving device at different values for the width of a noise modulation function spectrum and the number of receiver channels. It is proven that, in the case when the number of channels is high or when the power distribution of fluctuations in the noisy component of the signal distorted by a multiplicative noise is symmetric with respect to the $$k$$ th channel, the average value of measurement errors (false counts) is zero, i.e., there are no systematic measurement errors.