Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 7
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Full text in Russian (pdf)

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DOI  https://doi.org/10.30898/1684-1719.2020.7.13

UDC 621.396.8

 

Detection of signals affected by multiplicative interference in the presence of additive noise

 

V. M. Artyushenko 1, V. I. Volovach 2

1 Technological University, 42, Gagarin Street, Korolev 141070, Russia

2 Volga Region State University of Service, 4, Gagarin Street, Togliatti 445017, Russia

 

 The paper was received on July 15, 2020

 

Abstract. Issues related to estimating the effect of multiplicative noise on signal detected by a receiving device designed to process signals with both known and unknown initial phase exposed to additive noise are in the focus of this paper. It is shown that two cases of detection should be distinguished – detection of a signal in the true channel and detection of the presence of a signal for which the corresponding probabilities are determined. The characteristics of the output signal for the optimal receiver for the input signal with a known initial phase are determined, such as the average value and variance of the output signal, as well as the resulting output signal of the «untrue» channel in the presence of multiplicative noise. The distribution of the output signal of the above-mentioned channel of the receiver can be approximately described as normal. The characteristics of the output signal of the optimal receiver for the input signal with an unknown initial phase are determined. It is shown that for the described case (receiving signals with unknown initial phases against a background of white Gaussian noise), the envelope of the correlation integral can be used as the output signal; expressions for its definition are given. It is also shown that the probability distribution density (PDF) of the resulting output signal in the true channel in the absence of multiplicative noise is determined by the generalized Rayleigh law (Rice law), whereas in the «untrue» channels it is determined by the Rayleigh PDF. Expressions of the output signal of the optimal receiver and its quadrature components in the presence of multiplicative noise are obtained, as well as expressions of variance and covariance of the output signal for the «untrue» channel. The effect of multiplicative noise on the detection of signals with a known initial phase in the receiving device is determined. It is shown that in the absence of multiplicative noise, the probabilities of detection in the true and «untrue» channels can coincide. Expressions are obtained for determining the probability of detection in the true channel under the influence of fluctuation multiplicative noise. Moreover, the named probability is associated both with probabilistic parameters in the absence of noise and with the parameters of the signal and the affecting noise. It is shown that systems that use long duration signals or coherent bursts of pulses, regardless of the presence of frequency or phase modulation of the signal, are more vulnerable to multiplicative noise. We obtained the graphs of the probability of signal detection in the true and «untrue» channels of the receiving device exposed to fluctuation multiplicative noise, depending on the noise parameters for various values ​​of the detection probability and false alarms in the absence of noise. The influence of multiplicative noise on the detection of signals with an unknown initial phase in the receiving device including obtaining the expressions for different detection probabilities, such as using the Q-function in the true channel, and the variance of the output signal is determined. Also we obtained the graphs of the probability signal detecting in the true channel of the receiving device exposed to fluctuation multiplicative noise depending on the noise parameters at different values ​​of the probability of detection and false alarms, as well as for the density of the noise component of the signal that is the same for all channels. It is shown that the degree of influence of multiplicative noise on signal detection depends both on noise parameters and on signal parameters.

Key words: multiplicative noise, probability of reliable detection, probability of false detection, optimal receiving device, threshold level, reference signal.

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For citation:

Artyushenko V.M., Volovach V.I. Detection of signals affected by multiplicative interference in the presence of additive noise. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 7. https://doi.org/10.30898/1684-1719.2020.7.13 (In Russian)