Potential interference immunity of coherent reception of quadruple phase-manipulated radio signal in the presence of coherent harmonic interference

Abstract

Introduction: The known methods for calculating the interference immunity of radio signal reception in the presence of, for example, harmonic interference, often lead to significantly different numerical values. Each calculation technique of this type has its own algorithm for the resulting formula output, and these conclusions are based on a different level of “engineering rigor”. Purpose: To develop, оn the basis of linear transformation of coordinates, a correct method for calculating the error probability in the correlating reception of a four-fold phase-manipulated radio signal in the presence of coherent harmonic interference. Methods: Four-dimensional probability density of a vector of output voltages of the demodulator correlators in a four-fold integral was represented by a product of one-dimensional probability densities in the space of eigenvectors of the covariance matrix, in which two probability densities are Dirac delta functions. The quadruple integral is brought to double, with new integration limits defined from the plane equations bounding the integration region in this space. Results: Formulas were derived for accurate calculation of average probabilities of symbol and bit errors in coherent reception of a four-fold phase-manipulated radio signal in the presence of coherent harmonic interference. The derived exact formulas were used to plot the dependencies of the average probabilities of symbol and bit errors on the signal-to-noise ratio for the given interference-to-noise ratio and the given interference phase shift relative to the signal phase. It has been studied how the energy ratios of the signal and interference, as well as the interference phase shift, affect the probabilities of symbol and bit errors. It was found that the influence of a non-energy parameter equivalently leads to a change in the energy ratios. Practical relevance: The results of the research can be used in assessing the communication efficiency under interference. The developed technique will allow you to accurately determine the energy characteristics of a radio channel providing the required quality for the reception of transmitted messages in presence of harmonic interference.