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Statistical Properties of the Radiation Field of a Phased Antenna Array in Relation to the Problem of Formation of Nulls in Its Radiation Pattern


A.O. Manichev

Analytical expressions for determination of the elements of the correlation matrix for the radiation field of a phased antenna array (PAA) with an arbitrary amplitude distribution are derived for a two-level model of random non-stationary distortions in the amplitude-phase distribution (APD), which is typical of modular PAAs. These analytical expressions are attained for both the Gaussian and the uniform distributions of phase distortions. Amplitude distortions are arbitrarily distributed. Conditions for elimination of the well-known phenomenon of strong correlation between fluctuations of the PAA radiation pattern in the directions symmetrical relative to the maximum of the non-distorted radiation pattern are found. If these conditions are met, it is possible to avoid unwanted increase in the mean pattern level in the direction symmetric to the direction of a null formed via the method proposed by Hans Steyskal. Spatial structure of the background level of the mean power pattern is analyzed. This background level determines mean value of nulls attained in the pattern of a PAA with given parameters. It is shown that in the presence of correlated distortions of the APD, the level of the background component of the radiation pattern substantially increases in the regions of first sidelobes. This effect increases the level of the synthesized nulls in this special region. Quantitative estimates for the minimum number of the PAA elements (modules), for which the real and imaginary components of the field fluctuations are distributed according to the Gaussian law regardless of the distribution of the PAA distortions, are obtained. A generalized distribution law for the field amplitude in the nulls of the mean voltage pattern is proposed. This law is valid when the real and imaginary parts of field fluctuations are statistically dependent on each other and have unequal variances. This distribution law can be used to obtain accurate probabilistic estimates of the amplitude of the PAA field in the nulls of the mean pattern for an arbitrary phase distribution over the PAA and for any values of the APD distortion parameters, securing Gaussian distribution of the real and imaginary components of the PAA radiation field.
June 24, 2020
May 29, 2020

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